Factorial repeated-measures ANOVA The data will be arranged in a manner similar to a one-factor repeated-measures design: one subject per row and one column per observation. However, for multi-factor designs, each column represents a combination of conditions, and you should (but don't have to) organize columns systematically, like this (where the as are for one factor and its levels and the bs for another factor and its levels): a1b1 a1b2 a1b3 a2b1 a2b2 a2b3 a3b1 a3b2 a3b3 This will help when you execute the ANOVA. Notice that the a factor changes "slowly" from column to column and the b factor changes "rapidly". Knowing which factors change quickly and slowly can help execute the ANOVA. An example appears below. This is from a design in which subjects see faces of three types (normal/original; with the eyes and mouth upside-down; or negative versions, as in photographic film) and in three orientations (upright/0 degrees; sideways/90 degrees; or flipped/180 degrees): To carry out the ANOVA, follow these commands (which are illustrated in part at right): click on Analyze > General Linear Model > Repeated Measures name both of within-subjects factors and enter the number of levels of each factor; I recommend naming the slow-changing factor first (although this isn't required); then Define them move the variable names to the Within-Subjects Variables box; order matters, which is why SPSS provides the indices in parentheses; make sure the levels of the different factors match up with the indices! click on Plots, Options, etc., for descriptive statistics and other good stuff, then click OK Exercise #1 Perform the omnibus ANOVA on the SAB.sav data and put the Test of Within-Subjects Effects table into an email or a Word document to send my way ([email protected]). Mixed-factor ANOVA The data will be arranged in a manner similar to a one-factor RM design: one subject per row and one column per observation. However, in addition to variables for each level of the repeated-measures factor(s), there must be a column for each between-subjects factor to identify which level of this factor the subject is nested within. An example of the layout of a two-factor (one between, one within) design appears at left below. And the analysis, which proceeds via Analyze > GLM > Repeated Measures > Define, name factor, Number of Levels, Add > Define, should end up looking like the image at right below, just before clicking OK (and maybe you should consider adding plots or asking for descriptive statistics and effect-sizes, too). The output looks like that at below right. Tests of Withi n-Subjects Effects Measure: MEASUR E_1 Exercise #2 Open the mixed-factor.sav file and delete day3. Now carry out the omnibus ANOVA and put the Test of Within-Subjects Effects and the Tests of Between-Subject Effects into the email or Word document from Exercise #1. Sourc e day Sphericity Assumed Greenhouse-Geisser Huy nh-Feldt Lower-bound day * display Sphericity Assumed Greenhouse-Geisser Huy nh-Feldt Lower-bound Error(day ) Sphericity Assumed Greenhouse-Geisser Huy nh-Feldt Lower-bound Ty pe III Sum of Squares 752.889 752.889 752.889 752.889 113.778 113.778 113.778 113.778 77. 333 77. 333 77. 333 77. 333 df 2 1. 427 1. 997 1. 000 4 2. 854 3. 994 2. 000 18 12. 842 17. 973 9. 000 Mean Square 376.444 527.627 377.015 752.889 28. 444 39. 868 28. 488 56. 889 4. 296 6. 022 4. 303 8. 593 F 87. 621 87. 621 87. 621 87. 621 6. 621 6. 621 6. 621 6. 621 Sig. .000 .000 .000 .000 .002 .007 .002 .017 Tests of Between-Subjects Effects Measure: MEASURE_1 Transf ormed Variable: Av erage Sourc e Interc ept display Error Ty pe III Sum of Squares 25175. 111 270.222 56. 667 df 1 2 9 Mean Square 25175. 111 135.111 6. 296 F 3998.400 21. 459 Sig. .000 .000

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