1. home and garden
2. home furnishings
3. rugs and carpets

Geometrical Analysis of Facial Aesthetics
Submitted by
Seow Jing Wen, Kevin
Department of
Mechanical Engineering
In partial fulfillment of the
requirements for the Degree of
Bachelor of Engineering
National University of Singapore
Session 2009/2010
i
Summary
This project will attempt to discover salient geometrical features which describe an
attractive face.
A survey on facial attractiveness was conducted to establish the ‘ground truth’
on the facial attractiveness of 76 survey subjects, 40 male and 36 female. The survey
with 100 respondents provided interesting insights. Female respondents to the survey
rated male subjects more harshly than male respondents (p<0.05). There was no
significant difference in the ratings female and male respondents gave to female
subjects.
This project employed 3 types of facial measurements – 2D photo images, 3D
stereophotogrammetric images and manual anthropometric measurements taken
from plaster casts. 3D image measurements were found to be comparable to manual
cast measurements. 2D photogrammetry was shown to be significantly less accurate
than manual or 3D measurements. Point curvature measurements of 3D images,
previously not attempted in describing an attractive face, was employed in this project.
Statistical analysis comparing survey results and facial measurements
uncovered some measurements, specific to gender, which proved statistically
significant in describing an attractive face. Attractive male survey subjects were found
to have larger nasion heights (p<0.05) and nose lengths (p<0.05) than less attractive
male survey subjects. They also had shorter nose widths (p<0.05). Attractive female
survey subjects had shorter bottom 3rd of faces (p<0.05) than less attractive female
survey subjects.
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ii
Acknowledgements
The author wishes to convey his appreciation to Associate Professor Lee Heow Pueh for
his supervision in this Project.
Additionally, thanks must go to Dr Lee Shu Jin from the Division of Plastic and
Reconstructive Surgery, National University Hospital for providing the database of
faces. Ms Eileen Heng from the same division also aided in the 3D photography of the
database.
The author would also like to express his gratitude to Ms Suhailah and Ms Munirah,
interns from Ngee Ann Polytechnic, for their assistance in corroborating the facial
measurements.
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Table of Contents
i
Summary ................................................................................................................................. i
ii
Acknowledgements................................................................................................................ ii
iii
List of Figures ........................................................................................................................ iv
iv
List of Tables .......................................................................................................................... v
1
Introduction ....................................................................................................................... 1
2
3
4
1.1
Brief History ............................................................................................................... 1
1.2
Measurement Methods ............................................................................................. 2
1.3
Facial Attractiveness Surveys ..................................................................................... 3
Survey................................................................................................................................. 7
2.1
Survey database description ...................................................................................... 7
2.2
Survey Procedure and Considerations ....................................................................... 7
2.3
Survey Analysis ........................................................................................................... 9
Measurements ................................................................................................................. 15
3.1
Different Measurement Methods............................................................................ 15
3.2
Analysis of Measurements Methods ....................................................................... 20
Investigation of Geometrical Measurements describing Facial Attractiveness .............. 33
4.1
Analysis for Males .................................................................................................... 33
4.2
Analysis for Females................................................................................................. 37
4.3
Discussions on Analysis ............................................................................................ 39
5
Conclusion ........................................................................................................................ 42
6
References ....................................................................................................................... 43
7
Appendix .......................................................................................................................... 46
iii
iii
List of Figures
1. Diagrams of measurements and landmarks for 2D profile view
2. Diagram of landmarks for 2D full face measurements
3(a). Scatter plot of n-prn Manual against n-prn 3D
3(b). Scatter plot of difference in n-prn (Manual-3D) against mean n-prn (Manual & 3D)
4(a). Scatter plot of n-sn Manual against n-sn 3D
4(b). Scatter plot of difference in n-sn (Manual-3D) against mean n-sn (Manual & 3D)
5(a). Scatter plot of n-prn/n-sn Manual against n-prn/n-sn 3D.
5(b). Scatter plot of difference in n-prn/n-sn (Manual-3D) against mean n-prn/n-sn
(Manual & 3D)
6(a). Scatter plot of nasion height/n-sn Manual against n-prn/n-sn 3D
6(b). Scatter plot of difference in n-prn/n-sn (Manual-3D) against mean n-prn/n-sn
(Manual & 3D)
7(a). Scatter plot of al-al/en-en 2D full face against al-al/en-en Manual
7(b). Scatter plot of difference in al-al/en-en (2D-Manual) against mean al-al/en-en (2D
& Manual)
8(a). Scatter plot of al-al/ex-ex 2D full face against al-al/ex-ex Manual
8(b). Scatter plot of difference in al-al/ex-ex (2D-Manual) against mean al-al/ex-ex (2D
& Manual)
9(a). Scatter plot of en-en/ex-ex 2D full face against en-en/ex-ex Manual
9(b). Scatter plot of difference in en-en/ex-ex (2D-Manual) against mean en-en/ex-ex
(2D & Manual)
10(a). Scatter plot of ex-en right/ex-ex 2D full face against ex-en right/ex-ex Manual
10(b). Scatter plot of difference in ex-en right/ex-ex (2D-Manual) against mean ex-en
right/ex-ex (2D & Manual)
11(a). Scatter plot of ex-en left/ex-ex 2D full face against ex-en left/ex-ex Manual
11(b). Scatter plot of difference in ex-en left/ex-ex (2D-Manual) against mean ex-en
left/ex-ex /ex-ex (2D & Manual)
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iv
List of Tables
Table 1: Measurements that demonstrate strongest relationship with facial
attractiveness for males
Table 2: Individual Regression Analysis for measurements that demonstrate strongest
relationship with facial attractiveness for males
Table 3: Significant measurements from Student’s t-test between top 8 and bottom 8
males ranked according to facial attractiveness average rating
Table 4: Measurements that demonstrate strongest relationship with facial
attractiveness for females
Table 5: Individual Regression Analysis for measurements that demonstrate strongest
relationship with facial attractiveness for females
Table 6: Significant measurements from Student’s t-test between top 8 and bottom 8
females ranked according to facial attractiveness average rating
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1
Introduction
This project will employ pre-existing anthropometric facial measurements as
well as utilize new point curvature measurements made possible with 3D imaging in
attempting to identify the salient facial features that constitute an attractive face.
1.1
Brief History
Facial beauty has been a societal evolutionary concern since time immemorial.
Leonardo da Vinci’s neoclassical canons were one of the first attempts to define
aesthetic proportions of the face; an example of the canons being that the distance
between the eyes is equal to the width of each eye.
In more recent times, Leslie G. Farkas – a plastic and reconstructive surgeon –
has defined the field of facial anthropometry, describing countless soft tissue
measurements to characterize the face[1].
Meanwhile, significant social science literature has attempted to identify the
factors which describe an attractive face. The established physical cues thus far are the
facial averageness, symmetry, neoteny, sexual dimorphism cues[2-3]; found
contributory to facial attractiveness.
Thus it has become evident that facial attractiveness is far more objective and
universal than the oft quoted axiom ‘beauty is in the eye of the beholder’.
At the same time, the advent of greater computing power and 3D photo
imaging has allowed researchers to be able to perform point curvature measurements
1
on faces. However, the powers of 3D imaging and its associated sophisticated
measurements have never been harnessed to describe an attractive face.
1.2
Measurement Methods
The scope of this Final Year Project involves geometrical measurements; thus it
was natural to concentrate on available literature detailing measurements
characterizing the face.
1.2.1
2D Photogrammetry
2D photo images of subjects have been used extensively in the definition of
geometric measurements. Commonly, subjects’ anterior and lateral views are captured
and then analysed by marking landmarks on the face. The definitions of various angles
and length measurements to characterize faces were pioneered by Powell and
Humphreys[4]. These measurements have been incorporated into modern plastic
surgery. This project employs some of the measurements they have defined.
2D photo images suffer from being less accurate than the later methods in
reflecting the facial measurements. Numerous shortcomings include photographic
distortion, loss of depth perspective, lack of resolution [5-7].
1.2.2
Facial Anthropometry
Farkas [8] made a very involved study with over 130 soft tissue measurements
per face to try to characterize an attractive face. The use of such soft tissue
measurements have been claimed to be more accurate than 2D photogrammetry[6].
These manual measurements require the physical participation of subjects, extracting
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anthropometric measurements from their faces. In this project, the anthropometric
manual measurements were instead taken from plaster casts of subjects.
1.2.3
3D Stereophotogrammetry
A relatively new technique of measurement is 3D stereophotogrammetry. It
involves the capture of multiple photo images from differing positions, the images are
then processed by photo image software to form 3D images. The use of 3D photo
images in measurement of facial morphology has been shown to be useful and
comparable to manual facial anthropometric measurements[7]. Furthermore, 3D
images can be readily revisited when the need arises, a strength manual
anthropometry does not possess.
Additionally, 3D stereophotogrammetry offers the added advantage of being
able to measure point curvature of facial features, a mode of measurement employed
in this project[9-10].
The use of the three aforementioned forms of measurement will be employed
in this project. Efforts will be undertaken to explore the relevance and relation
between these three differing modes of measurement.
1.3
Facial Attractiveness Surveys
Since this project aims to discover the geometrical features which describe an
attractive face, a prior review of literature regarding the conducting of facial surveys
was made.
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1.3.1
Presentation of face views
Prior literature [11] has shown that ‘there is a moderately high correlation
between ratings assigned to live subjects and photographs of the same subject’. A
subjects’ rank of attractiveness was also contingent upon the views of the face shown.
A study [12] was conducted to determine the relationship between the subject’s view
shown to respondents and its corresponding effect on the subject’s facial
attractiveness rating. The study found that the Pearson correlation between full front
face ratings and profile view ratings was 0.68. Evidently, perception of facial
attractiveness is dependent upon the views presented with no single view representing
the complete perception. Philips et al [13] have suggested that multiple views of
subjects should be shown at the same time to solicit ratings. Other authors [3, 14]
have also pointed out the benefits of including a three quarters or oblique view of the
faces to give cognizance to the depth of the face.
1.3.2
Methods of rating facial attractiveness
A review of the literature illustrated that there are mainly 3 methods of rating facial
attractiveness[15]:
1. Visual Analog Scale – A face is rated from least attractive to most attractive on a
numerical scoring scale, for example a Likert scale.
2. Comparative Ratio Scale – A face is presented with a predetermined score on a
similar Likert scale. All subsequent faces are rated and scored with respect to
this face.
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3. Ranking Scale – A group of faces are rated and arranged from least to most
attractive. This ranking is done without scoring.
The Ranking Scale gives a good order of facial attractiveness. However it does not
indicate the degree to which a face may be more facially attractive or unattractive than
its nearest neighbours.
The Comparative Ratio Scale presents some inherent bias in predetermining a score
for a face. The Visual Analog Scale, modeled after the common Likert Scale is relatively
robust. A study comparing the Comparative Ratio Scale and Visual Analog Scale
demonstrated that there was no significant difference in ratings between both
scales[15].
1.3.3
Facial Attractiveness ratings across ethnicities
Most studies on facial attractiveness have been limited to a single ethnic group.
It is evident from many reports that the facial properties and proportions of faces differ
over ethnicities. Significant differences in facial proportions have been found in African
American, Caucasian and Chinese faces[16-19].
However, in attempting to discover ideal facial proportions, limiting studies to
ethnic groups would not provide as varied a distribution of measurements. The
argument for limiting facial attractiveness studies to single ethnicities was the fear that
people of different ethnicities would be unable to rate the facial attractiveness of
another ethnicity. This fear was ultimately unfounded. Cunningham’s study [20] where
Asian, Hispanic students and white Americans rated the attractiveness of Asian,
Hispanic, black, and white photographed women found mean correlation between
5
groups in facial attractiveness ratings of 0.93. Such findings were further repeated in a
study [21] where Chinese and US orthodontists rated Chinese and white patients.
While there were some differences in rating between white and Chinese orthodontists
for white and Chinese faces, the differences were insignificant. However, the present
study still focuses on Asians, with a majority of the subjects Asians.
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2
Survey
2.1
Survey database description
The survey database consisted of a total of 76 subjects, 40 male and 36 female.
They were of Asian, Eurasian and Caucasian ancestry. Of the male subjects, 22 were
Asian, 12 Eurasian and 6 Caucasian. Of the female subjects, 22 were Asian, 12 Eurasian
and 2 Caucasian.
There were 100 survey respondents. The respondent gender ratio was roughly
equal - 52 female, 48 male. They were students from the National University of
Singapore (NUS). The ethnic makeup of the respondents was 80 Chinese, 12 Indian and
8 Malay. The respondents were between 19-27 years of age; with a mean age of 21.47
years.
(For consistency of term usage, survey respondents will be addressed as
‘respondents’ in all future references; survey subjects will be addressed as ‘subjects’.)
2.2
2.2.1
Survey Procedure and Considerations
Facial Views Presented
As discussed earlier, it was beneficial to exhibit multiple views of the face since
the rating of a subject’s facial attractiveness was shown to be dependent on different
views and not consistently on one view. Thus 3 views were employed; the full face,
profile and oblique view.
7
2.2.2
Visual Analog Scale (VAS) employed
Respondents viewed the subjects’ faces projected on a screen and were told to
rate the subjects for facial attractiveness on a Likert scale of 1 - 7, 1 being the least
facially attractive and 7 the most attractive.
The VAS was intended for use as an interval scale, not ordinal scale. The spacing
of the response levels from 1 – 7 on the survey form were equally spaced to highlight
the symmetry of distribution between the differing levels. Respondents were also
specifically told in the survey form as well as verbally reminded that a score of 7 would
indicate that the subject was in the top one-seventh of the populace in terms of facial
attractiveness.
The response levels were limited to 1 – 7 because additional response levels
would cause the scale to lose its significance, given that the quality respondents were
judging was latent.
2.2.3
Comparison effects
A concern was that survey respondents would engage in comparative scaling
amongst faces – assigning a rating by comparing to the previous face displayed.
Comparative scaling amongst faces would affect the spread of the data, potentially
causing bunching of ratings in parts of the scale. To circumvent this phenomenon,
survey respondents were told in the survey form as well as verbally to rate subject
faces with respect to the general populace. They was thus primed to rate the faces
based on an impression of the subject’s attractiveness according to the general
populace.
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2.2.4
Display time of subjects
Respondents were given 8 seconds to rate each subject. In trial runs of the
survey, respondents’ feedback was that 8 seconds was the optimum time to rate.
Given the significantly large number of faces, an overly lengthy survey would tire
respondents out and possibly contribute to inaccurate survey results.
2.2.5
Random order of faces
The faces were displayed in random order. This is to reduce the possible effect
of biasing because faces were rated in comparison to the general populace. Hence
individual subject ratings were less affected by the order of faces shown.
2.2.6
Semantics and interpretation
Consistent with current literature, the term used to describe the desired facial
quality was ‘facially attractive’. Semantics were important in this case - words like
‘beautiful’, ‘pretty’ or ‘handsome’ connote values and appear to bias to differing types
of beauty. Hence ‘facially attractive’ was a neutral term in the appraisal of beauty.
2.3
2.3.1
Survey Analysis
General results
The mean rating for male faces was 3.53 with a standard deviation of 1.124.
The mean rating for female faces was 3.59 with a standard deviation of 1.157. One may
observe that these mean ratings are lower than the face of average attractiveness
(which would be rated at 4). This phenomenon has been repeatedly observed in
studies on facial attractiveness. In a study [22] of 76 facial subjects rated by 100
9
respondents, the mean score of subjects was 4.41 when scored upon 10. Farkas’ study
[8] on attractive faces used photo images of 115 male subjects, 200 female subjects,
out of which 70 were male fashion models and 50 female fashion models. Only 21
males and 34 females were rated as above average, lesser than the number of fashion
models used.
2.3.2
Testing for reliability
Cronbach’s coefficient alpha [23] was tested on the survey results and returned
a high value of 0.966, demonstrating the reliability of the data. This value showed that
respondents’ ratings were consistent for the subjects.
Cronbach’s alpha is not a proof for unidimensionality – in this case, that the
respondents were rating solely for facial attractiveness. However, respondents were
told to judge subjects solely on facial attractiveness and they returned consistent and
inter-related ratings on subjects Therefore it is reasonable to deduce that they were
judging based on the expressed criterion.
2.3.3
Testing for normality
Survey respondent data was then tested for normality by running the 100
survey responses through a battery of normality tests per subject (the results of which
can be found in the Appendix 1. These tests have been organized into 2 runs, one for
male subjects, another for female subjects.
The mathematical normality tests, Kolmogorov-Smirnov and Shapiro-Wilk tests,
both indicated that the ratings for male subjects across 100 respondents was not
10
normal. This result was not unexpected. Though 100 respondents represent a
substantial number, it remained insufficient to make up for the lack of resolution in a 7
point scale. However, the use of a 7 point scale was justified in order to ensure that the
ratings gathered were coherent and relevant, since a larger scale would have diluted its
accuracy.
To conclude that the respondent data was not normal would have been shortsighted. A check of all the histograms illustrating the spread of ratings for 100
respondents demonstrated a strong central tendency with tails on both sides.
A review of the normal Q-Q plots also showed that the ratings did in fact adhere
closely to the normal distribution. The only deviations were at the tail ends of the Q-Q
plots. For all subjects, respondents consistently rated more high scores and less low
scores than predicted by a normal distribution. One can speculate on the consistent
deviation observed. The nature of the survey involved judgment of the facial
attractiveness of a person. Therefore it was likely that respondents were more inclined
to give high scores and less inclined to give low scores – it would appear uncharitable
to give subjects very low scores.
Finally, despite failing the Kolmogorov-Smirnov and Shapiro-Wilk tests, the
survey results did demonstrate strong central tendency. Using the median or mode
rating of each subject’s face would result in little variation in their assigned ratings
given a 7 point scale, resulting in an unfair loss of ratings resolution. Thus the existence
of a strong central tendency and normality in form suggests that the mean would be a
better gauge of the subjects’ attractiveness rating.
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2.3.4
Testing for gender difference/bias
It was hypothesized that gender differences might affect ratings - same gender
respondents and subjects may rate their gender more favourably. Thus we tested for
difference in ratings by gender.
The average score by respondent’s gender for each of the subjects (Subject 176) was found. This then meant that for each subject, we had the average score given
by male respondents and average score by female respondents.
High Pearson correlations between female respondents’ ratings and male
respondents’ ratings were found. The correlation between average score of female
respondents on all subjects and average score of male respondents on all subjects was
0.933. The high correlations were expected since each gender average was scoring the
same subject. It also provided justification for the conduction of a paired t-test.
A paired t-test was run to determine if the respondent’s gender affected rating
of the subjects (Appendix 2). The t-test revealed that female respondents rated all
subjects lower than male respondents by a mean of 0.08144. This was statistically
significant (p<0.04). Female respondents also rated male subjects lower than male
respondents by a mean of 0.116; also statistically significant (p<0.05). However, the
difference in ratings between female and male respondents for female subjects was
not statistically significant.
2.3.5
Testing for difference in ratings due to subject ethnicity
It was hypothesized that the ethnicity of the subjects might contribute to a
difference in rating. The average rating of each subject across all respondents was
12
found. The subjects were characterized according to their ethnicity; namely Asian,
Eurasian, Caucasian.
2.3.5.1
Male Subjects
For the male subjects, Welch’s ANOVA was carried out to discover if there was
a significant difference in the mean ratings for different ethnicities. The mean rating
and standard deviation of Asian males was 3.37 ± 0.43, of Eurasian males 3.72 ± 0.50,
of Caucasian males 3.75 ± 0.48.
Welch’s ANOVA was carried out instead of the typical one-way ANOVA because
it could account for slight variations in sample size and variance, as is the case in our
survey data. The results demonstrated that there was a significant difference in mean
ratings for different ethnicities (p=0.091), significant at the 10% level. This finding
warranted further investigation.
Therefore, independent Student’s t-tests between ethnicities were executed.
The t-test between Asians and Eurasian males was significantly different at 5% level
(p=0.037). This suggests that Eurasian males were rated more highly than Asian males.
Their mean difference in rating was 0.36, about a third of a grade.
The t-test between Asian and Caucasian ratings showed significant difference at
10% level (p=0.068). Similarly, this suggests Caucasians were consistently rated higher
than Asians, with a mean difference in rating of 0.38.
The t-test between Eurasian and Caucasian subjects revealed no significant
difference in their ratings.
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The male subjects were then arranged according to their average ratings. The
top 8 in terms of facial attractiveness consisted of 3 Asians, 3 Eurasians and 2
Caucasians; the bottom 8 consisted of 5 Asians, 2 Eurasians and 1 Caucasian. The
results appear to correspond to the findings of the t-tests.
2.3.5.2
Female Subjects
The number of female Caucasian subjects in our survey was limited to 2. Hence
they were omitted in this analysis. Instead, an independent Student’s t-test was run
between Asian and Eurasian subjects. Results demonstrated that there was no
significant difference between the ratings received by Asian and Eurasian subjects.
The top 8 females in terms of facial attractiveness consisted of 6 Asians and 2 Eurasians;
the bottom 8 consisted of 6 Asians and 2 Eurasians. This finding once again appears to
agree with the t-test.
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3
Measurements
3.1
Different Measurement Methods
For each subject in the database, 2 2D photo images (full face and side profile),
a plaster cast and a 3D photo image were used for measurements.
3.1.1
2D Measurements
For 2D measurements, the full face and side profile of each subject were each
printed on an A4 sized paper. Landmarks were marked on the face and measurements
taken using ruler and protractor.
The measurements used can be found in Powell & Humphreys’ ‘Proportions of
the Aesthetic Face’[4], as well as Farkas’ ‘Anthropometry of the Head and Face’[1].
3.1.1.1
2D Side Profile
The measurements from the side profile include 4 angular measurements and 4
length measurements. The 4 angular measurements are nasofrontal angle (NFr),
nasofacial angle(NFa), nasolabial angle (NLa) and nasomental angle (NMe). The 4
length measurements are from nasion to pronasion(n-prn), nasion to subnasale (n-sn),
nasion height (perpendicular distance from front of eye to nasion), and nasal
protrusion (length of perpendicular on n-sn to prn). These measurements are all
illustrated in Figure 1 below.
15
Figure 1: Diagrams of measurements and landmarks for 2D profile view
16
3.1.1.2
2D Full face
The full face measurements consisted of numerous measurements; 4 face
measurements, 6 eye measurements, 1 nose measurement.
The 4 face measurements are: trichion to gnathion (tr-gn), top third of face
from trichion to glabella (tr-g), middle third of face from glabella to subnasale (g-sn),
bottom third of face from subnasale to gnathion (sn-gn).
The 6 eye measurements are: endocanthion to exocanthion (en-ex) both left
and right, endocanthion to endocanthion, exocanthion to exocanthion (ex-ex),
palpebrale superius to palbebrale inferius (ps-pi) both left and right.
The nose measurement is alare to alare (al-al). The landmarks for measurement
are illustrated in Figure 2 below.
Figure 2: Diagram of landmarks for 2D full face measurements
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3.1.2
Manual cast measurements
The cast measurements are similar to the measurements from the 2D images.
They are: al-al, en-ex both left and right, en-en, ex-ex, n-prn, n-sn. Measurements were
repeated from those initially taken from the 2D photo for purposes of comparison. As
mentioned earlier, manual measurements were reputed to be more accurate than 2D
photo measurements.
Cast measurements were taken twice at separate times and then averaged.
They were also taken solely by the project author in order to ensure consistency and
prevent inter-observer error[5]. Not all measurements were available from all casts.
Some of the casts were not broad enough to record the exocanthion landmark. This
resulted in the loss of the en-ex and ex-ex measurements. However, the al-al, en-en, nprn, n-sn measurements were recorded for all casts.
2Ds photos were not scaled. Hence only indices and angles could be derived
from them. The empirical measurements were instead provided by both the casts as
well as 3D photo images.
3.1.3
3D photo image measurements
The 3D image measurements also had measurements similar to those of 2D
photo images and manual casts. These measurements were taken to corroborate
across the 3 differing methodologies. They were nasion height, n-prn, n-sn, nasal tip
protrusion.
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3.1.3.1
Point curvature measurements
The advent of 3D images has meant that point curvatures on a 3d image can
now be readily calculated. No known prior study on facial attractiveness has attempted
to incorporate measurements using curvature. Such curvature measurements,
however, have been used in studies on facial recognition[10, 24].
In particular, 2 measurements have been extracted for use in this project. The
first is the Gaussian curvature on the pronasion. As the most anterior point of the face,
it describes the local shape at that point.
The other curvature measurement is the average minimum curvature along the
nose ridge from the nasion to the pronasion. The minimum curvature gives the
curvature along the nasal dorsal line, since the maximum curvature along the line
describes the curvature across the nose. A high average indicates a hooked nose or
‘Roman nose’, while a low average indicates a straight nose or ‘ski slope nose’[9].
Importantly, these measurements have been demonstrated to have
discriminatory ability – their (between cluster variance)/(within cluster variance) is
significant.
Generation of indices
3.1.4
The linear measurements allowed formulation of some indices, relating
empirical measurements to one another. Such indices have been used extensively in
anthropometric studies, primarily because of the inter-relatedness of the features of
the face.
19
Some of the indices generated in this project were due to necessity.
Unfortunately, the database of 2D photos was not scaled consistently. This meant that
the empirical lengths could not be discerned. Hence, in order to make the
measurements relevant, they had to be scaled to other measurements on view.
A table of indices, with their corresponding feature, as well as the medium of
measurement can be found in Appendix 4.
3.2
Analysis of Measurements Methods
Given the use of multiple mediums for measurement, effort was made to
understand their relation and accuracy. There was no need to employ Student’s t-tests
or Wilcoxon signed-rank tests in this analysis. Such tests investigate the possibility that
the mean is identical between both measurements. This possibility is hardly in doubt
given the measurements were taken from the same subject.
The following analysis is based on Bland and Altman’s ‘Statistical methods for
assessing agreement between two methods of clinical measurement’[25].
3D images and manual cast measurements
3.2.1
Between the 3D image and manual cast, 2 linear measurements and 1 index
could be compared. They were n-prn, n-sn and n-prn/n-sn. The scatter plot was plotted
for each subject’s measurement taken on the manual cast against the subject’s
measurement taken on the 3D image. There were 76 points, one for each of the 76
subjects.
20
3.2.1.1
Nasion to pronasion (n-prn)
n-prn
5.5
difference n-prn(Manual -3D)
0.8
n-prn Manual
5.0
4.5
difference n-prn(Manual -3D) VS
mean n-prn
0.6
0.4
0.2
0.0
-0.2 3.0
4.0
4.0
5.0
6.0
-0.4
-0.6
3.5
3.5
4.0
4.5
n-prn 3D
5.0
5.5
-0.8
mean n-prn
3(a)
3(b)
Figure 3(a) Scatter plot of n-prn Manual against n-prn 3D. (b) Scatter plot of difference
in n-prn (Manual-3D) against mean n-prn (Manual & 3D)
The scatter plot (Figure 3a) generated for n-prn showed that most subjects
recorded very similar measurements from both manual and 3D. Hence there is much
clustering around the line of equality. A majority of the measurements that deviated
from the line of equality had larger manual measurements than 3D measurements.
A plot of difference between both n-prn measurements against the mean of
both n-prn measurements was made (Figure 3b). There were several distinctly large
differences in n-prn measurement, but these were consistent across the range of
averaged n-prn. This suggests that the n-prn length did not affect the difference
between both measurement methods.
The mean difference for n-prn is 0.107cm with a standard deviation of 0.243.
Therefore the limits of agreement are -0.379cm and 0.592cm; 95% of the differences in
measurement of n-prn will fall within these limits, assuming the distribution is normal.
21
3.2.1.2
Nasion to subnasale
n-sn
6.5
difference n-sn (Manual -3D) VS
mean n-sn
0.4
0.3
difference n-sn (Manual -3D)
6.0
n-sn Manual
5.5
5.0
4.5
4.0
4.0
4.5
5.0
5.5
n-sn 3D
6.0
6.5
0.2
0.1
0.0
-0.1 4.0
5.0
6.0
-0.2
-0.3
-0.4
-0.5
-0.6
mean n-sn
4(a)
4(b)
Figure 4(a) Scatter plot of n-sn Manual against n-sn 3D. (b) Scatter plot of difference in
n-sn (Manual-3D) against mean n-sn (Manual & 3D)
The scatter plot (Figure 4a) generated for n-sn showed that while clustering
around the line of equality was quite tight, 3D measurements of n-sn were consistently
slightly larger than manual measurements
Again a plot of difference between n-sn measurements against mean of n-sn
measurements was made (Figure 4b). The mean difference for n-sn is -0.136cm with a
standard deviation of 0.189. Therefore the limits of agreement are -0.513cm and
0.242cm.
22
3.2.1.3
Index of n-prn/n-sn
n-prn/n-sn Manual
0.95
0.90
0.85
0.80
0.75
difference n-prn/n-sn (Manual -3D)
n-prn/n-sn
1.00
0.14
difference n-prn/n-sn (Manual -3D)
VS mean n-prn/n-sn
0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.02 0.7
0.70
0.70 0.75 0.80 0.85 0.90 0.95 1.00
n-prn/n-sn 3D
-0.04
0.8
0.9
1.0
mean n-prn/n-sn
5(a)
5(b)
Figure 5(a) Scatter plot of n-prn/n-sn Manual against n-prn/n-sn 3D. (b) Scatter plot of
difference in n-prn/n-sn (Manual-3D) against mean n-prn/n-sn (Manual & 3D)
The scatter plot for n-prn/n-sn showed that the index was consistently larger on
manual measurements than 3D. This phenomenon is probably due to the fact that n-sn
was consistently larger in 3D measurements. As the divisor in this index, it caused the
index values for 3D measurements to be smaller than for manual measurement.
Compounded by the fact that n-prn, the numerator in the index, was measured as
marginally larger in Manual measurements as evidenced by its mean difference of
0.107; these two factors combined to make n-prn/n-sn shift away from the line of
equality.
The mean difference for n-prn/n-sn is 0.0419 with a standard deviation of
0.0330; with corresponding limits of agreement at -0.0242 and 0.108.
23
3.2.1.4
Relation between manual measurements and 3D measurements
Prior studies have shown that the measurements derived from stereographic
3D photographs are comparable to those taken from manual measurements.
Ghoddousi et al[7] made a detailed comparison of facial measurements
between different mediums; 3D stereophotogrammetry, manual patient
measurements and 2D photo images.
3D photo images of a caliper were taken. The length measurements of the
caliper taken from the 3D photo were found to have a difference of -0.23mm between
physical caliper measurement and 3D length measurement. The difference from 0 was
statistically significant. However from the perspective of the the measurement of
anthropometric features, the difference is negligible. This example served to establish
the accuracy of 3D stereophotogrammetry in length measurement.
Ghoddousi et al recorded n-sn for 6 subjects. The median difference between
3D and manual measurements was found to be 3.04mm. The median difference in this
project for 76 subjects was 1.36mm, the average difference was 1.36mm. The results
of n-sn for this project appear to confirm the previous literature.
Given the insignificant error of measurement introduced by 3D photo imagery
as shown by Ghoddousi, this must suggest that much of the errors arose from location
of the landmarks.
In a study to evaluate the accuracy of a laser scanner in facial measurents, Aung
et al [26] noted that the location of the subnasale (sn) landmark in 3D images was
24
highly reliable; the nasion (n) and pronasion (prn) were reliable. Indeed this author
found the subnasale was easily located in both 3D images and manual measurement.
Estimation is required in locating the nasion and pronasion in 3D images since
these points are best located by palpitation. Ghoddousi et al [7]commented that
though a 3D images did not allow one to palpate to discover the nasion, it did not seem
to adversely affect the accuracy of such locations.
For the manual measurements, location of the nasion and pronasion was
marginally more difficult than location of the subnasale. A larger degree of estimation
was required than for the subnasale.
The measurements in this project appear to corroborate previous findings as
well as the observations of this author. The difference in n-sn measurements had a
significantly smaller standard deviation of 0.189cm compared to the difference in n-prn
measurements with a standard deviation of 0.243cm. Clustering of the points in the nsn plot were tighter around the line of equality than n-prn plot.
As Tessier asserted, the use of proportion indices is useful[27], especially in the
following cases when absolute measurements cannot be found. However, they suffer
from a problem of compounding the error of measurements involved – as
demonstrated by the differences in n-prn/n-sn.
3.2.2
2D side profile and 3D images
Between the 3D image and 2D side profile, 3 indices could be compared. They
were n-prn/n-sn, Baum Method and nasion height/n-prn. Analysis similar to that
25
performed between 3D image and manual measurements was carried out. As not all
plots were significant, the less significant ones have been placed in Appendix 5.
3.2.2.1
Index: Nasion height/n-sn
nasion height/n-sn
0.4
0.3
0.2
difference nasion hgt/n-sn (3D-2D)
nasion height/n-sn 3D
0.2
difference nasion hgt/n-sn (3D-2D) VS
average nasion hgt/n-sn
0.15
0.1
0.05
0
-0.05 0
0.1
0.1
0.2
0.3
0.4
-0.1
-0.15
0
0
0.1
0.2
0.3
nasion height/n-sn 2D profile
0.4
-0.2
average nasion hgt/n-sn
6(a)
6(b)
Figure 6(a) Scatter plot of nasion height/n-sn Manual against n-prn/n-sn 3D. (b) Scatter
plot of difference in n-prn/n-sn (Manual-3D) against mean n-prn/n-sn (Manual & 3D)
The plot of nasion height/n-sn appear bunched at the lower regions. Nasion
height is a relatively small measurement – most subjects do not have very large nasion
heights.
The mean difference for nasion height/n-sn is -0.0486 with a standard deviation
of 0.0506; with corresponding limits of agreement at -0.150 and 0.0525.
3.2.2.2
Relation between 2D side profile and 3D measurement
It is readily observed that the nasion height/n-sn is consistently larger in 2D
measurement than 3D measurement. This may be due to the procedure involved in
26
measuring nasion height. The 2D profile views are photographed with subjects’ eyes
open. Nasion height is then the perpendicular distance from the plane of the most
anterior point of the eye to the nasion. In the making of the the cast however, subjects
have their eyes closed. This means that the 3D photo images of the casts measure the
nasion height from the plane of the most anterior point of the eyelid which covers the
eye. While the difference is small and fairly consistent across all subjects, it is
significant enough to contribute to a consistently reported larger index in 2D than
manual measurement.
Nonetheless, it must be commented that nasion heights taken from 3D photo
images are likely to be more accurate. This is due to the difficulty in capturing an
accurate 2D side profile image of a subject. Mild tilts or rotation of the head result in a
deviation from the actual nasion height. In addition, Farkas et al [6] state that the facial
profile line observed may not be the true line.
A particular shortcoming of 2D measurements is the lack of resolution. In spite
of making relatively large prints of photographs, the measurements recorded remain
empirically small. Rulers are not very accurate, only capable of measuring to the
nearest 0.5mm. Hence 2D photographs are more suitable for measuring large
measurements such as face proportions; less suitable for finer measurements, of which
nasion height is one of them.
3.2.3
2D fullface view and manual measurements
Between the 3D image and 2D fullface view, 5 indices could be compared. They
were al-al/en-en, al-al/ex-ex, en-en/ex-ex, ex-en left/ex-ex, ex-en right/ex-ex. Similar
27
analysis was conducted. However, only the al-al/en-en index had the plots of 76
subjects. The rest of the indices had plots of 36 subjects (due to the variability of the
plaster cast).
al-al/en-en
difference al-al/en-en (2D Manual) VS average al-al/en-en
difference al-al/en-en (2D - Manual)
1.30
al-al/en-en 2D fullface
1.20
1.10
1.00
0.30
0.20
0.10
0.00
-0.10
0.90
0.8
1
1.2
1.4
-0.20
0.80
0.8
0.9
1
1.1
1.2
al-al/en-en Manual
1.3
-0.30
average al-al/en-en
7(a)
7(b)
Figure 7(a) Scatter plot of al-al/en-en 2D full face against al-al/en-en Manual (b)
Scatter plot of difference in al-al/en-en (2D-Manual) against mean al-al/en-en (2D &
Manual)
al-al/ex-ex
0.55
difference al-al/ex-ex (2D - Manual)
al-al/ex-ex 2D fullface
0.12
0.5
difference al-al/ex-ex (2D Manual) VS average al-al/ex-ex
0.1
0.08
0.45
0.06
0.4
0.04
0.35
0.02
0.3
0.3
0.35
0.4
0.45
0.5
al-al/ex-ex Manual
0.55
0
-0.02
0.3
0.4
0.5
average al-al/ex-ex
8(a)
8(b)
Figure 8(a) Scatter plot of al-al/ex-ex 2D full face against al-al/ex-ex Manual. (b) Scatter
plot of difference in al-al/ex-ex (2D-Manual) against mean al-al/ex-ex (2D & Manual)
28
The al-al length against both en-en and ex-ex was greater in 2D full face images
than manual cast measurements. Previous studies [6] have also shown that al-al is
longer in photogrammetric images than in manual measurements. The differences in
length were recorded as 2.4mm and 4mm in separate studies. Farkas has stated that
distortions caused by photography and, in the case of al-al, lack of adequate resolution
in photographs has contributed to difference in measurements.
en-en/ex-ex
0.46
0.08
difference en-en/ex-ex (2D Manual)
en-en/ex-ex 2D fullface
0.44
difference en-en/ex-ex (2D Manual) VS average en-en/ex-ex
0.06
0.42
0.04
0.4
0.02
0.38
0
-0.02
0.36
0.35
0.4
0.45
-0.04
0.34
0.34 0.36 0.38 0.4 0.42 0.44 0.46
en-en/ex-ex Manual
-0.06
average en-en/ex-ex
9(a)
9(b)
Figure 9(a) Scatter plot of en-en/ex-ex 2D full face against en-en/ex-ex Manual. (b)
Scatter plot of difference in en-en/ex-ex (2D-Manual) against mean en-en/ex-ex (2D &
Manual)
En-en and ex-ex were declared to be relatively reliable measurements in 2D
photos[6]. This finding however cannot be confirmed with the results in this project.
The scatter plot was disperse and lay away from the line of equality. However, the
deviation from the line of equality was quite uniform. The findings in this regard are
less conclusive and more such measurements may be required to shed some light to
this finding.
29
ex-en right/ex-ex
difference ex-en right/ex-ex (2D Manual) VS average ex-en
0.04
right/ex-ex
ex-enrt/ex-ex 2D fullface
difference ex-en right/ex-ex (2D Manual)
0.35
0.03
0.33
0.02
0.01
0.31
0
-0.01 0.28
0.29
0.3
0.32
0.34
-0.02
-0.03
0.27
0.27
0.29
0.31
0.33
ex-enrt/ex-ex Manual
0.35
-0.04
average ex-en right/ex-ex
10(a)
10(b)
Figure 10(a) Scatter plot of ex-en right/ex-ex 2D full face against ex-en right/ex-ex
Manual. (b) Scatter plot of difference in ex-en right/ex-ex (2D-Manual) against mean
ex-en right/ex-ex (2D & Manual)
difference ex-en left/ex-ex (2D Manual) VS average ex-en left/ex0.04
ex
ex-en left/ex-ex
difference ex-en left/ex-ex (2D Manual
0.36
ex-en left/ex-ex 2D fullface
0.34
0.02
0.32
0.3
0
-0.02
0.25
0.3
0.35
-0.04
0.28
-0.06
0.26
0.26
0.28
0.3
0.32 0.34
ex-en left/ex-ex Manual
0.36
-0.08
average ex-en left/ex-ex
11(a)
11(b)
Figure 11(a) Scatter plot of ex-en left/ex-ex 2D full face against ex-en left/ex-ex Manual.
(b) Scatter plot of difference in ex-en left/ex-ex (2D-Manual) against mean ex-en
left/ex-ex (2D & Manual)
The lengths of the eyes (ex-en) are underreported in 2D photo images, similar
for both left and right eye. In another investigation on 2D photogrammetry, Farkas
30
states that the two-dimensional nature of print makes it incapable to measure the arcs
on the face since depth knowledge is lost[28]. In a similar manner, the eyes lie along a
curve that runs from the ears to the front of the face. Hence in 2D photographs, the
length of the eyes captured do not account for the slight curve of the eyes backward
towards the ears. Thus ex-en tends to be reported to be greater in manual
measurement than 2D measurement.
3.2.4
Conclusion on the relation for 3 mediums of measurements
Corroborating with other studies, 3D facial measurements have been
demonstrated to be accurate, with accuracy similar to manual measurements.
Ghoddoussi et al [7] showed that the measurement of absolute distance of objects
from 3D photo images was sufficiently accurate, with an error of no clinical significance.
Therefore the error in 3D facial measurements arises mainly from landmark
identification [29-30]. The primary shortcoming of 3D measurements is the inability to
palpate. This may present greater problems when attempting to identify landmarks like
the glabella which are dependent on the bone. However, for the purposes of the more
discrete landmarks, 3D photo images have accuracy comparable to that of manual
measurements. They have also been shown to have higher repeatability than manual
measurements – the ability to rotate the 3D image and zoom aids measurement in this
regard[7].
Despite the apparent shortcomings of 2D photogrammetry in terms of
resolution and distortion, many authors agree that 2D photo images remain relevant in
facial anthropometry[6]. An example would be the previously mentioned eye lengths.
31
While the eye lengths may be underreported, one cannot discount the importance of a
subject’s full face view in the evaluation of aesthetic beauty. Merely seeking the
supposed ‘true’ length of the eye discounts the importance of the full face view. It
remains true that daily interactions and photographs taken involve the full face view.
Not all measurements are subject to significant error, Farkas [6] has reported
that much of the accurate measurements are those that record inclination/angles.
Such angles are more cumbersome to determine manually.
Hence, further analysis in this project takes all 3 methods of measurement on
its own merit. The project investigates all 3 methods and their relevance to facial
attractiveness.
32
4
Investigation of Geometrical Measurements describing Facial Attractiveness
With the geometric measurements and results of the survey, we were ready to
attempt to discover the constituents of an attractive face. The subjects were separated
into their genders for the statistical analysis.
As a first investigation, scatter plots of the numerous geometric measurements
were plotted against the averaged survey ratings. All scatter plots can be found in
Appendix 6. Regression analysis was then run on the more salient factors. Student’s ttests analysis of the measurements of the top 8 subjects in terms of facial
attractiveness was run against the bottom 8 for each gender. The t-tests were run to
discern if there were significant differences in the measurement means of the both
groups.
4.1
4.1.1
Analysis for Males
Scatter plots
From the scatter plot, measurements which showed the strongest and most
coherent relationship with the averaged survey ratings were identified and are as
follows in Table 1.
Measurement
Medium
Linear R-square value
Nasion height
3D
0.18
n-sn
Cast
0.121
Nasal index (al-al/n-prn)
Cast
0.12
Nasion height/n-sn
3D
0.118
Nasolabial angle
2D
0.116
n-sn
3D
0.107
Table 1 Measurements that demonstrate strongest relationship with facial
attractiveness for males
33
4.1.2
Regression Analysis
Regression analysis for each variable was run individually with the average
ratings as the dependent variable. The salient information like coefficients and
significance has been included in the table below. The regression analysis reports can
be found in Appendix 7.
Measurement
Medium
Coefficients
Significance
Nasion height [mm]
3D
0.063
0.006
n-sn [cm]
Cast
0.593
0.028
Nasal index (al-al/n-prn) Cast
-1.617
0.029
Nasion height/n-sn
3D
2.689
0.030
Nasolabial angle
2D
0.012
0.032
[degrees]
n-sn [mm]
3D
0.057
0.039
Table 2 Individual Regression Analysis for measurements that demonstrate strongest
relationship with facial attractiveness for males
A stepwise regression with these measurements was run. Care was taken not to
repeat variables. From Table 2, it can be observed that nasion height, n-sn, nasal index
and nasolabial angle were the 4 independent variables most suitable for the stepwise
regression. The results of the stepwise regression revealed that the best results were
obtained with nasion height as the sole independent variable.
4.1.3
Student’s t-tests
Independent Student’s t-tests for all measurements were run between the 2
groups; one group being the top 8 rated in facial attractiveness, the other group the
bottom 8. The complete list of t-tests can be found in Appendix 8. The variables which
had a significance level of less than 0.05 are shown here in Table 3. The mean
differences shown are bottom 8 subtracted from top 8.
34
Independent Samples Test
Assumptions=Equal variances assumed
Sig. (2tailed)
.038
.003
.009
.001
.041
t-test for Equality of Means
95% Confidence
Interval of the
Difference
Mean
Std. Error
Lower
Upper
Difference Difference
-0.248
0.108
-0.479
-0.016
-0.523
0.144
-0.833
-0.213
0.169
0.056
0.049
0.289
0.231
0.057
0.107
0.354
2.912
1.296
0.132
5.692
al-al (cast) [cm]
en-en (cast) [cm]
n-prn /en-en (cast)
n-sn/en-en (cast)
nasion height (3D)
[mm]
Table 3 Significant measurements from Student’s t-test between top 8 and bottom 8
males ranked according to facial attractiveness average rating
Farkas [8] found, in his attempt to describe an attractive face, that the
attractive male face had a deep nasal root. The length of the endocanthion to sellion
sagittal (en-se sag), a measurement analogous to nasion height, was larger in attractive
faces.
The findings in this regression analysis and Student’s t-test appear to
corroborate his findings. The regression analysis showed that the nasion height was a
statistically significant variable in predicting the average survey rating. However, the
coefficient and R-square was not particularly high – a 5mm increase in nasion height
would result in a 0.315 increase in average grade. The R-square was 0.18, which
indicated that about one-fifth of the variation is explained by the model.
The Student’s t-test did demonstrate that the nasion height difference between
the top 8 and bottom 8 was statistically significant at the 5% level. The mean difference
35
was close to 3mm. These findings suggest that attractive men did indeed have larger
nasion heights.
The nose height (n-sn) also features prominently in the regression results; the
larger the nose height, the higher the survey attractiveness ratings. In the t-test
analysis, the nose height was found to be important as well. The top 8 had larger nose
heights than the bottom eight. However, the increase in nose height was contingent
upon the distance between the endocanthions of the left and right eye.
The distance between endocanthions appeared a relevant variable in the
difference between more attractive and less attractive males. The top 8 males had a
smaller distance between the eyes (en-en) than bottom 8 males by a mean of 5mm.
The en-en measurement manifests thrice in the t-tests. This seems to contradict with
Farkas’ observation in his study that en-en was found to be identical between the most
attractive and least attractive. However, another study [15] did demonstrate that a
computer manipulated increase in inter-eye distance of subjects significantly lowered
their attractiveness ratings. Therefore it is plausible that there is an optimum distance
between endocanthions in relation to the face and the least attractive males subjects
in this project had eyes too widely set apart.
The nose width (al-al) was also found to be important. From the regression
analysis, a smaller nose width relative to n-prn resulted in higher attractiveness ratings.
In the t-tests, the nose widths of top 8 males varied from those of the bottom 8; with a
nose width a mean of 2.5mm smaller. The Chinese nose has been shown previously to
be wider than the Caucasian nose[16, 31]. Plastic surgeons are often approached to
36
reduce the alare flare of Asian noses. The survey database in this project consisted of
subjects of different ethnicities, thus there was a larger range of nose widths. It would
be unfair to claim that Asians are less facially attractive than other ethnicities. Indeed
there was adequate representation of Asians in the top 8 subjects. However, the
results do indicate that smaller alare widths do contribute to facial attractiveness. Thus
this finding gives credence to the argument that smaller nose widths are more
aesthetically pleasing.
4.2
4.2.1
Analysis for Females
Scatter plots
As before, measurements which showed the strongest relationships with the
averaged ratings in the scatter plot were identified and shown in Table 4.
Measurement
Medium
Linear R-square value
rd
Bottom 3 /tr-gn
2D
0.211
rd
rd
Top 3 /bottom 3
2D
0.176
ex-en right/ex-ex
2D
0.162
rd
rd
Middle 3 /bottom 3
2D
0.146
rd
Top 3 /tr-gn
2D
0.114
Table 4 Measurements that demonstrate strongest relationship with facial
attractiveness for females
4.2.2
Regression Analysis
Measurement
Medium
Coefficients
Significance
Bottom 3rd/tr-gn
2D
-14.445
0.005
Top 3rd/bottom 3rd
2D
2.597
0.011
ex-en right/ex-ex
2D
-18.682
0.015
rd
rd
Middle 3 /bottom 3
2D
3.704
0.021
rd
Top 3 /tr-gn
2D
9.702
0.044
Table 5 Individual Regression Analysis for measurements that demonstrate strongest
relationship with facial attractiveness for females
37
Again, linear regression analysis was run, the results are shown in Table 5.
A stepwise regression was run with only 2 variables, bottom 3rd/tr-gn and top
3rd/tr-gn. The ex-en right/ex-ex was discarded. This was because ex-en left/ex-ex
demonstrated little significance in relation to describing the averaged ratings. Also, exen right/en-en did not demonstrate any significance. Hence ex-en right/ex-ex
presented itself as an anomaly. Similarly, the middle 3rd/bottom 3rd was discarded
because other ratios like middle 3rd/tr-gn and middle 3rd/top 3rd did not show up as
statistically significant. Thus it was deduced that the significance of the bottom 3rd as
the numerator caused this variable to appear statistically significant.
4.2.3
Student’s t-tests
The significant results of Student’s t-tests follows in Table 6.
Independent Samples Test
Assumptions=Equal variances assumed
t-test for Equality of Means
95% Confidence
Interval of the
Difference
Sig. (2Mean
Std. Error
tailed)
Difference Difference
Lower
Upper
.021
-0.012
0.005
-0.022
-0.002
ex-en average/ex-ex
(fullface)
ex-en right/ex-ex
.003
-0.018
0.005
-0.029
-0.007
(fullface)
middle3rd/bottom3rd
.010
0.088
0.030
0.025
0.152
(fullface)
bottom 3rd/tr-gn_f
.019
-0.030
0.011
-0.054
-0.006
(fullface)
Table 6 Significant measurements from Student’s t-test between top 8 and bottom 8
females ranked according to facial attractiveness average rating
38
The regression analysis indicates that a smaller bottom 3rd of the face (also
known as lower face) relative to the entire face height (tr-gn) predicts a more
attractive face. This finding is also exhibited in the t-test – the top 8 had a smaller
lower face than the bottom 8, with a mean difference of 0.03 in proportion. The
smaller lower face can be related to the sexual dimorphism cue expressed in current
facial beauty literature [2, 32]. The sexual dimorphism cue suggests that estrogen
inhibits the lateral growth of the mandible and chin, resulting in a shorter lower jaw
and hence lower face. Female subjects with such sexually dimorphic traits indicate a
strong immune system. Thus smaller lower faces for females are thought to be
regarded as more facially attractive.
The ex-en right/ex-ex and ex-en average/ex-ex indices show up in the t-tests as
well. Their relevance remains questionable. The regression analysis implies that the
shorter the length of the right eye, the more attractive the face. Further investigation
with a regression analysis for the left eye however indicates that the larger the length
of left eye, the more attractive the face. This contradictory relationship thus suggests
that this finding is an anomalous one. In the t-test, we see that the top 8 do have
shorter eye lengths compared to the bottom 8. However, the mean difference is slight
at 0.018. The average ex-ex length among female subjects is 9.49cm – the mean
difference is therefore 1.7mm.
4.3
Discussions on Analysis
Linear regression analysis assumes a linear relationship between a
measurement and attractiveness rating. This assumption is highly unlikely to be the
39
case. Indeed, current literature demonstrates averageness as a trait that contributes to
facial attractiveness, suggesting a prototypical model of the aesthetic proportions –
indicating that facial features have to be proportionate to the face [2, 22]. Hence, a
large increase in nasion length does not necessarily guarantee males a large increase in
attractiveness rating. However, a regression analysis has its merits. Within the range of
the largest and smallest values of a measurement in the study, there remains the
possibility that the relationship between the measurement and attractiveness is fairly
linear. This can be seen from the observation that the nose width (al-al), nasion height
and nose height (n-sn) all vary in the same direction from both regression analysis and
Student’s t-tests.
The point curvature measurements generated did not relate strongly to
attractiveness ratings. This finding does not however make point curvature
measurements irrelevant in describing an attractive face. Just as few length
measurements have been found to be very salient in describing attractive faces,
greater exploration of point curvature analysis of the face is required to determine its
effectiveness.
The strongest predictor of facial attractiveness, nasion height for males and
lower 3rd of the face for females, had R-square values of 0.18 and 0.211 respectively.
This indicates that these measurements explained approximately one-fifth of the
variation in the ratings.
These are not particularly high R-square values. However, it would be
imprudent to expect a select group of measurements to definitively explain a quality so
40
latent; the attractiveness of a face. Indeed the high inter-relatedness and complexity of
features of the face make the identification of these measurements much harder.
Hence, the discovery of some salient features which help describe an attractive face
and corroborate with prevailing literature has proved useful.
41
5
Conclusion
In this project, the author has sought to establish the salient features which
describe an attractive face. Over 50 variables in the form of angular and length
measurements, proportion indices and point curvatures were introduced in this
attempt.
In the course of constructing a database of faces rated for attractiveness, a
survey on facial attractiveness was conducted. The survey revealed interesting results.
Female respondents rated male subjects more harshly than male respondents.
However, there was no significant difference in the ratings female and male
respondents gave to female subjects. The 7 point Likert scale was also shown to be
adequate in capturing facial attractiveness of subjects.
Three mediums of geometrical measurements were used – from 2D photos, 3D
stereophotogrammetric images and manual anthropometry. Manual and 3D photos
were shown to have very good agreement. 2D photos were less in agreement with the
other mediums but remained useful. Point curvature analysis from 3D photos was also
introduced in this project.
However, the point curvature measurements did not demonstrate predictive
ability in facial attractiveness. Other geometrical measurements were found to be
significant. More attractive male survey subjects had significantly larger nasion heights,
nose lengths and smaller nose widths than less attractive male subjects. More
attractive females had smaller bottom 3rd of face than less attractive females. The
findings do relate to and confirm the findings of existing literature.
42
6
1.
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45
7
Appendix
46
Appendix 1: Survey Ratings Distribution (Males)
Case Processing Summary
subject_m
Cases
Valid
N
rating_m
Missing
Percent
N
Total
Percent
N
Percent
M01
100
100.0%
0
.0%
100
100.0%
M02
100
100.0%
0
.0%
100
100.0%
M03
100
100.0%
0
.0%
100
100.0%
M04
100
100.0%
0
.0%
100
100.0%
M05
100
100.0%
0
.0%
100
100.0%
M06
100
100.0%
0
.0%
100
100.0%
M07
100
100.0%
0
.0%
100
100.0%
M08
100
100.0%
0
.0%
100
100.0%
M09
100
100.0%
0
.0%
100
100.0%
M10
100
100.0%
0
.0%
100
100.0%
M11
100
100.0%
0
.0%
100
100.0%
M12
100
100.0%
0
.0%
100
100.0%
M13
100
100.0%
0
.0%
100
100.0%
M14
100
100.0%
0
.0%
100
100.0%
M15
100
100.0%
0
.0%
100
100.0%
M16
100
100.0%
0
.0%
100
100.0%
M17
100
100.0%
0
.0%
100
100.0%
M18
100
100.0%
0
.0%
100
100.0%
M19
100
100.0%
0
.0%
100
100.0%
M20
100
100.0%
0
.0%
100
100.0%
M21
100
100.0%
0
.0%
100
100.0%
M22
100
100.0%
0
.0%
100
100.0%
M23
100
100.0%
0
.0%
100
100.0%
M24
100
100.0%
0
.0%
100
100.0%
M25
100
100.0%
0
.0%
100
100.0%
M26
100
100.0%
0
.0%
100
100.0%
M27
100
100.0%
0
.0%
100
100.0%
M28
100
100.0%
0
.0%
100
100.0%
M29
100
100.0%
0
.0%
100
100.0%
M30
100
100.0%
0
.0%
100
100.0%
M31
100
100.0%
0
.0%
100
100.0%
M32
100
100.0%
0
.0%
100
100.0%
dimension1
M33
100
100.0%
0
.0%
100
100.0%
M34
100
100.0%
0
.0%
100
100.0%
M35
100
100.0%
0
.0%
100
100.0%
M36
100
100.0%
0
.0%
100
100.0%
M37
100
100.0%
0
.0%
100
100.0%
M38
100
100.0%
0
.0%
100
100.0%
M39
100
100.0%
0
.0%
100
100.0%
M40
100
100.0%
0
.0%
100
100.0%
Descriptives
subject_m
rating_m
M01
Statistic
Mean
4.13
95% Confidence Interval for
Lower Bound
3.95
Mean
Upper Bound
4.31
5% Trimmed Mean
4.17
Median
4.00
Variance
.801
Std. Deviation
.895
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
M02
Std. Error
.090
-.606
.241
Kurtosis
.500
.478
Mean
2.94
.091
95% Confidence Interval for
Lower Bound
2.76
Mean
Upper Bound
3.12
5% Trimmed Mean
2.94
Median
3.00
Variance
.825
Std. Deviation
.908
Minimum
1
Maximum
5
Range
4
Interquartile Range
1
Skewness
Kurtosis
-.045
.241
.055
.478
M03
Mean
3.33
95% Confidence Interval for
Lower Bound
3.15
Mean
Upper Bound
3.51
5% Trimmed Mean
3.33
Median
3.00
Variance
.809
Std. Deviation
.900
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
M04
M05
.090
-.112
.241
Kurtosis
.642
.478
Mean
3.95
.088
95% Confidence Interval for
Lower Bound
3.78
Mean
Upper Bound
4.12
5% Trimmed Mean
3.97
Median
4.00
Variance
.775
Std. Deviation
.880
Minimum
2
Maximum
6
Range
4
Interquartile Range
2
Skewness
-.083
.241
Kurtosis
-.473
.478
3.28
.094
Mean
95% Confidence Interval for
Lower Bound
3.09
Mean
Upper Bound
3.47
5% Trimmed Mean
3.27
Median
3.00
Variance
.891
Std. Deviation
.944
Minimum
1
Maximum
5
Range
4
Interquartile Range
1
Skewness
.071
.241
Kurtosis
M06
M07
Mean
.478
3.10
.092
95% Confidence Interval for
Lower Bound
2.92
Mean
Upper Bound
3.28
5% Trimmed Mean
3.10
Median
3.00
Variance
.838
Std. Deviation
.916
Minimum
1
Maximum
5
Range
4
Interquartile Range
1
Skewness
-.121
.241
Kurtosis
-.183
.478
2.92
.107
Mean
95% Confidence Interval for
Lower Bound
2.71
Mean
Upper Bound
3.13
5% Trimmed Mean
2.91
Median
3.00
Variance
1.145
Std. Deviation
1.070
Minimum
1
Maximum
5
Range
4
Interquartile Range
2
Skewness
Kurtosis
M08
-.664
Mean
.011
.241
-.523
.478
3.50
.108
95% Confidence Interval for
Lower Bound
3.29
Mean
Upper Bound
3.71
5% Trimmed Mean
3.49
Median
3.50
Variance
1.162
Std. Deviation
1.078
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
Kurtosis
M09
M10
M11
Mean
.074
.241
-.681
.478
3.81
.099
95% Confidence Interval for
Lower Bound
3.61
Mean
Upper Bound
4.01
5% Trimmed Mean
3.82
Median
4.00
Variance
.984
Std. Deviation
.992
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
-.177
.241
Kurtosis
-.088
.478
3.28
.107
Mean
95% Confidence Interval for
Lower Bound
3.07
Mean
Upper Bound
3.49
5% Trimmed Mean
3.30
Median
3.00
Variance
1.153
Std. Deviation
1.074
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
-.034
.241
Kurtosis
-.282
.478
3.30
.088
Mean
95% Confidence Interval for
Lower Bound
3.13
Mean
Upper Bound
3.47
5% Trimmed Mean
3.30
Median
3.00
Variance
.778
Std. Deviation
.882
Minimum
1
Maximum
5
Range
4
Interquartile Range
M12
M13
M14
1
Skewness
-.090
.241
Kurtosis
-.063
.478
3.05
.099
Mean
95% Confidence Interval for
Lower Bound
2.85
Mean
Upper Bound
3.25
5% Trimmed Mean
3.06
Median
3.00
Variance
.977
Std. Deviation
.989
Minimum
1
Maximum
5
Range
4
Interquartile Range
2
Skewness
-.166
.241
Kurtosis
-.232
.478
2.81
.108
Mean
95% Confidence Interval for
Lower Bound
2.60
Mean
Upper Bound
3.02
5% Trimmed Mean
2.78
Median
3.00
Variance
1.166
Std. Deviation
1.080
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
.389
.241
Kurtosis
.019
.478
Mean
3.27
.096
95% Confidence Interval for
Lower Bound
3.08
Mean
Upper Bound
3.46
5% Trimmed Mean
3.24
Median
3.00
Variance
.926
Std. Deviation
.962
Minimum
1
Maximum
6
M15
M16
Range
5
Interquartile Range
1
Skewness
.194
.241
Kurtosis
.262
.478
Mean
4.07
.092
95% Confidence Interval for
Lower Bound
3.89
Mean
Upper Bound
4.25
5% Trimmed Mean
4.08
Median
4.00
Variance
.854
Std. Deviation
.924
Minimum
2
Maximum
7
Range
5
Interquartile Range
1
Skewness
.016
.241
Kurtosis
.591
.478
Mean
4.01
.100
95% Confidence Interval for
Lower Bound
3.81
Mean
Upper Bound
4.21
5% Trimmed Mean
4.02
Median
4.00
Variance
1.000
Std. Deviation
1.000
Minimum
1
Maximum
6
Range
5
Interquartile Range
2
Skewness
M17
-.144
.241
Kurtosis
.294
.478
Mean
3.27
.131
95% Confidence Interval for
Lower Bound
3.01
Mean
Upper Bound
3.53
5% Trimmed Mean
3.24
Median
3.00
Variance
1.714
Std. Deviation
1.309
Minimum
1
Maximum
7
Range
6
Interquartile Range
2
Skewness
Kurtosis
M18
M19
M20
Mean
.173
.241
-.195
.478
3.22
.097
95% Confidence Interval for
Lower Bound
3.03
Mean
Upper Bound
3.41
5% Trimmed Mean
3.23
Median
3.00
Variance
.941
Std. Deviation
.970
Minimum
1
Maximum
5
Range
4
Interquartile Range
1
Skewness
-.119
.241
Kurtosis
-.233
.478
3.36
.114
Mean
95% Confidence Interval for
Lower Bound
3.13
Mean
Upper Bound
3.59
5% Trimmed Mean
3.37
Median
3.00
Variance
1.303
Std. Deviation
1.142
Minimum
1
Maximum
7
Range
6
Interquartile Range
1
Skewness
.166
.241
Kurtosis
.277
.478
Mean
2.58
.091
95% Confidence Interval for
Lower Bound
2.40
Mean
Upper Bound
2.76
5% Trimmed Mean
2.58
Median
3.00
Variance
.832
Std. Deviation
.912
Minimum
1
Maximum
5
Range
4
Interquartile Range
1
Skewness
Kurtosis
M21
Mean
-.470
.478
3.14
.106
Lower Bound
2.93
Mean
Upper Bound
3.35
5% Trimmed Mean
3.14
Median
3.00
Variance
1.132
Std. Deviation
1.064
Minimum
1
Maximum
6
Range
5
Interquartile Range
2
Kurtosis
Mean
.177
.241
-.234
.478
3.78
.120
95% Confidence Interval for
Lower Bound
3.54
Mean
Upper Bound
4.02
5% Trimmed Mean
3.78
Median
4.00
Variance
1.446
Std. Deviation
1.203
Minimum
1
Maximum
6
Range
5
Interquartile Range
2
Skewness
Kurtosis
M23
.241
95% Confidence Interval for
Skewness
M22
.125
Mean
.045
.241
-.482
.478
3.86
.103
95% Confidence Interval for
Lower Bound
3.65
Mean
Upper Bound
4.07
5% Trimmed Mean
3.86
Median
4.00
Variance
1.071
Std. Deviation
1.035
Minimum
1
Maximum
7
Range
6
Interquartile Range
1
Skewness
M24
-.048
.241
Kurtosis
.916
.478
Mean
3.43
.092
95% Confidence Interval for
Lower Bound
3.25
Mean
Upper Bound
3.61
5% Trimmed Mean
3.41
Median
3.00
Variance
.854
Std. Deviation
.924
Minimum
2
Maximum
6
Range
4
Interquartile Range
1
Skewness
Kurtosis
M25
M26
Mean
.131
.241
-.434
.478
3.67
.093
95% Confidence Interval for
Lower Bound
3.48
Mean
Upper Bound
3.86
5% Trimmed Mean
3.69
Median
4.00
Variance
.870
Std. Deviation
.933
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
-.129
.241
Kurtosis
-.169
.478
3.33
.097
Mean
95% Confidence Interval for
Lower Bound
3.14
Mean
Upper Bound
3.52
5% Trimmed Mean
3.30
Median
3.00
M27
Variance
.951
Std. Deviation
.975
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
.425
.241
Kurtosis
.088
.478
Mean
4.25
.111
95% Confidence Interval for
Lower Bound
4.03
Mean
Upper Bound
4.47
5% Trimmed Mean
4.28
Median
4.00
Variance
1.240
Std. Deviation
1.114
Minimum
1
Maximum
7
Range
6
Interquartile Range
1
Skewness
M28
-.333
.241
Kurtosis
.141
.478
Mean
3.93
.106
95% Confidence Interval for
Lower Bound
3.72
Mean
Upper Bound
4.14
5% Trimmed Mean
3.92
Median
4.00
Variance
1.116
Std. Deviation
1.057
Minimum
2
Maximum
6
Range
4
Interquartile Range
2
Skewness
Kurtosis
M29
Mean
.090
.241
-.383
.478
3.74
.105
95% Confidence Interval for
Lower Bound
3.53
Mean
Upper Bound
3.95
5% Trimmed Mean
3.74
Median
M30
M31
M32
4.00
Variance
1.103
Std. Deviation
1.050
Minimum
1
Maximum
6
Range
5
Interquartile Range
2
Skewness
-.098
.241
Kurtosis
-.451
.478
3.00
.101
Mean
95% Confidence Interval for
Lower Bound
2.80
Mean
Upper Bound
3.20
5% Trimmed Mean
2.99
Median
3.00
Variance
1.010
Std. Deviation
1.005
Minimum
1
Maximum
6
Range
5
Interquartile Range
2
Skewness
.244
.241
Kurtosis
.231
.478
Mean
3.05
.101
95% Confidence Interval for
Lower Bound
2.85
Mean
Upper Bound
3.25
5% Trimmed Mean
3.04
Median
3.00
Variance
1.018
Std. Deviation
1.009
Minimum
1
Maximum
6
Range
5
Interquartile Range
2
Skewness
.200
.241
Kurtosis
.011
.478
Mean
4.59
.124
95% Confidence Interval for
Lower Bound
4.34
Mean
Upper Bound
4.84
M33
5% Trimmed Mean
4.60
Median
5.00
Variance
1.537
Std. Deviation
1.240
Minimum
2
Maximum
7
Range
5
Interquartile Range
2
Skewness
-.113
.241
Kurtosis
-.521
.478
3.46
.110
Mean
95% Confidence Interval for
Lower Bound
3.24
Mean
Upper Bound
3.68
5% Trimmed Mean
3.42
Median
3.00
Variance
1.221
Std. Deviation
1.105
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
Kurtosis
M34
M35
Mean
.333
.241
-.413
.478
4.37
.115
95% Confidence Interval for
Lower Bound
4.14
Mean
Upper Bound
4.60
5% Trimmed Mean
4.39
Median
4.00
Variance
1.326
Std. Deviation
1.152
Minimum
2
Maximum
7
Range
5
Interquartile Range
1
Skewness
-.161
.241
Kurtosis
-.394
.478
4.00
.112
Mean
95% Confidence Interval for
Lower Bound
3.78
Mean
Upper Bound
5% Trimmed Mean
4.00
Median
4.00
Variance
1.253
Std. Deviation
1.119
Minimum
1
Maximum
7
Range
6
Interquartile Range
2
Skewness
M36
M37
M38
4.22
-.132
.241
Kurtosis
.136
.478
Mean
4.36
.098
95% Confidence Interval for
Lower Bound
4.17
Mean
Upper Bound
4.55
5% Trimmed Mean
4.37
Median
4.00
Variance
.960
Std. Deviation
.980
Minimum
2
Maximum
7
Range
5
Interquartile Range
1
Skewness
-.124
.241
Kurtosis
-.011
.478
3.93
.098
Mean
95% Confidence Interval for
Lower Bound
3.74
Mean
Upper Bound
4.12
5% Trimmed Mean
3.93
Median
4.00
Variance
.955
Std. Deviation
.977
Minimum
1
Maximum
7
Range
6
Interquartile Range
2
Skewness
.076
.241
Kurtosis
.701
.478
Mean
3.84
.102
95% Confidence Interval for
Lower Bound
3.64
Mean
Upper Bound
4.04
5% Trimmed Mean
3.82
Median
4.00
Variance
1.045
Std. Deviation
1.022
Minimum
2
Maximum
6
Range
4
Interquartile Range
1
Skewness
Kurtosis
M39
M40
Mean
.155
.241
-.337
.478
3.28
.099
95% Confidence Interval for
Lower Bound
3.08
Mean
Upper Bound
3.48
5% Trimmed Mean
3.29
Median
3.00
Variance
.971
Std. Deviation
.986
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
.054
.241
Kurtosis
.234
.478
Mean
3.09
.098
95% Confidence Interval for
Lower Bound
2.90
Mean
Upper Bound
3.28
5% Trimmed Mean
3.09
Median
3.00
Variance
.951
Std. Deviation
.975
Minimum
1
Maximum
5
Range
4
Interquartile Range
2
Skewness
Kurtosis
.017
.241
-.462
.478
Tests of Normality
subject_m
Kolmogorov-Smirnova
Statistic
rating_m
dimension1
df
Shapiro-Wilk
Sig.
Statistic
df
Sig.
M01
.214
100
.000
.867
100
.000
M02
.246
100
.000
.892
100
.000
M03
.223
100
.000
.888
100
.000
M04
.213
100
.000
.886
100
.000
M05
.207
100
.000
.894
100
.000
M06
.217
100
.000
.897
100
.000
M07
.190
100
.000
.915
100
.000
M08
.179
100
.000
.916
100
.000
M09
.216
100
.000
.913
100
.000
M10
.193
100
.000
.924
100
.000
M11
.233
100
.000
.889
100
.000
M12
.220
100
.000
.905
100
.000
M13
.200
100
.000
.914
100
.000
M14
.200
100
.000
.902
100
.000
M15
.240
100
.000
.892
100
.000
M16
.226
100
.000
.908
100
.000
M17
.162
100
.000
.941
100
.000
M18
.210
100
.000
.904
100
.000
M19
.184
100
.000
.930
100
.000
M20
.218
100
.000
.892
100
.000
M21
.212
100
.000
.921
100
.000
M22
.162
100
.000
.933
100
.000
M23
.234
100
.000
.909
100
.000
M24
.211
100
.000
.889
100
.000
M25
.208
100
.000
.901
100
.000
M26
.252
100
.000
.898
100
.000
M27
.191
100
.000
.925
100
.000
M28
.204
100
.000
.912
100
.000
M29
.188
100
.000
.919
100
.000
M30
.230
100
.000
.910
100
.000
M31
.210
100
.000
.915
100
.000
M32
.160
100
.000
.936
100
.000
M33
.211
100
.000
.915
100
.000
M34
.198
100
.000
.928
100
.000
M35
.230
100
.000
.923
100
.000
M36
.203
100
.000
.911
100
.000
M37
.211
100
.000
.908
100
.000
M38
.198
100
.000
.910
100
.000
M39
.242
100
.000
.904
100
.000
M40
.197
100
.000
.906
100
.000
a. Lilliefors Significance Correction
Histograms
Stem-and-Leaf Plots
rating_m Stem-and-Leaf Plot for
subject_m= M01
Frequency
Stem &
3.00 Extremes
20.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
39.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
36.00
5 .
.00
5 .
.00
5 .
.00
5 .
.00
5 .
2.00
6 .
Stem width:
Each leaf:
Leaf
(=<2.0)
00000000000000000000
000000000000000000000000000000000000000
000000000000000000000000000000000000
00
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M02
Frequency
Stem &
6.00
1
.00
1
.00
1
.00
1
.00
1
22.00
2
.00
2
.00
2
.00
2
.00
2
48.00
3
.00
3
.00
3
.00
3
.00
3
20.00
4
4.00 Extremes
Stem width:
Each leaf:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Leaf
000000
0000000000000000000000
000000000000000000000000000000000000000000000000
00000000000000000000
(>=5.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M03
Frequency
Stem &
3.00 Extremes
11.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
44.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
35.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
6.00
5 .
1.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
00000000000
00000000000000000000000000000000000000000000
00000000000000000000000000000000000
000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M04
Frequency
4.00
.00
27.00
.00
41.00
.00
26.00
.00
2.00
Stem width:
Each leaf:
Stem &
Leaf
2
2
3
3
4
4
5
5
6
0000
.
.
.
.
.
.
.
.
.
000000000000000000000000000
00000000000000000000000000000000000000000
00000000000000000000000000
00
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M05
Frequency
Stem &
1.00 Extremes
21.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
37.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
31.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
10.00
5 .
Stem width:
Each leaf:
Leaf
(=<1.0)
000000000000000000000
0000000000000000000000000000000000000
0000000000000000000000000000000
0000000000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M06
Frequency
Stem &
4.00 Extremes
20.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
43.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
28.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
5.00
5 .
Stem width:
Each leaf:
Leaf
(=<1.0)
00000000000000000000
0000000000000000000000000000000000000000000
0000000000000000000000000000
00000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M07
Frequency
10.00
.00
24.00
.00
37.00
.00
22.00
.00
7.00
Stem width:
Each leaf:
Stem &
1
1
2
2
3
3
4
4
5
.
.
.
.
.
.
.
.
.
Leaf
0000000000
000000000000000000000000
0000000000000000000000000000000000000
0000000000000000000000
0000000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M08
Frequency
Stem &
1.00 Extremes
19.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
30.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
31.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
17.00
5 .
2.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
0000000000000000000
000000000000000000000000000000
0000000000000000000000000000000
00000000000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M09
Frequency
Stem &
1.00 Extremes
8.00
2 .
.00
2 .
Leaf
(=<1.0)
00000000
.00
2
.00
2
.00
2
27.00
3
.00
3
.00
3
.00
3
.00
3
40.00
4
.00
4
.00
4
.00
4
.00
4
21.00
5
3.00 Extremes
Stem width:
Each leaf:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
000000000000000000000000000
0000000000000000000000000000000000000000
000000000000000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M10
Frequency
Stem &
5.00 Extremes
17.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
37.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
28.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
12.00
5 .
1.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
00000000000000000
0000000000000000000000000000000000000
0000000000000000000000000000
000000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M11
Frequency
Stem &
2.00 Extremes
Leaf
(=<1.0)
14.00
.00
.00
.00
.00
44.00
.00
.00
.00
.00
32.00
.00
.00
.00
.00
8.00
Stem width:
Each leaf:
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
5
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
00000000000000
00000000000000000000000000000000000000000000
00000000000000000000000000000000
00000000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M12
Frequency
7.00
.00
19.00
.00
42.00
.00
26.00
.00
6.00
Stem width:
Each leaf:
Stem &
1
1
2
2
3
3
4
4
5
.
.
.
.
.
.
.
.
.
Leaf
0000000
0000000000000000000
000000000000000000000000000000000000000000
00000000000000000000000000
000000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M13
Frequency
10.00
.00
.00
.00
.00
30.00
.00
.00
.00
Stem &
1
1
1
1
1
2
2
2
2
.
.
.
.
.
.
.
.
.
Leaf
0000000000
000000000000000000000000000000
.00
2
37.00
3
.00
3
.00
3
.00
3
.00
3
16.00
4
7.00 Extremes
Stem width:
Each leaf:
.
.
.
.
.
.
.
0000000000000000000000000000000000000
0000000000000000
(>=5.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M14
Frequency
Stem &
2.00 Extremes
19.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
38.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
34.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
5.00
5 .
2.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
0000000000000000000
00000000000000000000000000000000000000
0000000000000000000000000000000000
00000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M15
Frequency
Stem &
5.00 Extremes
18.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
47.00
4 .
.00
4 .
Leaf
(=<2.0)
000000000000000000
00000000000000000000000000000000000000000000000
.00
4
.00
4
.00
4
26.00
5
.00
5
.00
5
.00
5
.00
5
3.00
6
1.00 Extremes
Stem width:
Each leaf:
.
.
.
.
.
.
.
.
.
00000000000000000000000000
000
(>=7.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M16
Frequency
1.00
.00
5.00
.00
21.00
.00
45.00
.00
21.00
.00
7.00
Stem width:
Each leaf:
Stem &
1
1
2
2
3
3
4
4
5
5
6
.
.
.
.
.
.
.
.
.
.
.
Leaf
0
00000
000000000000000000000
000000000000000000000000000000000000000000000
000000000000000000000
0000000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M17
Frequency
10.00
.00
17.00
.00
31.00
.00
25.00
.00
13.00
.00
3.00
.00
1.00
Stem &
1
1
2
2
3
3
4
4
5
5
6
6
7
.
.
.
.
.
.
.
.
.
.
.
.
.
Leaf
0000000000
00000000000000000
0000000000000000000000000000000
0000000000000000000000000
0000000000000
000
0
Stem width:
Each leaf:
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M18
Frequency
Stem &
4.00 Extremes
17.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
41.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
29.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
9.00
5 .
Stem width:
Each leaf:
Leaf
(=<1.0)
00000000000000000
00000000000000000000000000000000000000000
00000000000000000000000000000
000000000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M19
Frequency
Stem &
5.00 Extremes
16.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
35.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
29.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
13.00
5 .
Leaf
(=<1.0)
0000000000000000
00000000000000000000000000000000000
00000000000000000000000000000
0000000000000
2.00 Extremes
Stem width:
Each leaf:
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M20
Frequency
Stem &
11.00
1
.00
1
.00
1
.00
1
.00
1
37.00
2
.00
2
.00
2
.00
2
.00
2
36.00
3
.00
3
.00
3
.00
3
.00
3
15.00
4
1.00 Extremes
Stem width:
Each leaf:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Leaf
00000000000
0000000000000000000000000000000000000
000000000000000000000000000000000000
000000000000000
(>=5.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M21
Frequency
5.00
.00
22.00
.00
39.00
.00
23.00
.00
10.00
.00
1.00
Stem width:
Each leaf:
Stem &
Leaf
1
1
2
2
3
3
4
4
5
5
6
00000
.
.
.
.
.
.
.
.
.
.
.
0000000000000000000000
000000000000000000000000000000000000000
00000000000000000000000
0000000000
0
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M22
Frequency
2.00
.00
12.00
.00
28.00
.00
31.00
.00
18.00
.00
9.00
Stem width:
Each leaf:
Stem &
1
1
2
2
3
3
4
4
5
5
6
.
.
.
.
.
.
.
.
.
.
.
Leaf
00
000000000000
0000000000000000000000000000
0000000000000000000000000000000
000000000000000000
000000000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M23
Frequency
Stem &
2.00 Extremes
6.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
24.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
46.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
17.00
5 .
5.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
000000
000000000000000000000000
0000000000000000000000000000000000000000000000
00000000000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M24
Frequency
Stem &
17.00
2
.00
2
.00
2
.00
2
.00
2
35.00
3
.00
3
.00
3
.00
3
.00
3
37.00
4
.00
4
.00
4
.00
4
.00
4
10.00
5
1.00 Extremes
Stem width:
Each leaf:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Leaf
00000000000000000
00000000000000000000000000000000000
0000000000000000000000000000000000000
0000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M25
Frequency
Stem &
1.00 Extremes
8.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
34.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
38.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
18.00
5 .
1.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
00000000
0000000000000000000000000000000000
00000000000000000000000000000000000000
000000000000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M26
Frequency
Stem &
1.00 Extremes
17.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
44.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
26.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
10.00
5 .
2.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
00000000000000000
00000000000000000000000000000000000000000000
00000000000000000000000000
0000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M27
Frequency
Stem &
7.00 Extremes
15.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
35.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
32.00
5 .
.00
5 .
.00
5 .
.00
5 .
.00
5 .
10.00
6 .
1.00 Extremes
Stem width:
Each leaf:
Leaf
(=<2.0)
000000000000000
00000000000000000000000000000000000
00000000000000000000000000000000
0000000000
(>=7.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M28
Frequency
9.00
.00
24.00
.00
40.00
.00
19.00
.00
8.00
Stem width:
Each leaf:
Stem &
2
2
3
3
4
4
5
5
6
.
.
.
.
.
.
.
.
.
Leaf
000000000
000000000000000000000000
0000000000000000000000000000000000000000
0000000000000000000
00000000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M29
Frequency
1.00
.00
11.00
.00
29.00
.00
34.00
.00
22.00
.00
3.00
Stem width:
Each leaf:
Stem &
1
1
2
2
3
3
4
4
5
5
6
.
.
.
.
.
.
.
.
.
.
.
Leaf
0
00000000000
00000000000000000000000000000
0000000000000000000000000000000000
0000000000000000000000
000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M30
Frequency
6.00
.00
23.00
.00
44.00
.00
Stem &
1
1
2
2
3
3
.
.
.
.
.
.
Leaf
000000
00000000000000000000000
00000000000000000000000000000000000000000000
20.00
.00
6.00
.00
1.00
Stem width:
Each leaf:
4
4
5
5
6
.
.
.
.
.
00000000000000000000
000000
0
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M31
Frequency
5.00
.00
24.00
.00
40.00
.00
24.00
.00
6.00
.00
1.00
Stem width:
Each leaf:
Stem &
Leaf
1
1
2
2
3
3
4
4
5
5
6
00000
.
.
.
.
.
.
.
.
.
.
.
000000000000000000000000
0000000000000000000000000000000000000000
000000000000000000000000
000000
0
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M32
Frequency
5.00
.00
14.00
.00
28.00
.00
28.00
.00
20.00
.00
5.00
Stem width:
Each leaf:
Stem &
Leaf
2
2
3
3
4
4
5
5
6
6
7
00000
.
.
.
.
.
.
.
.
.
.
.
00000000000000
0000000000000000000000000000
0000000000000000000000000000
00000000000000000000
00000
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M33
Frequency
Stem &
1.00 Extremes
19.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
35.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
27.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
14.00
5 .
4.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
0000000000000000000
00000000000000000000000000000000000
000000000000000000000000000
00000000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M34
Frequency
Stem &
6.00 Extremes
17.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
28.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
34.00
5 .
.00
5 .
.00
5 .
.00
5 .
.00
5 .
13.00
6 .
2.00 Extremes
Stem width:
Each leaf:
Leaf
(=<2.0)
00000000000000000
0000000000000000000000000000
0000000000000000000000000000000000
0000000000000
(>=7.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M35
Frequency
1.00
.00
10.00
.00
16.00
.00
43.00
.00
22.00
.00
7.00
.00
1.00
Stem width:
Each leaf:
Stem &
1
1
2
2
3
3
4
4
5
5
6
6
7
.
.
.
.
.
.
.
.
.
.
.
.
.
Leaf
0
0000000000
0000000000000000
0000000000000000000000000000000000000000000
0000000000000000000000
0000000
0
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M36
Frequency
Stem &
3.00 Extremes
15.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
36.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
36.00
5 .
.00
5 .
.00
5 .
.00
5 .
.00
5 .
9.00
6 .
1.00 Extremes
Stem width:
Each leaf:
Leaf
(=<2.0)
000000000000000
000000000000000000000000000000000000
000000000000000000000000000000000000
000000000
(>=7.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M37
Frequency
1.00
.00
4.00
.00
27.00
.00
42.00
.00
22.00
.00
3.00
.00
1.00
Stem width:
Each leaf:
Stem &
1
1
2
2
3
3
4
4
5
5
6
6
7
.
.
.
.
.
.
.
.
.
.
.
.
.
Leaf
0
0000
000000000000000000000000000
000000000000000000000000000000000000000000
0000000000000000000000
000
0
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M38
Frequency
Stem &
9.00
2
.00
2
.00
2
.00
2
.00
2
28.00
3
.00
3
.00
3
.00
3
.00
3
39.00
4
.00
4
.00
4
.00
4
.00
4
18.00
5
6.00 Extremes
Stem width:
Each leaf:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Leaf
000000000
0000000000000000000000000000
000000000000000000000000000000000000000
000000000000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M39
Frequency
Stem &
4.00 Extremes
13.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
46.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
26.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
10.00
5 .
1.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
0000000000000
0000000000000000000000000000000000000000000000
00000000000000000000000000
0000000000
(>=6.0)
1
1 case(s)
rating_m Stem-and-Leaf Plot for
subject_m= M40
Frequency
4.00
.00
24.00
.00
38.00
.00
27.00
.00
7.00
Stem width:
Each leaf:
Stem &
Leaf
1
1
2
2
3
3
4
4
5
0000
.
.
.
.
.
.
.
.
.
000000000000000000000000
00000000000000000000000000000000000000
000000000000000000000000000
0000000
1
1 case(s)
Normal Q-Q Plots
Detrended Normal Q-Q Plots
Appendix 1: Survey Ratings Distribution (Female)
Case Processing Summary
subject_f
Cases
Valid
N
rating_f
Missing
Percent
N
Total
Percent
N
Percent
F01
100
100.0%
0
.0%
100
100.0%
F02
100
100.0%
0
.0%
100
100.0%
F03
100
100.0%
0
.0%
100
100.0%
F04
100
100.0%
0
.0%
100
100.0%
F05
100
100.0%
0
.0%
100
100.0%
F06
100
100.0%
0
.0%
100
100.0%
F07
100
100.0%
0
.0%
100
100.0%
F08
100
100.0%
0
.0%
100
100.0%
F09
100
100.0%
0
.0%
100
100.0%
F10
100
100.0%
0
.0%
100
100.0%
F11
100
100.0%
0
.0%
100
100.0%
F12
100
100.0%
0
.0%
100
100.0%
F13
100
100.0%
0
.0%
100
100.0%
F14
100
100.0%
0
.0%
100
100.0%
F15
100
100.0%
0
.0%
100
100.0%
F16
100
100.0%
0
.0%
100
100.0%
F17
100
100.0%
0
.0%
100
100.0%
F18
100
100.0%
0
.0%
100
100.0%
F19
100
100.0%
0
.0%
100
100.0%
F20
100
100.0%
0
.0%
100
100.0%
F21
100
100.0%
0
.0%
100
100.0%
F22
100
100.0%
0
.0%
100
100.0%
F23
100
100.0%
0
.0%
100
100.0%
F24
100
100.0%
0
.0%
100
100.0%
F25
100
100.0%
0
.0%
100
100.0%
F26
100
100.0%
0
.0%
100
100.0%
F27
100
100.0%
0
.0%
100
100.0%
F28
100
100.0%
0
.0%
100
100.0%
F29
100
100.0%
0
.0%
100
100.0%
F30
100
100.0%
0
.0%
100
100.0%
F31
100
100.0%
0
.0%
100
100.0%
F32
100
100.0%
0
.0%
100
100.0%
dimension1
F33
100
100.0%
0
.0%
100
100.0%
F34
100
100.0%
0
.0%
100
100.0%
F35
100
100.0%
0
.0%
100
100.0%
F36
100
100.0%
0
.0%
100
100.0%
Descriptivesa
subject_f
rating_f
F01
Statistic
Mean
2.68
95% Confidence Interval for
Lower Bound
2.52
Mean
Upper Bound
2.84
5% Trimmed Mean
2.69
Median
3.00
Variance
.664
Std. Deviation
.815
Minimum
1
Maximum
5
Range
4
Interquartile Range
1
Skewness
F02
.082
-.030
.241
Kurtosis
.033
.478
Mean
4.86
.104
95% Confidence Interval for
Lower Bound
4.65
Mean
Upper Bound
5.07
5% Trimmed Mean
4.87
Median
5.00
Variance
1.091
Std. Deviation
1.045
Minimum
2
Maximum
7
Range
5
Interquartile Range
2
Skewness
F03
Std. Error
-.256
.241
Kurtosis
.236
.478
Mean
3.81
.095
95% Confidence Interval for
Lower Bound
3.62
Mean
Upper Bound
4.00
5% Trimmed Mean
3.80
Median
4.00
Variance
.903
Std. Deviation
.950
Minimum
2
Maximum
6
Range
4
Interquartile Range
1
Skewness
Kurtosis
F04
F05
F06
Mean
.032
.241
-.046
.478
3.17
.108
95% Confidence Interval for
Lower Bound
2.96
Mean
Upper Bound
3.38
5% Trimmed Mean
3.17
Median
3.00
Variance
1.173
Std. Deviation
1.083
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
.092
.241
Kurtosis
.146
.478
Mean
3.60
.094
95% Confidence Interval for
Lower Bound
3.41
Mean
Upper Bound
3.79
5% Trimmed Mean
3.60
Median
4.00
Variance
.889
Std. Deviation
.943
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
.000
.241
Kurtosis
.071
.478
Mean
2.65
.101
95% Confidence Interval for
Lower Bound
2.45
Mean
Upper Bound
2.85
5% Trimmed Mean
2.63
Median
3.00
Variance
1.018
Std. Deviation
1.009
Minimum
1
Maximum
5
Range
4
Interquartile Range
1
Skewness
Kurtosis
F07
Mean
-.497
.478
3.07
.096
Lower Bound
2.88
Mean
Upper Bound
3.26
5% Trimmed Mean
3.07
Median
3.00
Variance
.914
Std. Deviation
.956
Minimum
1
Maximum
5
Range
4
Interquartile Range
2
Kurtosis
Mean
.000
.241
-.418
.478
4.71
.096
95% Confidence Interval for
Lower Bound
4.52
Mean
Upper Bound
4.90
5% Trimmed Mean
4.74
Median
5.00
Variance
.915
Std. Deviation
.957
Minimum
2
Maximum
7
Range
5
Interquartile Range
1
Skewness
F09
.241
95% Confidence Interval for
Skewness
F08
.151
-.515
.241
Kurtosis
.314
.478
Mean
4.51
.100
95% Confidence Interval for
Lower Bound
4.31
Mean
Upper Bound
5% Trimmed Mean
4.51
Median
4.00
Variance
1.000
Std. Deviation
1.000
Minimum
2
Maximum
7
Range
5
Interquartile Range
1
Skewness
Kurtosis
F10
Mean
.241
-.528
.478
3.42
.087
Lower Bound
3.25
Mean
Upper Bound
3.59
5% Trimmed Mean
3.41
Median
3.00
Variance
.751
Std. Deviation
.867
Minimum
2
Maximum
5
Range
3
Interquartile Range
1
Kurtosis
Mean
.109
.241
-.609
.478
3.30
.101
95% Confidence Interval for
Lower Bound
3.10
Mean
Upper Bound
3.50
5% Trimmed Mean
3.28
Median
3.00
Variance
1.020
Std. Deviation
1.010
Minimum
1
Maximum
7
Range
6
Interquartile Range
1
Skewness
Kurtosis
F12
.065
95% Confidence Interval for
Skewness
F11
4.71
Mean
.324
.241
1.277
.478
3.70
.099
95% Confidence Interval for
Lower Bound
3.50
Mean
Upper Bound
3.90
5% Trimmed Mean
3.69
Median
4.00
Variance
.980
Std. Deviation
.990
Minimum
2
Maximum
6
Range
4
Interquartile Range
1
Skewness
Kurtosis
F13
Mean
.241
-.356
.478
2.53
.092
95% Confidence Interval for
Lower Bound
2.35
Mean
Upper Bound
2.71
5% Trimmed Mean
2.50
Median
2.00
Variance
.837
Std. Deviation
.915
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
Kurtosis
F14
.000
Mean
.676
.241
1.326
.478
2.66
.101
95% Confidence Interval for
Lower Bound
2.46
Mean
Upper Bound
2.86
5% Trimmed Mean
2.64
Median
3.00
Variance
1.015
Std. Deviation
1.007
Minimum
1
Maximum
5
Range
4
Interquartile Range
1
Skewness
Kurtosis
.125
.241
-.488
.478
F15
Mean
3.37
95% Confidence Interval for
Lower Bound
3.20
Mean
Upper Bound
3.54
5% Trimmed Mean
3.36
Median
3.00
Variance
.700
Std. Deviation
.837
Minimum
2
Maximum
5
Range
3
Interquartile Range
1
Skewness
Kurtosis
F16
Mean
.241
-.490
.478
2.37
.080
Lower Bound
2.21
Mean
Upper Bound
2.53
5% Trimmed Mean
2.36
Median
2.00
Variance
.639
Std. Deviation
.800
Minimum
1
Maximum
4
Range
3
Interquartile Range
1
Kurtosis
F17
.158
95% Confidence Interval for
Skewness
Mean
.074
.241
-.424
.478
2.83
.085
95% Confidence Interval for
Lower Bound
2.66
Mean
Upper Bound
3.00
5% Trimmed Mean
2.80
Median
3.00
Variance
.728
Std. Deviation
.853
Minimum
1
Maximum
5
Range
4
Interquartile Range
1
Skewness
.084
.436
.241
F18
Kurtosis
.230
.478
Mean
3.75
.095
95% Confidence Interval for
Lower Bound
3.56
Mean
Upper Bound
3.94
5% Trimmed Mean
3.74
Median
4.00
Variance
.896
Std. Deviation
.947
Minimum
2
Maximum
6
Range
4
Interquartile Range
1
Skewness
Kurtosis
F19
F20
Mean
.087
.241
-.256
.478
3.67
.094
95% Confidence Interval for
Lower Bound
3.48
Mean
Upper Bound
3.86
5% Trimmed Mean
3.68
Median
4.00
Variance
.890
Std. Deviation
.943
Minimum
2
Maximum
6
Range
4
Interquartile Range
1
Skewness
-.100
.241
Kurtosis
-.580
.478
4.83
.101
Mean
95% Confidence Interval for
Lower Bound
4.63
Mean
Upper Bound
5.03
5% Trimmed Mean
4.84
Median
5.00
Variance
1.011
Std. Deviation
1.006
Minimum
3
Maximum
7
Range
4
Interquartile Range
2
F21
Skewness
-.136
.241
Kurtosis
-.780
.478
4.31
.083
Mean
95% Confidence Interval for
Lower Bound
4.15
Mean
Upper Bound
4.47
5% Trimmed Mean
4.30
Median
4.00
Variance
.681
Std. Deviation
.825
Minimum
2
Maximum
6
Range
4
Interquartile Range
1
Skewness
Kurtosis
F22
F23
Mean
.025
.241
-.046
.478
4.08
.090
95% Confidence Interval for
Lower Bound
3.90
Mean
Upper Bound
4.26
5% Trimmed Mean
4.08
Median
4.00
Variance
.802
Std. Deviation
.895
Minimum
2
Maximum
6
Range
4
Interquartile Range
1
Skewness
.099
.241
Kurtosis
.360
.478
Mean
3.04
.097
95% Confidence Interval for
Lower Bound
2.85
Mean
Upper Bound
3.23
5% Trimmed Mean
3.02
Median
3.00
Variance
.948
Std. Deviation
.974
Minimum
1
Maximum
6
Range
5
Interquartile Range
2
Skewness
Kurtosis
F24
F25
F26
Mean
.187
.241
-.006
.478
3.50
.104
95% Confidence Interval for
Lower Bound
3.29
Mean
Upper Bound
3.71
5% Trimmed Mean
3.46
Median
3.00
Variance
1.081
Std. Deviation
1.040
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
.523
.241
Kurtosis
.171
.478
Mean
2.84
.091
95% Confidence Interval for
Lower Bound
2.66
Mean
Upper Bound
3.02
5% Trimmed Mean
2.84
Median
3.00
Variance
.823
Std. Deviation
.907
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
.242
.241
Kurtosis
.691
.478
Mean
3.81
.093
95% Confidence Interval for
Lower Bound
3.63
Mean
Upper Bound
3.99
5% Trimmed Mean
3.83
Median
4.00
Variance
.863
Std. Deviation
.929
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
F27
-.150
.241
Kurtosis
.045
.478
Mean
3.76
.106
95% Confidence Interval for
Lower Bound
3.55
Mean
Upper Bound
3.97
5% Trimmed Mean
3.74
Median
4.00
Variance
1.114
Std. Deviation
1.055
Minimum
2
Maximum
7
Range
5
Interquartile Range
2
Skewness
Kurtosis
F28
Mean
.241
-.172
.478
2.93
.093
95% Confidence Interval for
Lower Bound
2.74
Mean
Upper Bound
3.12
5% Trimmed Mean
2.93
Median
3.00
Variance
.874
Std. Deviation
.935
Minimum
1
Maximum
5
Range
4
Interquartile Range
2
Skewness
Kurtosis
F29
.182
Mean
.066
.241
-.368
.478
4.40
.107
95% Confidence Interval for
Lower Bound
4.19
Mean
Upper Bound
4.61
5% Trimmed Mean
4.41
Median
4.00
Variance
1.152
Std. Deviation
1.073
Minimum
2
F30
Maximum
7
Range
5
Interquartile Range
1
Skewness
-.060
.241
Kurtosis
-.135
.478
3.88
.100
Mean
95% Confidence Interval for
Lower Bound
3.68
Mean
Upper Bound
4.08
5% Trimmed Mean
3.87
Median
4.00
Variance
.996
Std. Deviation
.998
Minimum
2
Maximum
6
Range
4
Interquartile Range
2
Skewness
Kurtosis
F31
F32
Mean
.121
.241
-.483
.478
3.95
.093
95% Confidence Interval for
Lower Bound
3.77
Mean
Upper Bound
4.13
5% Trimmed Mean
3.97
Median
4.00
Variance
.856
Std. Deviation
.925
Minimum
2
Maximum
6
Range
4
Interquartile Range
2
Skewness
-.212
.241
Kurtosis
-.157
.478
3.64
.090
Mean
95% Confidence Interval for
Lower Bound
3.46
Mean
Upper Bound
3.82
5% Trimmed Mean
3.63
Median
4.00
Variance
.819
Std. Deviation
.905
Minimum
2
Maximum
6
Range
4
Interquartile Range
1
Skewness
Kurtosis
F33
F34
F35
Mean
.030
.241
-.075
.478
3.45
.102
95% Confidence Interval for
Lower Bound
3.25
Mean
Upper Bound
3.65
5% Trimmed Mean
3.44
Median
4.00
Variance
1.038
Std. Deviation
1.019
Minimum
1
Maximum
6
Range
5
Interquartile Range
1
Skewness
-.067
.241
Kurtosis
-.161
.478
4.24
.110
Mean
95% Confidence Interval for
Lower Bound
4.02
Mean
Upper Bound
4.46
5% Trimmed Mean
4.26
Median
4.00
Variance
1.215
Std. Deviation
1.102
Minimum
2
Maximum
7
Range
5
Interquartile Range
1
Skewness
-.169
.241
Kurtosis
-.320
.478
3.97
.098
Mean
95% Confidence Interval for
Lower Bound
3.78
Mean
Upper Bound
4.16
5% Trimmed Mean
3.97
Median
4.00
Variance
.959
Std. Deviation
.979
Minimum
2
Maximum
6
Range
4
Interquartile Range
2
Skewness
Kurtosis
F36
Mean
.061
.241
-.300
.478
3.92
.091
95% Confidence Interval for
Lower Bound
3.74
Mean
Upper Bound
4.10
5% Trimmed Mean
3.93
Median
4.00
Variance
.822
Std. Deviation
.907
Minimum
2
Maximum
6
Range
4
Interquartile Range
2
Skewness
-.089
.241
Kurtosis
-.156
.478
a. There are no valid cases for rating_f when subject_f = .000. Statistics cannot be computed for
this level.
Tests of Normalityb
subject_f
Kolmogorov-Smirnova
Statistic
rating_f
dimension1
df
Shapiro-Wilk
Sig.
Statistic
df
Sig.
F01
.263
100
.000
.871
100
.000
F02
.223
100
.000
.916
100
.000
F03
.239
100
.000
.897
100
.000
F04
.212
100
.000
.919
100
.000
F05
.214
100
.000
.907
100
.000
F06
.190
100
.000
.907
100
.000
F07
.199
100
.000
.904
100
.000
F08
.269
100
.000
.888
100
.000
F09
.215
100
.000
.909
100
.000
F10
.236
100
.000
.874
100
.000
F11
.187
100
.000
.897
100
.000
F12
.229
100
.000
.901
100
.000
F13
.239
100
.000
.872
100
.000
F14
.192
100
.000
.907
100
.000
F15
.251
100
.000
.868
100
.000
F16
.248
100
.000
.862
100
.000
F17
.241
100
.000
.869
100
.000
F18
.214
100
.000
.901
100
.000
F19
.227
100
.000
.894
100
.000
F20
.187
100
.000
.897
100
.000
F21
.256
100
.000
.875
100
.000
F22
.276
100
.000
.875
100
.000
F23
.196
100
.000
.907
100
.000
F24
.255
100
.000
.894
100
.000
F25
.230
100
.000
.887
100
.000
F26
.211
100
.000
.900
100
.000
F27
.180
100
.000
.911
100
.000
F28
.200
100
.000
.900
100
.000
F29
.182
100
.000
.925
100
.000
F30
.182
100
.000
.908
100
.000
F31
.242
100
.000
.893
100
.000
F32
.245
100
.000
.888
100
.000
F33
.225
100
.000
.912
100
.000
F34
.185
100
.000
.923
100
.000
F35
.208
100
.000
.907
100
.000
F36
.235
100
.000
.895
100
.000
a. Lilliefors Significance Correction
b. There are no valid cases for rating_f when subject_f = .000. Statistics cannot be computed for
this level.
Histograms
Stem-and-Leaf Plots
rating_f Stem-and-Leaf Plot for
subject_f= F01
Frequency
Stem &
Leaf
7.00
1 . 0000000
.00
1 .
.00
1 .
.00
1 .
.00
1 .
32.00
2 . 00000000000000000000000000000000
.00
2 .
.00
2 .
.00
2 .
.00
2 .
48.00
3 . 000000000000000000000000000000000000000000000000
.00
3 .
.00
3 .
.00
3 .
.00
3 .
12.00
4 . 000000000000
1.00 Extremes
(>=5.0)
Stem width:
Each leaf:
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F02
Frequency
2.00
.00
7.00
.00
24.00
.00
42.00
.00
20.00
.00
5.00
Stem width:
Each leaf:
Stem &
2
2
3
3
4
4
5
5
6
6
7
Leaf
. 00
.
. 0000000
.
. 000000000000000000000000
.
. 000000000000000000000000000000000000000000
.
. 00000000000000000000
.
. 00000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F03
Frequency
Stem &
Leaf
9.00
2 . 000000000
.00
2 .
.00
2 .
.00
2 .
.00
2 .
25.00
3 . 0000000000000000000000000
.00
3 .
.00
3 .
.00
3 .
.00
3 .
46.00
4 . 0000000000000000000000000000000000000000000000
.00
4 .
.00
4 .
.00
4 .
.00
4 .
16.00
5 . 0000000000000000
4.00 Extremes
(>=6.0)
Stem width:
Each leaf:
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F04
Frequency
Stem &
Leaf
7.00 Extremes
(=<1.0)
16.00
2 . 0000000000000000
.00
2 .
.00
2 .
.00
2 .
.00
2 .
42.00
3 . 000000000000000000000000000000000000000000
.00
3 .
.00
3 .
.00
3 .
.00
3 .
25.00
4 . 0000000000000000000000000
.00
4 .
.00
4 .
.00
4 .
.00
4 .
8.00
5 . 00000000
2.00 Extremes
(>=6.0)
Stem width:
Each leaf:
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F05
Frequency
Stem &
1.00 Extremes
10.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
34.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
40.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
13.00
5 .
2.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
0000000000
0000000000000000000000000000000000
0000000000000000000000000000000000000000
0000000000000
(>=6.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F06
Frequency
Stem &
13.00
1 .
.00
1 .
.00
1 .
.00
1 .
.00
1 .
32.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
35.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
17.00
4 .
3.00 Extremes
Stem width:
Each leaf:
Leaf
0000000000000
00000000000000000000000000000000
00000000000000000000000000000000000
00000000000000000
(>=5.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F07
Frequency
4.00
.00
24.00
.00
39.00
.00
27.00
.00
6.00
Stem width:
Each leaf:
Stem &
1
1
2
2
3
3
4
4
5
Leaf
. 0000
.
. 000000000000000000000000
.
. 000000000000000000000000000000000000000
.
. 000000000000000000000000000
.
. 000000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F08
Frequency
Stem &
Leaf
2.00 Extremes
(=<2.0)
9.00
3 . 000000000
.00
3 .
.00
3 .
.00
3 .
.00
3 .
24.00
4 . 000000000000000000000000
.00
4 .
.00
4 .
.00
4 .
.00
4 .
47.00
5 . 00000000000000000000000000000000000000000000000
.00
5 .
.00
5 .
.00
5 .
.00
5 .
17.00
6 . 00000000000000000
1.00 Extremes
(>=7.0)
Stem width:
Each leaf:
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F09
Frequency
Stem &
Leaf
1.00 Extremes
14.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
37.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
30.00
5 .
.00
5 .
.00
5 .
.00
5 .
.00
5 .
17.00
6 .
1.00 Extremes
Stem width:
Each leaf:
(=<2.0)
00000000000000
0000000000000000000000000000000000000
000000000000000000000000000000
00000000000000000
(>=7.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F10
Frequency
14.00
.00
.00
.00
.00
41.00
.00
.00
.00
.00
34.00
.00
.00
.00
.00
11.00
Stem width:
Each leaf:
Stem &
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
5
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Leaf
00000000000000
00000000000000000000000000000000000000000
0000000000000000000000000000000000
00000000000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F11
Frequency
Stem &
Leaf
3.00 Extremes
(=<1.0)
17.00
2 . 00000000000000000
.00
2 .
.00
2 .
.00
2 .
.00
2 .
37.00
3 . 0000000000000000000000000000000000000
.00
3 .
.00
3 .
.00
3 .
.00
3 .
36.00
4 . 000000000000000000000000000000000000
.00
4 .
.00
4 .
.00
4 .
.00
4 .
5.00
5 . 00000
2.00 Extremes
(>=6.0)
Stem width:
Each leaf:
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F12
Frequency
Stem &
13.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
26.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
42.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
16.00
5 .
3.00 Extremes
Stem width:
Each leaf:
Leaf
0000000000000
00000000000000000000000000
000000000000000000000000000000000000000000
0000000000000000
(>=6.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F13
Frequency
Stem &
10.00
1 .
.00
1 .
.00
1 .
.00
1 .
.00
1 .
42.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
36.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
10.00
4 .
2.00 Extremes
Stem width:
Each leaf:
Leaf
0000000000
000000000000000000000000000000000000000000
000000000000000000000000000000000000
0000000000
(>=5.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F14
Frequency
Stem &
13.00
1 .
.00
1 .
.00
1 .
.00
1 .
.00
1 .
31.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
36.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
17.00
4 .
3.00 Extremes
Stem width:
Each leaf:
Leaf
0000000000000
0000000000000000000000000000000
000000000000000000000000000000000000
00000000000000000
(>=5.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F15
Frequency
14.00
.00
.00
.00
.00
44.00
.00
.00
.00
.00
33.00
.00
.00
.00
.00
9.00
Stem &
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
5
Stem width:
Each leaf:
Leaf
. 00000000000000
.
.
.
.
. 00000000000000000000000000000000000000000000
.
.
.
.
. 000000000000000000000000000000000
.
.
.
.
. 000000000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F16
Frequency
13.00
.00
.00
.00
.00
44.00
.00
.00
.00
.00
36.00
.00
.00
.00
.00
7.00
Stem width:
Each leaf:
Stem &
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
4
Leaf
. 0000000000000
.
.
.
.
. 00000000000000000000000000000000000000000000
.
.
.
.
. 000000000000000000000000000000000000
.
.
.
.
. 0000000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F17
Frequency
Stem &
Leaf
3.00
1 . 000
.00
1 .
.00
1 .
.00
1 .
.00
1 .
33.00
2 . 000000000000000000000000000000000
.00
2 .
.00
2 .
.00
2 .
.00
2 .
46.00
3 . 0000000000000000000000000000000000000000000000
.00
3 .
.00
3 .
.00
3 .
.00
3 .
14.00
4 . 00000000000000
4.00 Extremes
(>=5.0)
Stem width:
Each leaf:
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F18
Frequency
Stem &
Leaf
9.00
2 . 000000000
.00
2 .
.00
2 .
.00
2 .
.00
2 .
30.00
3 . 000000000000000000000000000000
.00
3 .
.00
3 .
.00
3 .
.00
3 .
41.00
4 . 00000000000000000000000000000000000000000
.00
4 .
.00
4 .
.00
4 .
.00
4 .
17.00
5 . 00000000000000000
3.00 Extremes
(>=6.0)
Stem width:
Each leaf:
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F19
Frequency
Stem &
Leaf
12.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
29.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
40.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
18.00
5 .
1.00 Extremes
Stem width:
Each leaf:
000000000000
00000000000000000000000000000
0000000000000000000000000000000000000000
000000000000000000
(>=6.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F20
Frequency
10.00
.00
28.00
.00
33.00
.00
27.00
.00
2.00
Stem width:
Each leaf:
Stem &
3
3
4
4
5
5
6
6
7
Leaf
. 0000000000
.
. 0000000000000000000000000000
.
. 000000000000000000000000000000000
.
. 000000000000000000000000000
.
. 00
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F21
Frequency
Stem &
1.00 Extremes
13.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
47.00
4 .
.00
4 .
Leaf
(=<2.0)
0000000000000
00000000000000000000000000000000000000000000000
.00
.00
.00
32.00
.00
.00
.00
.00
7.00
4
4
4
5
5
5
5
5
6
Stem width:
Each leaf:
.
.
.
. 00000000000000000000000000000000
.
.
.
.
. 0000000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F22
Frequency
Stem &
Leaf
4.00 Extremes
(=<2.0)
17.00
3 . 00000000000000000
.00
3 .
.00
3 .
.00
3 .
.00
3 .
53.00
4 . 00000000000000000000000000000000000000000000000000000
.00
4 .
.00
4 .
.00
4 .
.00
4 .
19.00
5 . 0000000000000000000
.00
5 .
.00
5 .
.00
5 .
.00
5 .
7.00
6 . 0000000
Stem width:
Each leaf:
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F23
Frequency
4.00
.00
26.00
.00
38.00
.00
27.00
.00
Stem &
1
1
2
2
3
3
4
4
Leaf
. 0000
.
. 00000000000000000000000000
.
. 00000000000000000000000000000000000000
.
. 000000000000000000000000000
.
4.00
.00
1.00
5 .
5 .
6 .
Stem width:
Each leaf:
0000
0
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F24
Frequency
Stem &
1.00 Extremes
12.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
44.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
27.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
11.00
5 .
5.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
000000000000
00000000000000000000000000000000000000000000
000000000000000000000000000
00000000000
(>=6.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F25
Frequency
6.00
.00
.00
.00
.00
28.00
.00
.00
.00
.00
45.00
.00
.00
Stem &
1
1
1
1
1
2
2
2
2
2
3
3
3
Leaf
. 000000
.
.
.
.
. 0000000000000000000000000000
.
.
.
.
. 000000000000000000000000000000000000000000000
.
.
.00
3 .
.00
3 .
19.00
4 .
2.00 Extremes
Stem width:
Each leaf:
0000000000000000000
(>=5.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F26
Frequency
Stem &
Leaf
1.00 Extremes
(=<1.0)
5.00
2 . 00000
.00
2 .
.00
2 .
.00
2 .
.00
2 .
31.00
3 . 0000000000000000000000000000000
.00
3 .
.00
3 .
.00
3 .
.00
3 .
40.00
4 . 0000000000000000000000000000000000000000
.00
4 .
.00
4 .
.00
4 .
.00
4 .
21.00
5 . 000000000000000000000
2.00 Extremes
(>=6.0)
Stem width:
Each leaf:
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F27
Frequency
Stem &
Leaf
12.00
2 . 000000000000
.00
2 .
29.00
3 . 00000000000000000000000000000
.00
3 .
34.00
4 . 0000000000000000000000000000000000
.00
4 .
22.00
5 . 0000000000000000000000
.00
5 .
2.00
6 . 00
1.00 Extremes
(>=7.0)
Stem width:
1
Each leaf:
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F28
Frequency
5.00
.00
28.00
.00
40.00
.00
23.00
.00
4.00
Stem width:
Each leaf:
Stem &
1
1
2
2
3
3
4
4
5
Leaf
. 00000
.
. 0000000000000000000000000000
.
. 0000000000000000000000000000000000000000
.
. 00000000000000000000000
.
. 0000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F29
Frequency
Stem &
4.00 Extremes
15.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
34.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
33.00
5 .
.00
5 .
.00
5 .
.00
5 .
.00
5 .
12.00
6 .
2.00 Extremes
Stem width:
Each leaf:
Leaf
(=<2.0)
000000000000000
0000000000000000000000000000000000
000000000000000000000000000000000
000000000000
(>=7.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F30
Frequency
7.00
.00
30.00
.00
36.00
.00
22.00
.00
5.00
Stem &
2
2
3
3
4
4
5
5
6
Stem width:
Each leaf:
Leaf
. 0000000
.
. 000000000000000000000000000000
.
. 000000000000000000000000000000000000
.
. 0000000000000000000000
.
. 00000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F31
Frequency
7.00
.00
21.00
.00
45.00
.00
24.00
.00
3.00
Stem &
2
2
3
3
4
4
5
5
6
Stem width:
Each leaf:
Leaf
. 0000000
.
. 000000000000000000000
.
. 000000000000000000000000000000000000000000000
.
. 000000000000000000000000
.
. 000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F32
Frequency
11.00
.00
.00
.00
.00
30.00
.00
.00
.00
.00
45.00
Stem &
2
2
2
2
2
3
3
3
3
3
4
.
.
.
.
.
.
.
.
.
.
.
Leaf
00000000000
000000000000000000000000000000
000000000000000000000000000000000000000000000
.00
4 .
.00
4 .
.00
4 .
.00
4 .
12.00
5 .
2.00 Extremes
Stem width:
Each leaf:
000000000000
(>=6.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F33
Frequency
Stem &
2.00 Extremes
17.00
2 .
.00
2 .
.00
2 .
.00
2 .
.00
2 .
29.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
40.00
4 .
.00
4 .
.00
4 .
.00
4 .
.00
4 .
10.00
5 .
2.00 Extremes
Stem width:
Each leaf:
Leaf
(=<1.0)
00000000000000000
00000000000000000000000000000
0000000000000000000000000000000000000000
0000000000
(>=6.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F34
Frequency
Stem &
7.00 Extremes
17.00
3 .
.00
3 .
.00
3 .
.00
3 .
.00
3 .
33.00
4 .
.00
4 .
.00
4 .
.00
4 .
Leaf
(=<2.0)
00000000000000000
000000000000000000000000000000000
.00
4 .
32.00
5 .
.00
5 .
.00
5 .
.00
5 .
.00
5 .
10.00
6 .
1.00 Extremes
Stem width:
Each leaf:
00000000000000000000000000000000
0000000000
(>=7.0)
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F35
Frequency
6.00
.00
25.00
.00
41.00
.00
22.00
.00
6.00
Stem &
2
2
3
3
4
4
5
5
6
Stem width:
Each leaf:
Leaf
. 000000
.
. 0000000000000000000000000
.
. 00000000000000000000000000000000000000000
.
. 0000000000000000000000
.
. 000000
1
1 case(s)
rating_f Stem-and-Leaf Plot for
subject_f= F36
Frequency
6.00
.00
24.00
.00
45.00
.00
22.00
.00
3.00
Stem width:
Each leaf:
Stem &
2
2
3
3
4
4
5
5
6
Leaf
. 000000
.
. 000000000000000000000000
.
. 000000000000000000000000000000000000000000000
.
. 0000000000000000000000
.
. 000
1
1 case(s)
Normal Q-Q Plots
Detrended Normal Q-Q Plots
Appendix 2: Paired T-Test for Gender Bias
P aired S amples S tatis tic s
Pair 1
Pair 2
Pair 3
76
Std. Deviation
.62776
Std. Error
Mean
.07201
f_subs_rate_ave_all
Mean
3.5200
N
m_subs_rate_ave_all
3.6014
76
.53196
.06102
f_subs_rate_ave_m
3.4764
40
.54888
.08679
m_subs_rate_ave_m
3.5922
40
.43370
.06857
f_subs_rate_ave_f
3.5684
36
.71005
.11834
m_subs_rate_ave_f
3.6117
36
.62975
.10496
P aired S amples C orrelations
Pair 1
f_subs_rate_ave_all &
m_subs_rate_ave_all
N
76
Correlation
.933
Sig.
Pair 2
f_subs_rate_ave_m &
m_subs_rate_ave_m
40
.904
.000
Pair 3
f_subs_rate_ave_f &
m_subs_rate_ave_f
36
.955
.000
.000
P aired S amples T es t
Paired Differences
95% Confidence
Interval of the
Difference
Mean
-.08144
Std.
Deviation
.23214
Std. Error
Mean
.02663
Lower
-.13448
Upper
-.02839
t
-3.058
df
75
Sig. (2-tailed)
.003
Pair 1
f_subs_rate_ave_all m_subs_rate_ave_all
Pair 2
f_subs_rate_ave_m m_subs_rate_ave_m
-.11575
.24324
.03846
-.19354
-.03795
-3.009
39
.005
Pair 3
f_subs_rate_ave_f m_subs_rate_ave_f
-.04331
.21612
.03602
-.11644
.02981
-1.203
35
.237
Appendix 3: G ender B ias ANOV A and t-tes ts
Welch's Oneway ANOVA for Male Ethnic Bias
1: Asian
2: Eurasian
3: Caucasian
Des c riptives
ratings_m
N
Std.
Mean
Deviation Std. Error
3.3682
.42598
.09082
95% Confidence Interval for Mean
Lower Bound
3.1793
Upper Bound
3.5571
Minimum
2.58
Maximum
4.13
.14559
3.4029
4.0438
3.00
4.59
.47573
.19422
3.2508
4.2492
3.09
4.36
.48185
.07619
3.3779
3.6861
2.58
4.59
1.00
22
2.00
12
3.7233
.50433
3.00
6
3.7500
Total
40
3.5320
T es t of Homogeneity of V arianc es
ratings_m
Levene Statistic
.264
df1
df2
2
Sig.
.770
37
ANOV A
ratings_m
Between Groups
Sum of
Squares
1.315
2
Mean
Square
.657
.209
df
Within Groups
7.740
37
Total
9.055
39
F
3.143
R obus t T es ts of E quality of Means
ratings_m
Welch
Brown-Forsythe
Statistica
2.904
2.908
a. Asymptotically F distributed.
df1
2
df2
12.800
Sig.
.091
2
19.279
.079
Sig.
.055
Means P lots
T -T es t (Male 1-As ian, 2-E uras ian)
G roup S tatis tic s
race_m
N
ratings_m
1.00
22
Mean
3.3682
2.00
12
3.7233
Std. Deviation
Std. Error Mean
.42598
.09082
.50433
.14559
Independent S amples T es t
Assumptions=Equal variances assumed
Levene's Test for
Equality of Variances
t-test for Equality of Means
95% Confidence Interval of
the Difference
F
ratings_m
.486
Sig.
.491
t
-2.178
df
32
Sig. (2-tailed)
Mean Difference
.037
-.35515
Std. Error
Difference
.16309
Lower
-.68735
Upper
-.02296
T -T es t (Male 1-As ian,3-C auc as ian)
G roup S tatis tic s
race_m
N
ratings_m
1.00
22
Mean
3.3682
3.00
6
3.7500
Std. Deviation
Std. Error Mean
.42598
.09082
.47573
.19422
Independent S amples T es t
Assumptions=Equal variances assumed
Levene's Test for
Equality of Variances
t-test for Equality of Means
95% Confidence Interval of
the Difference
F
ratings_m
.137
Sig.
.714
t
-1.901
df
26
Sig. (2-tailed)
Mean Difference
.068
-.38182
Std. Deviation
Std. Error Mean
.50433
.14559
Std. Error
Difference
.20080
Lower
-.79458
Upper
.03094
T -T es t (Male 2-E uras ian,3-C auc as ian)
G roup S tatis tic s
race_m
N
ratings_m
2.00
12
Mean
3.7233
3.00
6
3.7500
.47573
.19422
Independent S amples T es t
Assumptions=Equal variances assumed
Levene's Test for
Equality of Variances
t-test for Equality of Means
95% Confidence Interval of
the Difference
F
ratings_m
.030
Sig.
.864
t
df
-.108
16
Sig. (2-tailed)
Mean Difference
-.02667
.916
Std. Deviation
Std. Error Mean
.76910
.16397
Std. Error
Difference
.24779
Lower
-.55195
Upper
.49862
Independent T -T es t F emale E thnic B ias
1: Asian
2: Eurasian
G roup S tatis tic s
race_f
N
ratings_f
1.00
22
Mean
3.5400
2.00
12
3.6200
.49448
.14274
Independent S amples T es t
Assumptions=Equal variances assumed
Levene's Test for
Equality of Variances
t-test for Equality of Means
95% Confidence Interval of
the Difference
ratings_f
F
2.982
Sig.
.094
t
df
-.324
32
Mean Difference
Sig. (2-tailed)
.748
-.08000
Std. Error
Difference
.24661
Lower
-.58233
Upper
.42233
Appendix 4: Table of Measurement Indices
Feature of index
Nose
Index
Baum Method (nasal tip
protrusion/n-sn)
n-prn/n-sn
nasion height/n-sn
Nasal index (al-al/n-prn)
Eye
ex-en right/ex-ex
ex-en leftt/ex-ex
en-en/ex-ex
Face
General
ex-en averaged/en-en
ex-en averaged/mideye
ex-en averaged/ex-ex
ex-ex/mideye
ps-pi averaged/middle 3rd
ps-pi averaged/ tr-gn
top 3rd/middle 3rd
top 3rd/bottom 3rd
middle 3rd/bottom 3rd
top 3rd/tr-gn
middle 3rd/tr-gn
bottom 3rd/tr-gn
al-al/ex-ex
al-al/en-en
al-al/ex-en (averaged)
al-al/mideye
n-prn/en-en
n-sn/en-en
Medium
2D side view
3D image
2D side view
3D image
Manual cast
2D side view
3D image
2D side view
Manual cast
2D fullface view
Manual cast
2D fullface view
Manual cast
2D fullface view
Manual cast
2D fullface view
2D fullface view
2D fullface view
2D fullface view
2D fullface view
2D fullface view
2D fullface view
2D fullface view
2D fullface view
2D fullface view
2D fullface view
2D fullface view
2D fullface view
Manual cast
2D fullface view
Manual cast
2D fullface view
2D fullface view
Manual cast
Manual cast
Appendix 5: Additional comparative measurement plots between 2D side profile and 3D images
n-prn/n-sn
1
difference n-prn/n-sn (3D-2D) VS
average nprn/nsn
0.15
difference n-prn/n-sn (3D-2D)
n-prn/n-sn 3D
0.95
0.9
0.1
0.05
0.85
0.8
0
-0.05
0.75
0.7
0.7
0.75
0.8 0.85 0.9 0.95
n-prn/n-sn 2D profile
1
0.7
0.75
0.8
0.85
0.9
0.95
-0.1
-0.15
average nprn/nsn
The scatter plot for n-prn/n-sn is somewhat disperse, though the trend is that the index is
consistently higher on 2D profile than 3D. The mean difference for n-prn/n-sn is 0.0310 with a
standard deviation of 0.0406; with corresponding limits of agreement at -0.112 and 0.0502.
Baum Method
5
difference Baum Method (3D-2D) VS
average Baum Method
1.2
difference Baum Method (3D-2D)
Baum Method 3D
4.5
4
3.5
3
2.5
2
2
2.5
3
3.5
4
4.5
Baum Method 2D profile
5
1
0.8
0.6
0.4
0.2
0
-0.2 2
-0.4
3
4
average Baum Method
The scatter plot is relatively tight though the point cloud is slightly above the line of equality.
The mean difference for Baum Method is 0.299 with a standard deviation of 0.312; with
corresponding limits of agreement at -0.324 and 0.923.
5
Appendix 6:
Correlations Plots for Males
Measurement VS Average Rating
Appendix 6:
Correlations Plots for Females
Measurement VS Average Rating
Appendix 7: Regression Results for Males
Regression
V ariables E ntered/R emoved b
Model
Variables
Entered
1
nasion
height_pa
a. All requested variables entered.
Variables
Removed
Method
. Enter
b. Dependent Variable: average
Model S ummary b
Model
R
.424a
1
Adjusted R
Std. Error of the
Square
Estimate
.158
.44214
R Square
.180
a. Predictors: (Constant), nasion height_p
b. Dependent Variable: average
A NOV A b
Model
1
Regression
Sum of
Squares
1.627
df
1
Mean Square
1.627
.195
Residual
7.428
38
Total
9.055
39
F
Sig.
.006a
8.321
a. Predictors: (Constant), nasion height_p
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
nasion height_p
3.127
Std. Error
.157
.063
.022
Standardized
Coefficients
Beta
t
.424
Sig.
19.937
.000
2.885
.006
a. Dependent Variable: average
R es iduals S tatis tic s a
Predicted Value
Residual
Std. Predicted
V
l Residual
Std.
Minimum
3.1901
Maximum
4.0620
Mean
3.5320
Std. Deviation
.20422
-.73558
1.01174
.00000
.43643
40
-1.674
2.595
.000
1.000
40
-1.664
2.288
.000
.987
40
a. Dependent Variable: average
N
40
R egres s ion
V ariables E ntered/R emoved b
Model
Variables
Entered
Variables
Removed
n-sn ave_ca
1
Method
. Enter
a. All requested variables entered.
b. Dependent Variable: average
Model S ummary b
Model
R
.348a
1
Adjusted R
Std. Error of the
Square
Estimate
.098
.45771
R Square
.121
a. Predictors: (Constant), n-sn ave_c
b. Dependent Variable: average
A NOV A b
Model
1
Sum of
Squares
1.094
Regression
df
1
Mean Square
1.094
.209
Residual
7.961
38
Total
9.055
39
F
Sig.
.028a
5.223
a. Predictors: (Constant), n-sn ave_c
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
.329
Std. Error
1.403
n-sn ave_c
.593
.259
Standardized
Coefficients
Beta
t
.348
Sig.
.234
.816
2.285
.028
a. Dependent Variable: average
R es iduals S tatis tic s a
Predicted Value
Residual
Std. Predicted
V
l Residual
Std.
Minimum
3.0886
Maximum
3.8615
Mean
3.5320
Std. Deviation
.16750
-.77857
.94179
.00000
.45180
40
-2.647
1.967
.000
1.000
40
-1.701
2.058
.000
.987
40
a. Dependent Variable: average
N
40
R egres s ion
V ariables E ntered/R emoved b
Model
Variables
Entered
nasal index
(al-al/nprn)_ca
1
Variables
Removed
Method
. Enter
a. All requested variables entered.
b. Dependent Variable: average
Model S ummary b
Model
R
.346a
1
Adjusted R
Std. Error of the
Square
Estimate
.096
.45804
R Square
.120
a. Predictors: (Constant), nasal index (al-al/n-prn)_c
b. Dependent Variable: average
A NOV A b
Model
1
Regression
Sum of
Squares
1.083
df
1
Mean Square
1.083
.210
Residual
7.972
38
Total
9.055
39
F
Sig.
.029a
5.161
a. Predictors: (Constant), nasal index (al-al/n-prn)_c
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
nasal index (alal/n-prn)_c
a. Dependent Variable: average
4.907
Std. Error
.610
-1.617
.712
Standardized
Coefficients
Beta
t
-.346
Sig.
8.048
.000
-2.272
.029
R es iduals S tatis tic s a
Predicted Value
Residual
Std. Predicted
V
l Residual
Std.
Minimum
3.1788
Maximum
3.8674
Mean
3.5320
Std. Deviation
.16662
-.85647
.88011
.00000
.45213
40
-2.120
2.013
.000
1.000
40
-1.870
1.921
.000
.987
40
a. Dependent Variable: average
N
40
R egres s ion
V ariables E ntered/R emoved b
Model
Variables
Entered
nasion
height/nsn_pa
1
Variables
Removed
Method
. Enter
a. All requested variables entered.
b. Dependent Variable: average
Model S ummary b
Model
R
.344a
1
Adjusted R
Std. Error of the
Square
Estimate
.095
.45839
R Square
.118
a. Predictors: (Constant), nasion height/n-sn_p
b. Dependent Variable: average
A NOV A b
Model
1
Regression
Sum of
Squares
1.070
df
1
Mean Square
1.070
.210
Residual
7.985
38
Total
9.055
39
F
Sig.
.030a
5.094
a. Predictors: (Constant), nasion height/n-sn_p
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
3.207
Std. Error
.161
nasion height/n-
2.689
1.191
Standardized
Coefficients
Beta
t
.344
Sig.
19.920
.000
2.257
.030
a. Dependent Variable: average
R es iduals S tatis tic s a
Predicted Value
Residual
Std. Predicted
V
l Residual
Std.
Minimum
3.2548
Maximum
3.9336
Mean
3.5320
Std. Deviation
.16567
-.77919
1.04472
.00000
.45247
40
-1.673
2.424
.000
1.000
40
-1.700
2.279
.000
.987
40
a. Dependent Variable: average
N
40
R egres s ion
V ariables E ntered/R emoved b
Model
Variables
Entered
1
nasolabial
angle_sa
a. All requested variables entered.
Variables
Removed
Method
. Enter
b. Dependent Variable: average
Model S ummary b
Model
R
.341a
1
Adjusted R
Std. Error of the
Estimate
Square
.093
.45897
R Square
.116
a. Predictors: (Constant), nasolabial angle_s
b. Dependent Variable: average
A NOV A b
Model
1
Regression
Sum of
Squares
1.050
df
1
Mean Square
1.050
.211
Residual
8.005
38
Total
9.055
39
F
Sig.
.032a
4.985
a. Predictors: (Constant), nasolabial angle_s
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
nasolabial
l average
a. Dependent Variable:
2.255
Std. Error
.576
.012
.006
Standardized
Coefficients
Beta
t
.341
Sig.
3.914
.000
2.233
.032
R es iduals S tatis tic s a
Predicted Value
Residual
Std. Predicted
V
l Residual
Std.
Minimum
3.1505
Maximum
3.8840
Mean
3.5320
Std. Deviation
.16410
-.94345
1.02925
.00000
.45305
40
-2.325
2.145
.000
1.000
40
-2.056
2.243
.000
.987
40
a. Dependent Variable: average
N
40
R egres s ion
V ariables E ntered/R emoved b
Model
Variables
Entered
Variables
Removed
n-sn_pa
1
Method
. Enter
a. All requested variables entered.
b. Dependent Variable: average
Model S ummary b
Model
R
.328a
1
Adjusted R
Std. Error of the
Square
Estimate
.084
.46119
R Square
.107
a. Predictors: (Constant), n-sn_p
b. Dependent Variable: average
A NOV A b
Model
1
Regression
Sum of
Squares
.973
df
1
Mean Square
.973
.213
Residual
8.082
38
Total
9.055
39
F
Sig.
.039a
4.573
a. Predictors: (Constant), n-sn_p
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
.419
Std. Error
1.457
n-sn_p
.057
.026
Standardized
Coefficients
Beta
t
.328
Sig.
.288
.775
2.138
.039
a. Dependent Variable: average
R es iduals S tatis tic s a
Predicted Value
Residual
Std. Predicted
V
l Residual
Std.
Minimum
3.2042
Maximum
3.8324
Mean
3.5320
Std. Deviation
.15792
-.84961
.93549
.00000
.45524
40
-2.076
1.902
.000
1.000
40
-1.842
2.028
.000
.987
40
a. Dependent Variable: average
N
40
R egres s ion
V ariables E ntered/R emoved a
Model
1
Variables
Entered
nasion
height_p
Variables
Removed
.
Method
Stepwise
(Criteria:
Probability-of-F-toenter <= .050,
Probability-of-F-toremove >= .100).
a. Dependent Variable: average
Model S ummary b
Model
R
.424a
1
Adjusted R
Std. Error of the
Square
Estimate
.158
.44214
R Square
.180
a. Predictors: (Constant), nasion height_p
b. Dependent Variable: average
A NOV A b
Model
1
Regression
Sum of
Squares
1.627
df
1
Mean Square
1.627
.195
Residual
7.428
38
Total
9.055
39
F
Sig.
.006a
8.321
a. Predictors: (Constant), nasion height_p
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
nasion height_p
3.127
Std. Error
.157
.063
.022
Standardized
Coefficients
Beta
t
.424
Sig.
19.937
.000
2.885
.006
a. Dependent Variable: average
E xc luded V ariables b
Model
Collinearity
Statistics
1.805
.079
Partial Correlation
.285
Tolerance
.948
nasal index (al-1.139
-.189a
al/n-prn)_c
nasolabial
1.356
.212a
l
a. Predictors in the Model: (Constant), nasion height_p
.262
-.184
.781
.183
.218
.862
Beta In
1
n-sn ave_c
b. Dependent Variable: average
.265a
t
Sig.
R es iduals S tatis tic s a
Predicted Value
Std. Predicted
V
l
Standard
Error
Minimum
3.1901
Maximum
4.0620
Mean
3.5320
Std. Deviation
.20422
N
-1.674
2.595
.000
1.000
40
.070
.197
.094
.030
40
40
of Predicted
Adjusted
P
di t d V l
Residual
3.1569
4.1426
3.5351
.21215
40
-.73558
1.01174
.00000
.43643
40
Std. Residual
-1.664
2.288
.000
.987
40
Stud. Residual
-1.710
2.319
-.003
1.010
40
Deleted
R
id Deleted
l
Stud.
-.77740
1.03908
-.00308
.45724
40
-1.757
2.470
.001
1.029
40
R
id Distance
l
Mahal.
.000
6.735
.975
1.456
40
Cook's Distance
.000
.207
.024
.037
40
Centered
.000
L
V l Variable: average
a. Dependent
.173
.025
.037
40
C harts
Appendix 7: Regression Results for Females
R egres s ion
V ariables E ntered/R emoved b
Model
1
Variables Entered
bottom 3rd/trgn_fa
Variables
Removed
Method
. Enter
a. All requested variables entered.
b. Dependent Variable: average
Model S ummary
Model
R
.459a
1
R Square
.211
Adjusted R
Std. Error of the
Square
Estimate
.187
.5985258
a. Predictors: (Constant), bottom 3rd/tr-gn_f
ANOV A b
Model
1
Regression
Sum of Squares
3.251
df
1
Mean Square
3.251
.358
Residual
12.180
34
Total
15.430
35
F
Sig.
.005a
9.074
a. Predictors: (Constant), bottom 3rd/tr-gn_f
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
bottom 3rd/tr-gn_f
a. Dependent Variable: average
8.672
Std. Error
1.690
-14.445
4.795
Standardized
Coefficients
Beta
t
-.459
Sig.
5.130
.000
-3.012
.005
R egres s ion
V ariables E ntered/R emoved b
Model
1
Variables Entered
top3rd/bottom3rd
_fa
Variables
Removed
Method
. Enter
a. All requested variables entered.
b. Dependent Variable: average
Model S ummary
Model
R
.419a
1
R Square
.176
Adjusted R
Std. Error of the
Square
Estimate
.152
.6115500
a. Predictors: (Constant), top3rd/bottom3rd_f
ANOV A b
Model
1
Regression
Sum of Squares
2.715
df
1
Mean Square
2.715
.374
Residual
12.716
34
Total
15.430
35
F
Sig.
.011a
7.259
a. Predictors: (Constant), top3rd/bottom3rd_f
b. Dependent Variable: average
C oeffic ients a
Model
Standardized
Coefficients
Unstandardized Coefficients
B
1
(Constant)
1.292
Std. Error
.859
top3rd/bottom3rd_f
2.597
.964
a. Dependent Variable: average
Beta
t
.419
Sig.
1.504
.142
2.694
.011
R egres s ion
V ariables E ntered/R emoved b
Model
Variables Entered
1
ex-enrt/ex-ex_f
Variables
Removed
Method
a
. Enter
a. All requested variables entered.
b. Dependent Variable: average
Model S ummary
Model
R
.403a
1
R Square
.162
Adjusted R
Std. Error of the
Square
Estimate
.137
.6166483
a. Predictors: (Constant), ex-enrt/ex-ex_f
ANOV A b
Model
1
Regression
Sum of Squares
2.502
df
1
Mean Square
2.502
.380
Residual
12.929
34
Total
15.430
35
F
Sig.
.015a
6.579
a. Predictors: (Constant), ex-enrt/ex-ex_f
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
ex-enrt/ex-ex_f
a. Dependent Variable: average
9.193
Std. Error
2.187
-18.682
7.283
Standardized
Coefficients
Beta
t
-.403
Sig.
4.203
.000
-2.565
.015
R egres s ion
V ariables E ntered/R emoved b
Model
1
Variables Entered
middle3rd/bottom
3rd_fa
Variables
Removed
Method
. Enter
a. All requested variables entered.
b. Dependent Variable: average
Model S ummary
Model
R
.383a
1
R Square
.146
Adjusted R
Std. Error of the
Square
Estimate
.121
.6224110
a. Predictors: (Constant), middle3rd/bottom3rd_f
ANOV A b
Model
1
Regression
Sum of Squares
2.259
df
1
Mean Square
2.259
.387
Residual
13.171
34
Total
15.430
35
F
Sig.
.021a
5.831
a. Predictors: (Constant), middle3rd/bottom3rd_f
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
middle3rd/bottom3rd_
f
a. Dependent Variable: average
.016
Std. Error
1.483
3.704
1.534
Standardized
Coefficients
Beta
t
.383
Sig.
.011
.992
2.415
.021
R egres s ion
V ariables E ntered/R emoved b
Model
Variables Entered
1
top3rd/tr-gn_f
Variables
Removed
Method
a
. Enter
a. All requested variables entered.
b. Dependent Variable: average
Model S ummary
Model
R
.338a
1
R Square
.114
Adjusted R
Std. Error of the
Square
Estimate
.088
.6339959
a. Predictors: (Constant), top3rd/tr-gn_f
ANOV A b
Model
1
Regression
Sum of Squares
1.764
df
1
Mean Square
1.764
.402
Residual
13.666
34
Total
15.430
35
F
Sig.
.044a
4.389
a. Predictors: (Constant), top3rd/tr-gn_f
b. Dependent Variable: average
C oeffic ients a
Model
Unstandardized Coefficients
B
1
(Constant)
top3rd/tr-gn_f
a. Dependent Variable: average
.588
Std. Error
1.436
9.702
4.631
Standardized
Coefficients
Beta
t
.338
Sig.
.410
.685
2.095
.044
R egres s ion
V ariables E ntered/R emoved a
Model
1
Variables Entered
bottom 3rd/tr-gn_f
Variables
Removed
.
Method
Stepwise
(Criteria:
Probability-of-F-toenter <= .050,
Probability-of-F-toremove >= .100).
a. Dependent Variable: average
Model S ummary
Model
R
.459a
1
Adjusted R
Std. Error of the
Square
Estimate
.187
.5985258
R Square
.211
a. Predictors: (Constant), bottom 3rd/tr-gn_f
ANOV A b
Model
1
Regression
Sum of Squares
3.251
df
1
Mean Square
3.251
.358
Residual
12.180
34
Total
15.430
35
F
Sig.
.005a
9.074
a. Predictors: (Constant), bottom 3rd/tr-gn_f
b. Dependent Variable: average
C oeffic ients a
Model
Standardized
Coefficients
Unstandardized Coefficients
B
1
(Constant)
bottom 3rd/tr-gn_f
8.672
Std. Error
1.690
-14.445
4.795
Beta
t
-.459
Sig.
5.130
.000
-3.012
.005
a. Dependent Variable: average
E xc luded V ariables b
Model
Collinearity
Statistics
Beta In
1
top3rd/tr-gn_f
t
a
.035
a. Predictors in the Model: (Constant), bottom 3rd/tr-gn_f
b. Dependent Variable: average
Sig.
.164
.871
Partial Correlation
.028
Tolerance
.514
Appendix 8: Top 8 and Bottom 8 Males t-test
G roup S tatis tic s
VAR00001
N
nasofrontal angle_s
nasofacial angle_s
nasomental angle_s
nasolabial angle_s
nasion level_s
Baum Method_s
nasion height/n-sn_s
n-prn/n-sn_s
al-al ave(cast)
n-prn ave_c
n-sn ave_c
en-en ave_c
n-prn ave/en-en ave_c
Mean
Std. Deviation
Std. Error Mean
1.00
8
138.500
5.831
2.062
2.00
8
138.375
6.346
2.244
1.00
8
30.688
2.187
0.773
2.00
8
31.563
3.087
1.092
1.00
8
132.063
4.330
1.531
2.00
8
131.625
5.712
2.019
1.00
8
108.500
12.840
4.540
2.00
8
99.438
17.361
6.138
1.00
8
2.000
0.756
0.267
2.00
8
2.125
0.991
0.350
1.00
8
3.189
0.297
0.105
2.00
8
3.136
0.393
0.139
1.00
8
0.189
0.089
0.031
2.00
8
0.176
0.046
0.016
1.00
8
0.857
0.024
0.009
2.00
8
0.873
0.034
0.012
1.00
8
3.936
0.248
0.088
2.00
8
4.184
0.179
0.063
1.00
8
4.793
0.258
0.091
2.00
8
4.762
0.370
0.131
1.00
8
5.548
0.224
0.079
2.00
8
5.346
0.290
0.103
1.00
8
3.727
0.243
0.086
2.00
8
4.250
0.328
0.116
1.00
8
1.293
0.130
0.046
2.00
8
1.124
0.091
0.032
n-sn ave/en-en ave_c
nasal index (al-al/n-prn)_c
n-prn/n-sn_c
al-al/en-en_c
nasion height_p
nasal tip protrusion_p
n-prn_p
n-sn_p
n-prn/n-sn_p
nasion height/n-sn_p
Baum Method_p
prn Gaussian curvature
average min curvature
al-al/ex-en ave_f
ex-en ave/mideye_f
ex-en ave/en-en_f
1.00
8
1.494
0.120
0.043
2.00
8
1.264
0.109
0.039
1.00
8
0.824
0.082
0.029
2.00
8
0.882
0.064
0.023
1.00
8
0.864
0.022
0.008
2.00
8
0.890
0.037
0.013
1.00
8
1.057
0.040
0.014
2.00
8
0.989
0.081
0.029
1.00
8
7.780
2.735
0.967
2.00
8
4.868
2.442
0.863
1.00
8
16.052
2.318
0.820
2.00
8
16.632
2.402
0.849
1.00
8
46.282
4.489
1.587
2.00
8
45.441
4.527
1.601
1.00
8
56.471
2.747
0.971
2.00
8
54.023
3.159
1.117
1.00
8
0.818
0.050
0.018
2.00
8
0.840
0.046
0.016
1.00
8
0.137
0.047
0.016
2.00
8
0.090
0.044
0.016
1.00
8
3.569
0.443
0.157
2.00
8
3.299
0.440
0.155
1.00
8
0.005
0.002
0.001
2.00
8
0.006
0.002
0.001
1.00
8
0.001
0.004
0.001
2.00
8
0.000
0.005
0.002
1.00
8
1.479
0.090
0.032
2.00
8
1.589
0.139
0.049
1.00
8
0.418
0.026
0.009
2.00
8
0.399
0.042
0.015
1.00
8
0.728
0.067
0.024
2.00
8
0.699
0.076
0.027
ex-en ave/ex-ex_f
al-al/en-en_f
al-al/mideye_f
en-en/ex-ex_f
ex-ex/mideye_f
ex-enrt/ex-ex_f
ex-enlt/ex-ex_f
al-al/ex-ex_f
ps-pi ave/mid3rd_f
ps-pi ave/tr-gn_f
top3rd/middle3rd_f
top3rd/bottom3rd_f
middle3rd/bottom3rd_f
top3rd/tr-gn_f
middle3rd/tr-gn_f
bottom 3rd/tr-gn_f
1.00
8
0.297
0.014
0.005
2.00
8
0.287
0.024
0.008
1.00
8
1.075
0.093
0.033
2.00
8
1.104
0.081
0.029
1.00
8
0.617
0.035
0.012
2.00
8
0.630
0.040
0.014
1.00
8
0.409
0.020
0.007
2.00
8
0.412
0.020
0.007
1.00
8
2.287
0.127
0.045
2.00
8
2.206
0.130
0.046
1.00
8
0.298
0.015
0.005
2.00
8
0.295
0.014
0.005
1.00
8
0.296
0.015
0.005
2.00
8
0.295
0.013
0.005
1.00
8
0.438
0.023
0.008
2.00
8
0.455
0.026
0.009
1.00
8
0.147
0.025
0.009
2.00
8
0.139
0.020
0.007
1.00
8
0.048
0.008
0.003
2.00
8
0.045
0.005
0.002
1.00
8
0.929
0.156
0.055
2.00
8
0.925
0.114
0.040
1.00
8
0.786
0.143
0.050
2.00
8
0.800
0.076
0.027
1.00
8
0.845
0.051
0.018
2.00
8
0.871
0.089
0.032
1.00
8
0.299
0.036
0.013
2.00
8
0.299
0.020
0.007
1.00
8
0.324
0.018
0.006
2.00
8
0.325
0.021
0.008
1.00
8
0.384
0.025
0.009
2.00
8
0.374
0.019
0.007
Independent S amples Tes t
Assumptions=Equal variances assumed
Variances
F
t-test for Equality of Means
Sig.
df
t
Mean
Std. Error
Sig. (2-tailed) Difference Difference
.968
0.125
3.047
.524
-0.875
1.338
.865
0.438
2.534
.255
9.063
7.634
.781
-0.125
0.441
.765
0.053
0.174
.714
0.013
0.035
.298
-0.016
0.015
.038
-0.248
0.108
.846
0.031
0.159
.141
0.202
0.130
.003
-0.523
0.144
.009
0.169
0.056
.001
0.231
0.057
.136
-0.058
0.037
nasofrontal angle_s
nasofacial angle_s
nasomental angle_s
nasolabial angle_s
nasion level_s
Baum Method_s
nasion height/n-sn_s
n-prn/n-sn_s
al-al ave(cast)
n-prn ave_c
n-sn ave_c
en-en ave_c
n-prn ave/en-en ave_c
n-sn ave/en-en ave_c
nasal index (al-al/nprn)_c
n-prn/n-sn_c
al-al/en-en_c
nasion height_p
nasal tip protrusion_p
n-prn_p
n-sn_p
n-prn/n-sn_p
nasion height/n-sn_p
Baum Method_p
prn Gaussian curvature
.061
1.372
1.993
1.603
.387
.920
4.613
.463
.714
1.684
.722
.499
1.405
.069
.891
.808
.261
.180
.226
.544
.354
.050
.507
.412
.215
.410
.491
.256
.797
.361
.041
-.654
.173
1.187
-.284
.305
.374
-1.080
-2.294
.197
1.562
-3.624
3.013
4.014
-1.583
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
4.235
3.998
.059
.184
.327
.211
.050
.018
.017
.015
.059
.065
.811
.675
.576
.653
.826
.895
.897
.905
-1.728
2.108
2.246
-.492
.373
1.654
-.894
2.101
1.226
-1.157
14
14
14
14
14
14
14
14
14
14
.106
.054
.041
.631
.715
.120
.386
.054
.240
.267
-0.026
0.068
2.912
-0.580
0.841
2.448
-0.022
0.048
0.271
-0.001
average min curvature
al-al/ex-en ave_f
ex-en ave/mideye_f
ex-en ave/en-en_f
ex-en ave/ex-ex_f
al-al/en-en_f
al-al/mideye_f
en-en/ex-ex_f
ex-ex/mideye_f
ex-enrt/ex-ex_f
ex-enlt/ex-ex_f
al-al/ex-ex_f
ps-pi ave/mid3rd_f
ps-pi ave/tr-gn_f
top3rd/middle3rd_f
top3rd/bottom3rd_f
middle3rd/bottom3rd_f
.395
.726
.209
.001
.348
.133
.369
.072
.074
.104
.065
.373
.338
2.142
.935
4.866
2.327
.540
.409
.654
.981
.565
.720
.553
.792
.790
.752
.802
.551
.571
.165
.350
.045
.149
.437
-1.872
1.089
.812
.965
-.662
-.672
-.353
1.245
.382
.117
-1.306
.782
.856
.057
-.243
-.705
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
.669
.082
.295
.430
.351
.519
.513
.729
.234
.709
.909
.213
.447
.407
.955
.811
.492
top3rd/tr-gn_f
middle3rd/tr-gn_f
bottom 3rd/tr-gn_f
2.694
.003
.740
.123
.959
.404
.027
-.080
.873
14
14
14
.979
.937
.397
Interval of the
Lower
Upper
-6.410
-3.744
-4.997
-7.311
-1.070
-0.321
-0.063
-0.048
-0.479
-0.310
-0.076
-0.833
0.049
0.107
-0.136
6.660
1.994
5.872
25.436
0.820
0.427
0.089
0.016
-0.016
0.373
0.480
-0.213
0.289
0.354
0.021
0.015
0.032
1.296
1.180
2.254
1.480
0.024
0.023
0.221
0.001
-0.059
-0.001
0.132
-3.112
-3.993
-0.727
-0.073
-0.001
-0.203
-0.003
0.006
0.136
5.692
1.951
5.676
5.622
0.030
0.096
0.744
0.001
0.001
-0.110
0.019
0.029
0.009
-0.029
-0.013
-0.004
0.080
0.003
0.001
-0.016
0.009
0.003
0.004
-0.014
-0.026
0.002
0.059
0.017
0.036
0.010
0.043
0.019
0.010
0.064
0.007
0.007
0.012
0.011
0.003
0.068
0.057
0.036
-0.004
-0.236
-0.018
-0.048
-0.011
-0.122
-0.053
-0.025
-0.058
-0.013
-0.014
-0.043
-0.015
-0.004
-0.143
-0.136
-0.104
0.006
0.016
0.056
0.106
0.030
0.064
0.028
0.018
0.218
0.019
0.016
0.010
0.033
0.010
0.151
0.108
0.052
0.000
-0.001
0.010
0.014
0.010
0.011
-0.031
-0.022
-0.014
0.031
0.021
0.034
Appendix 8: Top 8 and Bottom 8 Females t-test
G roup S tatis tic s
group
N
nasofrontal angle_s
nasofacial angle_s
nasomental angle_s
nasolabial angle_s
nasion level_s
Baum Method_s
nasion height/n-sn_s
n-prn/n-sn_s
al-al ave(cast)
n-prn ave_c
n-sn ave_c
en-en ave_c
ex-en rt_c
ex-en lt ave_c
1
8
Mean
140.813
Std. Deviation
7.8100
Std. Error Mean
2.7612
2
8
141.250
7.1464
2.5266
1
8
29.500
3.7607
1.3296
2
8
28.875
3.4304
1.2128
1
8
136.38
4.749
1.679
2
8
137.88
7.160
2.531
1
8
95.313
17.6553
6.2421
2
8
103.375
13.7834
4.8732
1
8
3.00
.535
.189
2
8
2.38
.916
.324
1
8
3.350303063
.4894941725
.1730623244
2
8
3.484642094
.5176027079
.1830001924
1
8
.12894796538
.044836701831
.015852167956
2
8
.10913258234
.044797983286
.015838478883
1
8
.8454473938
.02627258581
.00928876179
2
8
.8409310552
.02289453708
.00809444121
1
8
3.783188
.2232556
.0789328
2
8
3.826938
.1776116
.0627952
1
8
4.226563
.1450634
.0512877
2
8
4.069688
.4132885
.1461195
1
8
4.869563
.1393619
.0492719
2
8
4.856063
.3154736
.1115368
1
8
3.689875
.3454596
.1221384
2
8
3.695250
.2230165
.0788482
1
5
2.902300
.1926274
.0861456
2
6
2.985250
.1456886
.0594771
1
6
2.839500
.0833433
.0340247
2
7
2.952000
.1472212
.0556444
ex-ex ave_c
n-prn ave/en-en ave_c
n-sn ave/en-en ave_c
nasal index (al-al/n-prn)_c
n-prn/n-sn_c
ex-en rt/ex-ex_c
ex-en lt/ex-ex_c
al-al/ex-ex_c
en-en/ex-ex_c
al-al/en-en_c
nasion height_p
nasal tip protrusion_p
n-prn_p
n-sn_p
n-prn/n-sn_p
nasion height/n-sn_p
Baum Method_p
prn Gaussian curvature
1
4
9.262375
.4261591
.2130795
2
6
9.315833
.2798088
.1142315
1
8
1.154439913
.1170493747
.0413832033
2
8
1.105601016
.1393281168
.0492599281
1
8
1.331994038
.1538194458
.0543833866
2
8
1.317617873
.1104898227
.0390640514
1
8
.8955188463
.05273383753
.01864422706
2
8
.9477895848
.09456355987
.03343326722
1
8
.8683941738
.03382584753
.01195924308
2
8
.8369636426
.04605306632
.01628221774
1
4
.3049871800
.01802382736
.00901191368
2
6
.3208715436
.02151887591
.00878504430
1
4
.3013613550
.01246310624
.00623155312
2
6
.3143560111
.02039675347
.00832693973
1
4
.4007670150
.01367296737
.00683648369
2
6
.4096349563
.01477215049
.00603070518
1
4
.4069753050
.01996794710
.00998397355
2
6
.3964475529
.01990034064
.00812428005
1
8
1.0308729875
.08445049039
.02985775721
2
8
1.0372451088
.04888505447
.01728347676
1
8
3.579135238
1.3498160257
.4772320326
2
8
2.596704688
1.5972440718
.5647110572
1
8
13.70016388
1.879540405
.664517883
2
8
13.70154075
1.121162975
.396390971
1
8
41.59751725
1.898755868
.671311575
2
8
41.96578975
3.492884217
1.234921058
1
8
50.62266525
1.165553506
.412085394
2
8
51.64301575
3.248294710
1.148445609
1
8
.8222258988
.04399414467
.01555427901
2
8
.8126827930
.04741346152
.01676319008
1
8
.07063218475
.026467694856
.009357743258
2
8
.04938654867
.028310658905
.010009329446
1
8
3.748266713
.4500347864
.1591113246
2
8
3.782628210
.2719780077
.0961587468
1
7
.008406207243
.0021319403729
.0008057977195
2
8
.008380793155
.0035000961930
.0012374708764
average min curvature
al-al/ex-en ave_f
ex-en ave/mideye_f
ex-en ave/en-en_f
ex-en ave/ex-ex_f
al-al/en-en_f
al-al/mideye_f
en-en/ex-ex_f
ex-ex/mideye_f
ex-enrt/ex-ex_f
ex-enlt/ex-ex_f
al-al/ex-ex_f
ps-pi ave/mid3rd_f
ps-pi ave/tr-gn_f
top3rd/middle3rd_f
top3rd/bottom3rd_f
middle3rd/bottom3rd_f
top3rd/tr-gn_f
middle3rd/tr-gn_f
bottom 3rd/tr-gn_f
1
7
.001925810540
.0051298796161
.0019389122457
2
8
-.001722982937
.0051253286208
.0018120773118
1
8
1.565868363
.1475994932
.0521843013
2
8
1.458087558
.1643971965
.0581231862
1
8
.4112157338
.01511655250
.00534450839
2
8
.4369668661
.03358680473
.01187472869
1
8
.6971755050
.04432906424
.01567269096
2
8
.7642200508
.08273235502
.02925030463
1
8
.2917629413
.00582367749
.00205898092
2
8
.3038524408
.01179092759
.00416872243
1
8
1.0892900938
.09972358637
.03525761208
2
8
1.1035657882
.04737583260
.01674988625
1
8
.6421913325
.04178656716
.01477378250
2
8
.6328136977
.03640209362
.01287008362
1
8
.4196649650
.02193227434
.00775422996
2
8
.3999979923
.02565766788
.00907135547
1
8
2.204210125
.1793149920
.0633974234
2
8
2.278083997
.1856588022
.0656402990
1
8
.2889129775
.01029989902
.00364156422
2
8
.3069636160
.01007851634
.00356329363
1
8
.294613
.0069787
.0024674
2
8
.300741
.0181170
.0064053
1
8
.456281
.0366332
.0129518
2
8
.441472
.0351901
.0124416
1
8
.159179
.0138215
.0048866
2
8
.154522
.0274835
.0097169
1
8
.054054
.0052841
.0018682
2
8
.051937
.0095398
.0033728
1
8
.926477
.0905269
.0320061
2
8
.888964
.1000801
.0353837
1
8
.922823
.1099666
.0388791
2
8
.807930
.1192956
.0421774
1
8
.995198
.0542170
.0191686
2
8
.906967
.0638169
.0225627
1
8
.313957
.0250235
.0088471
2
8
.297670
.0251689
.0088985
1
8
.339455
.0098505
.0034827
2
8
.335864
.0143627
.0050780
1
8
.341811
.0176860
.0062529
2
8
.371688
.0266713
.0094297
Independent S amples T es t
Assumptions=Equal variances assumed
Levene's Test for Equality of
Variances
F
t-test for Equality of Means
Sig.
t
df
Sig. (2-tailed)
Mean
Difference
%
Interval of the
Difference
Std. Error
Difference
Lower
Upper
nasofrontal angle_s
.357
.560
-.117
14
.909
-0.438
3.743
-8.465
7.590
nasofacial angle_s
.072
.793
.347
14
.734
0.625
1.800
-3.235
4.485
nasomental angle_s
1.116
.309
-.494
14
.629
-1.500
3.038
-8.015
5.015
nasolabial angle_s
.713
.413
-1.018
14
.326
-8.063
7.919
-25.047
8.922
3.795
.396
.015
.298
.161
5.252
3.779
1.203
.248
.509
2.285
1.002
.449
6.597
.451
.020
.264
.072
.001
4.039
.305
.381
1.562
3.814
.159
.024
.830
.785
.233
.268
5.405
1.401
3.365
3.727
.703
.054
.027
.003
5.550
.004
2.706
4.647
.003
.010
.122
.003
2.108
2.878
.072
.540
.904
.594
.694
.038
.072
.291
.631
.491
.169
.334
.514
.022
.513
.891
.621
.796
.981
.064
.589
.547
.232
.071
.696
.879
.378
.392
.638
.613
.036
.256
.088
.074
.416
.820
.871
.957
.034
.948
.122
.049
.954
.922
.732
.957
.169
.112
1.667
-.533
.884
.367
-.434
1.013
.111
-.037
-.815
-1.652
-.242
.759
.215
-1.365
1.556
-1.213
-1.128
-.956
.819
-.185
1.329
-.002
-.262
-.836
.417
1.551
-.185
.017
1.375
1.380
-1.978
-2.020
-2.600
-.366
.479
1.648
-.810
-3.543
-.893
.825
.428
.549
.786
2.003
2.980
1.298
.583
-2.641
14
14
14
14
14
14
14
14
9
11
8
14
14
14
14
8
8
8
8
14
14
14
14
14
14
14
14
13
13
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
.118
.602
.391
.719
.671
.328
.913
.971
.436
.127
.815
.460
.833
.194
.142
.260
.292
.367
.437
.856
.205
.999
.797
.417
.683
.143
.856
.987
.192
.189
.068
.063
.021
.720
.640
.122
.432
.003
.387
.423
.675
.592
.445
.065
.010
.215
.569
.019
0.625
-0.134
0.020
0.005
-0.044
0.157
0.013
-0.005
-0.083
-0.113
-0.053
0.049
0.014
-0.052
0.031
-0.016
-0.013
-0.009
0.011
-0.006
0.982
-0.001
-0.368
-1.020
0.010
0.021
-0.034
0.000
0.004
0.108
-0.026
-0.067
-0.012
-0.014
0.009
0.020
-0.074
-0.018
-0.006
0.015
0.005
0.002
0.038
0.115
0.088
0.016
0.004
-0.030
0.375
0.252
0.022
0.012
0.101
0.155
0.122
0.145
0.102
0.068
0.221
0.064
0.067
0.038
0.020
0.013
0.012
0.009
0.013
0.034
0.739
0.774
1.406
1.220
0.023
0.014
0.186
0.002
0.003
0.078
0.013
0.033
0.005
0.039
0.020
0.012
0.091
0.005
0.007
0.018
0.011
0.004
0.048
0.057
0.030
0.013
0.006
0.011
-0.179
-0.675
-0.028
-0.022
-0.260
-0.175
-0.248
-0.317
-0.313
-0.262
-0.563
-0.089
-0.129
-0.134
-0.012
-0.046
-0.040
-0.030
-0.019
-0.080
-0.603
-1.661
-3.383
-3.637
-0.040
-0.008
-0.433
-0.003
-0.002
-0.060
-0.054
-0.138
-0.022
-0.098
-0.033
-0.006
-0.270
-0.029
-0.021
-0.024
-0.019
-0.006
-0.065
-0.008
0.025
-0.011
-0.010
-0.054
1.429
0.406
0.068
0.031
0.173
0.489
0.275
0.306
0.147
0.037
0.456
0.187
0.158
0.030
0.075
0.014
0.014
0.013
0.040
0.068
2.568
1.658
2.646
1.597
0.059
0.051
0.364
0.003
0.009
0.275
0.002
0.004
-0.002
0.069
0.051
0.045
0.122
-0.007
0.009
0.053
0.028
0.010
0.140
0.238
0.152
0.043
0.017
-0.006
nasion level_s
Baum Method_s
nasion height/n-sn_s
n-prn/n-sn_s
al-al ave(cast)
n-prn ave_c
n-sn ave_c
en-en ave_c
ex-en rt_c
ex-en lt ave_c
ex-ex ave_c
n-prn ave/en-en ave_c
n-sn ave/en-en ave_c
nasal index (al-al/n-prn)_c
n-prn/n-sn_c
ex-en rt/ex-ex_c
ex-en lt/ex-ex_c
al-al/ex-ex_c
en-en/ex-ex_c
al-al/en-en_c
nasion height_p
nasal tip protrusion_p
n-prn_p
n-sn_p
n-prn/n-sn_p
nasion height/n-sn_p
Baum Method_p
prn Gaussian curvature
average min curvature
al-al/ex-en ave_f
ex-en ave/mideye_f
ex-en ave/en-en_f
ex-en ave/ex-ex_f
al-al/en-en_f
al-al/mideye_f
en-en/ex-ex_f
ex-ex/mideye_f
ex-enrt/ex-ex_f
ex-enlt/ex-ex_f
al-al/ex-ex_f
ps-pi ave/mid3rd_f
ps-pi ave/tr-gn_f
top3rd/middle3rd_f
top3rd/bottom3rd_f
middle3rd/bottom3rd_f
top3rd/tr-gn_f
middle3rd/tr-gn_f
bottom 3rd/tr-gn_f