Psychophysics
心理物理学
Psychophysik Fechner (1860)
Psychophysics
物理刺激
環境
心
物理量
明るい
暗い
きれい
面白い
主観量
Psychophysics
Baird & Noma (1978), p.13, Figure 2.1
1
Psychophysics
Ernst H. Weber
1834
Psychophysics
Gustav Theodor Fechner
1860 “Element der Psychophysik”
2
Psychophysics
Stanley Smith (S. S.) Stevens
Psychophysics
Baird & Noma (1978)
“Psychophysics is commonly defined as the quantitative
branch of the study of perception, examining the relations
between observed stimuli and responses and the reasons for
those relations. This is, however, a very narrow view of the
influence it has had on much of psychology. Since its
inception, psychophysics has been based on the assumption
that the human perceptual system is a measuring instrument
yielding results (experiences, judgments, responses) that may
be systematically analyzed. Because of its long history (over
140 years), its experimental methods, data analyses, and
models of underlying perceptual and cognitive processes
have reached a high level of refinement. For this reason,
many techniques originally developed in psychophysics have
been used to unravel problems in learning, memory, attitude
measurement, and social psychology. In addition, scaling and
measurement theory have adapted these methods and
models to analyze decision making in contexts entirely
divorced from perception”
3
Psychophysics
Macmillan & Creelman (1991)
“Detection theory is a general psychophysical approach
to measuring performance. Its scope includes the
everyday experimentation of many psychologists, social
and medical scientists, and students of decision
processes.”
Green & Swets (1974)
“The (signal detection) theory provides a means of
analyzing the essential structure of the observer’s
decisions in psychophysical tasks ... suggestions for
appropriate procedure for data collection and analysis.”
Psychophysics
心理物理学的測定法
感覚尺度構成法（sensory scaling）
感覚能力の測定
実験課題
検出（detection）
弁別（discrimination）
同定（identification）
尺度化（scaling）
4
Psychophysics
閾（threshold）
• 絶対閾（absolute threshold）*
＊検出閾（detection threshold）
• 弁別閾（discrimination threshold）#
# 丁度可知差異（just noticeable difference, JND）
閾値測定法
1.
2.
3.
4.
調整法（method of adjustment）
極限法（method of limit）
恒常法（method of constant stimuli）
上下法（up-down method）*
＊段階法（staircase method）、適応法（adaptive
method）
Psychophysics
終了時点の刺激量＝閾値
弁別では
閾値＝｜標準刺激量ー終了時点の比較刺激量｜
１
２
３
４
・・・
ｎ
１
２
３
４
・・・
ｎ
上昇系列
下降系列
5
Psychophysics
心理測定関数
心理測定関数
P(Response)
1
0.75
0.5
0.25
0
0
2
4
6
Stimulus Magnitude
Psychophysics
心理測定関数
Psychometric function
1
P(+)
0.75
0.5
0.25
0
1.7 1.8 1.9 2.0 2.1 2.2 2.3
Line length (relative)
6
Psychophysics
A) 直線補間法
Psychometric function
1
P(+)
0.75
0.5
0.25
1.97
0
1.7 1.8 1.9 2.0 2.1 2.2 2.3
Line length (relative)
Psychophysics
B) 正規補間法
累積正規曲線（ogive）
心理測定関数
0.75
ogive
0.5
確率
P(Response)
1
0.25
0
0
2
4
Stimulus Magnitude
6
-2 -1 0 1 2
z値
7
Psychophysics
z変換と補正
長さ
"+"反応率
1.7
0.048
-1.66839
1.8
0.095
-1.30917
1.9
0.286
-0.56596
2.0
0.571
0.180016
2.1
0.810
0.876129
2.2
0.952
1.668391
2.3
1.000
NA
z値
0→1/(2N)
1→1-1/(2N)
N: 試行数
Psychophysics
z変換と補正
長さ
"+"反応率補正反応率
z値
1.7
0.048
0.048
-1.66839
1.8
0.095
0.095
-1.30917
1.9
0.286
0.286
-0.56596
2.0
0.571
0.571
0.180016
2.1
0.810
0.810
0.876129
2.2
0.952
0.952
1.668391
2.3
1.000
0.976
1.981
8
Psychophysics
z変換と補正
Normal interpolation
2.0
Z[P(+)]
1.0
0.0
-1.0
-2.0
1.7 1.8 1.9 2.0 2.1 2.2 2.3
Line length (relative)
z[P(+) = 0.5] = 0.0
Z = −12.937 + 6.5517 × L
L(Z = 0) = 12.937 / 6.5517 = 1.97
Psychophysics
C) 関数の当てはめ
ロジスティック関数
（logistic function）
P=
1
1 + exp(− a( x − x0 ))
Logistic function
1
a = 12.275, x0 = 1.9764
P(+)
0.75
0.5
0.25
0
1.7 1.8 1.9 2.0 2.1 2.2 2.3
Line length (relative)
9
Psychophysics
1-up 1-down
刺激強度
Yes (+) 次試行の強度をdown
No (+) 次試行の強度をup
（閾値）
1
2
3
4
5
6
7
8
9
10
試行
reversal（反転）
Psychophysics
1-up 1-down：例
法
11.0
10.0
音強度（dB）
9.0
8.0
7.0
6.0
5.0
4.0
0
5
10
15
20
25
30
35
試行
10
Psychophysics
変形上下法
transformed up-down method
1-up 2-down
P(No) = P(Yes)2 = 0.5
P(Yes) = 0.707
Psychophysics
1-up 2-down
連続２回の
刺激強度
Yes (×) 次試行の強度をdown
No (×) 次試行の強度をup
閾値
1
2
3
4
5
6
7
8
9
10
試行
11
Psychophysics
1-up 2-down：例
上下法
法
11.0
10.0
音強度（dB）
9.0
8.0
Yes
7.0
No
50%閾値
71%閾値
6.0
5.0
4.0
0
5
10
15
20
25
30
35
30
35
試行
Psychophysics
二重上下法
系列変
法
11.0
10.0
音強度（dB）
9.0
8.0
7.0
下降系列
上昇系列
6.0
5.0
4.0
0
5
10
15
20
25
試行
12
Psychophysics
フォン尺度
人工環境デザインハンドブック, 2007, p.109, 図4.22
Psychophysics
ソーン尺度
L = kI0.3 k：定数
Coren, Ward, & Enns, 1994, p.233, Figure 7-10
大串, 1987, p.101, 図10.5
13
Psychophysics
Weberの法則
∆I
I
I
Falmagne, 1986, p.1-32, Figure 1.14
Psychophysics
∆I
=k
I
Weberの法則
∆Ψ = c
Fechnerの仮定
Ψn = Ψn −1 + c
log I n = log I n −1 + log k ′
Ψ=
c
× log I （Fechnerの法則）
log k ′
14
Psychophysics
8
7
6
∆Ψ = c = 1
Ψn = Ψn −1 + 1
感覚量
5
4
3
2
Ψ0 1
0
0 1 2 3 4 5 6 7 8 9 1011121314151617
I0
刺激量
I n = (k + 1)× I n −1 = 2 × I n −1
∆I
= k =1
I
Psychophysics
14
Ψ = 1.0 + 1.4427 × log I
12
感覚量
10
8
6
4
2
0
0
50
100
150
200
250
300
刺激量
15
Psychophysics
14
1
× log I
log 2
= 1.0 + 1.4427 × log I
12
Ψ = 1 .0 +
Ψn = Ψn −1 + 1
感覚量
10
8
6
4
1
2
0
log(2)
0
1
2
3
4
5
6
log(刺激量)
I n = (k + 1)× I n −1 = 2 × I n −1
log I n = log 2 + log I n −1
16