Report

By Hui Bian Office for Faculty Excellence 1 Repeated measures ANOVA with SPSS One-way within-subjects ANOVA with SPSS One between and one within mixed design with SPSS Repeated measures MANOVA with SPSS How to interpret SPSS outputs How to report results 2 When the same measurement is made several times on each subject or case, such as Same group of people are pretested and post-tested on a dependent variable. Comparing the same subjects under several different treatments. Interested in the performance trends over time: is it linear, quadratic, or cubic? 3 Between and within factors Between factors: a grouping or classification variables such as sex, age, grade levels, treatment conditions etc. Within factors: is the one with multiple measures from a group of people such as time. 4 Assumptions Independence of the observations Violation is serious Multivariate normality Fairly robust against violation Sphericity Not necessary for the multivariate approach The variance-covariance matrices are the same across the cells formed by the between-subjects effects. 5 A simplest design One within-subjects factor One dependent variable A group of subjects measured at different points in time 6 Example: sample is from high school students. Research questions: 1. whether there is a significant change on frequency of drinking over time (3 months) before and after treatment; 2. whether the relationship between the within factor (time) and frequency of drinking is linear, quadratic, or cubic. Within-subjects factor: time. Dependent variable: frequency of drinking (a28 and b28). Two-time points data: a28 means baseline and b28 means 3-month posttest Two conditions: before treatment and after treatment 7 The design Conditions Subjects Before treatment After treatment 1 2 3 4 . . . n 8 Select Intervention group as our sample Go to Data Select Cases Check If conditions… Then click If 9 Let Conditions = 1 Then click Continue 10 Run Repeated Measures analysis Analyze General Linear Model Repeated Measures Type Time as Within-Subject Factor Name, type 2 as Number of Levels, then click Add Type dv1 as Measure Name (dv means dependent variable), then click Add 11 Then click Define 12 After Define you should get this window Move a28 to (1, dv1) Move b28 to (2, dv2) 13 We don’t have any between-subjects factors Click Options to get this Check Compare main effects even we have two levels for within-subjects factor. I just want to show the pair comparison function. 14 Click Plots to get this window 15 SPSS outputs Descriptive statistic results 16 SPSS outputs Within-subjects effect: results of two tables are same. 17 Correction options include Geenhouse-Geisser, Huyn-Feldt, and Lower-bound when sphericity is not assumed. They produce more conservative estimates. 18 SPSS outputs Within-subjects effect: if there is no homogeneity of dependent variable covariance matrix, the Sphericity is not assumed. We should use the correction options. 19 SPSS outputs The mathematical properties underlying the relationship between within-subjects factor and dependent variable. Test linear component of Time effect The linear component is not significant 20 SPSS outputs Plot 21 Quadratic Cubic 22 SPSS outputs Pairwise comparisons: the within-subjects factor only has two levels. So we get the same results as multivariate tests table shows. 23 Results One-way within-subjects ANOVA was performed to test whether there was a difference of frequency of drinking between before-treatment and after-treatment conditions. The observed F value was not statistically significant, F(1, 136) = .42, p = .52, partial η2 = .003, which indicated no difference of frequency of drinking over time. 24 Two-way mixed design Two independent factors: one is a between-subjects factor and one is a within-subjects factor One dependent variable. Tests null hypotheses about the effects of both the between-subjects factor and within-subjects factor. Tests the effect of interactions between factors. 25 Example: Research questions: whether there is a significant change on frequency of drinking over time (3 months) between intervention and control group. Within-subjects factor: time. Between-subjects factor: conditions (intervention vs. control). Dependent variable: frequency of drinking (a28 and b28). Two-time points data: a28 means baseline and b28 means 3-month posttest 26 The design Conditions Intervention Subjects Time 1 Time 2 Control Time 1 Time 2 1 2 3 4 . . . n 27 Run repeated measures analysis Select all cases Go to Analyze General Linear Model Repeated Measures The same procedure to define the within-subjects factor and dependent variable. Move Conditions to… 28 Click Options Click Plots 29 SPSS outputs Multivariate tests 30 SPSS outputs Estimated marginal means 31 SPSS outputs Plots 32 Results The intervention effect was analyzed using repeated measures ANOVA. There was no statically significant difference between intervention and control group over time on frequency of drinking, F(1,285) = .90, p = .34, partial η2 = .003. 33 Example Research questions: whether there is a significant change on drinking behaviors over time (3 months) between intervention and control groups; or whether there is an intervention effect on drinking behaviors. Within-subjects factor: time. Between-subjects factor: conditions (two levels) Dependent variables: frequency of drinking (a28 and b28), quantity of drinking (a31 and b31), and heavy drinking (a34 and b34). Two-time points data: baseline and posttest 34 Run repeated measures analysis Go to Analyze General Linear Model Repeated Measures We have three dependent variables Still one within-subjects factor Click Define 35 Move a28/b28, a31/b31, and a34/b34 to… 36 Options and Plots 37 SPSS outputs Multivariate tests 38 SPSS outputs Within-subjects effects 39 SPSS outputs Univariate tests 40 SPSS outputs Estimated marginal means 41 SPSS outputs Plots: dv1 (frequency of drinking) 42 SPSS outputs Plots: dv2 (quantity of drinking) 43 SPSS outputs Plots: dv3 (heavy drinking) 44 Results Repeated measures MANOVA test was conducted to test intervention effect on drinking behaviors. The results showed there was no difference between intervention and control group on frequency, quantity, and heavy drinking over time, F(3, 283) = 1.18, p = .32, η2 = .01. Univariate tests also indicated there was no intervention effect on individual drinking behavior, F(1, 285) = .90, p = .34, η2 = .003 for frequency, F(1, 285) = .67, p = .41, η2 = .002 for quantity, and F(1, 285) = .39, p = .53, η2 = .001 for heavy drinking. 45 Example (planned comparisons) One within-subjects factor: time One between-subjects factor: living condition (11r) One dependent variable: frequency of drinking (a28 and b28) 46 Contrasts are used to test for differences among the levels of a between-subjects factor. Go to Analyze General Linear Model Repeated Measures The same procedure to define within-subjects factor and dependent variable Click Contrasts 47 You should get the left window Choose Simple (simple means compares the mean of each level to the mean of a reference). Pull down 48 Decide which category of between-subjects factor is a reference category. The between-subjects factor is a11r: 1= Mother and father; 2 = Mother and stepfather; 3 = Mother; 4 = Others. Use 1 = Mother and father as a reference. Check First, then click Change 49 SPSS outputs 50 Meyers, L. S., Gamst, G., & Guarino, A. J. (2006). Applied multivariate research: design and interpretation. Thousand Oaks, CA: Sage Publications, Inc. Stevens, J. P. (2002). Applied multivariate statistics for the social sciences. Mahwah, NJ: Lawrence Erlbaum Associates, Inc. 51 52