By Hui Bian Office for Faculty Excellence 1  One-way ANOVA with SPSS  Two-way Factorial ANOVA with SPSS  How to interpret SPSS outputs  How to report results 2  We use 2009 Youth Risk Behavior Surveillance System (YRBSS, CDC) as an example.  YRBSS monitors priority health-risk behaviors and the prevalence of obesity and asthma among youth and young adults.  The target population is high school students  Multiple health behaviors include drinking, smoking, exercise, eating habits, etc. 3  ANOVA means Analysis of Variance  ANOVA: compare means of two or more levels of the independent variable  One independent variable  One dependent variable  The basic test uses F distribution  Comparing means is a special case of a regression analysis 4  The partitioning of the total sum of squares of deviations Total sum of Squares of deviations of DV Independent variable 1 Independent variable 2 Independent variable 3 Error 5  Research design  Between-subjects design*: different individuals are assigned to different groups (level of independent variable).  Within-subjects design: all the participants are exposed to several conditions. * This presentation only focuses on between-subject design. 6  Data considerations  Independent variable (factor variable) is categorical.  Dependent variable should be quantitative (interval level of measurement).  Assumptions  Independent: each group is an independent random sample from a normal population.  Normality: analysis of variance is robust to departures from normality, although the data should be symmetric.  Homogeneity: the groups should come from populations with equal variances. 7  Example:  Research design: between-subjects design  Research question: Is there a difference in sedentary behavior across four grade levels?  One independent variable: Grade with 4 levels: 9th, 10th, 11th, and 12th grade (Q3r).  One dependent variable: sedentary behavior (Q81: How many hours watch TV)  Higher score of Q81 = More hours on watching TV. 8  Running a one-way between-subjects ANOVA with SPSS.  Select Analyze General Linear Model Univariate  Move Q81  Move Q3r  Click Post Hoc 9  Post Hoc Comparisons  This analyses assess mean differences between all      combinations of pairs of groups (6 comparions) If the F ratios for the independent variable is significant To determine which groups differ from which It is a follow-up analysis Check Tukey checkbox Click Continue 10  Options In the Display box: check •Descriptive statistics •Estimate of effect size •Homogeneity test Click Continue Then click OK 11  SPSS output 12  SPSS output The Leven’s test is about equal variance. p = .48, means homogeneous variances across four groups. 13  SPSS output There was a significant difference across four grades in Q81, Q3r accounting for 1% of the total variance in Q81. 14  SPSS output 15  Results The one-way ANOVA test showed there was a statistically significant difference across grade levels in sedentary behavior, F (3, 15709) = 26.86, p <.01, partial η2 = .01. A Tukey HSD test indicated that 9th (M = 3.91, SD = 1.76) and 10th (M = 3.83, SD= 1.76) graders spent more time on watching TV on average school day than 11th (M = 3.65, SD = 1.71)and 12th (M = 3.61, SD = 1.71) graders did (p < .01). 16  Two-way between-subjects ANOVA  A factorial combination of two independent variables  Two main effects: comparing the means of the various levels of an independent variable. Each independent variable has its own main effect.  One interaction effect: reflects the effect associated with the various combinations of two independent variables. 17  Example:  Research design: between-subjects design  Research question: Is there a different relationship between grade levels and sedentary behavior across the gender?  Two independent variables: Grade with 4 levels: 9th, 10th, 11th, and 12th grade (Q3r); Gender (Q2) with two levels: female and male.  One dependent variable: sedentary behavior (Q81) 18  SPSS output It is significant, which means violation of homogeneity of variance. 19  Select Analyze General Linear Model Univariate  Click Plots 20  SPSS output The interaction effect is significant 21  SPSS output You might need to report this table for your paper 22  SPSS output 23  Post hoc comparison  Selecting Female (use select cases), then running one- way ANOVA (Tukey as Post hoc test).  Selecting Male (use select cases), then running one-way ANOVA (Tukey as Post hoc test). 24  Post hoc test for significant interaction effect Females Males 25  Results The sedentary behavior was analyzed by means of a two-way between-subjects ANOVA test with four levels of grade and two levels of gender. All effects were statistically significant. The interaction effect, F (3, 15687) = 2.73, p < .05, partial η2 = .001, was analyzed using one-way ANOVA and Tukey HSD comparison test. 26  Results For males, 9th and 10th graders spent more time on watching TV on average school day than 11th and 12th graders did. For females, the pattern was different. There was no difference found in sedentary behavior between 10th and 12th graders. Those results, collectively, produced the significant interaction effect. 27 Meyers, L. S., Gamst, G., & Guarino, A. J. (2006). Applied multivariate research: design and interpretation. Thousand Oaks, CA: Sage Publications, Inc. 28 29