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SPSS meets SPM All about Analysis of Variance

SPSS meets SPM All about Analysis of Variance. Introduction and definition of terms One-way between-subject ANOVA: An example One-way repeated measurement ANOVA Two-way repeated measurement ANOVA: Pooled and partitioned errors

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SPSS meets SPM All about Analysis of Variance

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  1. SPSS meets SPMAll about Analysis of Variance • Introduction and definition of terms • One-way between-subject ANOVA: An example • One-way repeated measurement ANOVA • Two-way repeated measurement ANOVA: • Pooled and partitioned errors • How to specify appropriate contrasts to test main effects • and interactions

  2. SPSS meets SPM

  3. Analysis of Variance Single Measures Repeated Measures Two-sample t-test Paired-sample-t-test ANOVA Repeated ANOVA between-subject ANOVA within-subject ANOVA F-test F-test Factors Levels K1 x K2 ANOVA Two Factors with K1 levels of one factor and K2 level of the second factor

  4. 2 x 2 repeated measurement ANOVA Two-way ANOVA 2 x 2 ANOVA Factor A Factor A Factor B Factor B Mixed Design Factor A Within-subject Factor Imaging Designs Factor B Between-subject Factor

  5. Fearful Neutral 2 x 2 repeated measurement ANOVA 2 x 2 ANOVA Factor A Factor A Factor B Main Effect B Factor B Main Effect A Interaction A X B 3 x 2 ANOVA Implicit Explicit Contrasts

  6. Grand mean Residual error One-way between-subject ANOVA An individual score is specified by Treatment effect

  7. General Principle of ANOVA FULL MODEL REDUCED MODEL Data represent a random variation around the grand mean Is the full model a significantly better model then the reduced model?

  8. Total Variation (SStotal) Treatment effect (SStreat) Error (SSerror) Partitions of Sums of Squares

  9. One-way ANOVA between subjects 1st levels betas from one voxel in amygdala • 2. • 3. • 4. • 5. ____________________________________ 4-different drug treatments (Factor A with p levels) ____________________________________ 1 2 3 4 ____________________________________ 2 3 6 5 1 4 8 5 3 3 7 5 3 5 4 3 1 0 10 2 _____________________________________ Sums(Ai) 10 15 35 20 _____________________________________ Means(Ai) 2 3 7 4 _____________________________________ One factor with p levels; i = 1…4 M subjects with n subjects per level Number of total observations = 20

  10. One way ANOVA Multiple Regression Do the drug treatment affect differently mean activation in the amygdala ? Do the drug treatments relate to the mean activation in the amygdala? ____________________________________ Drug treatment (Factor A with p levels) ____________________________________ 1 2 3 4 ____________________________________ 2 3 6 5 1 4 8 5 3 3 7 5 3 5 4 3 1 0 10 2 Dependent variable = 1st level betas extracted from the amygdala 1st level betas Drug treatments 2 1 3 3 1 3 4 3 5 0 6 8 7 4 10 5 5 5 3 2 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = X y a + b

  11. 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 One way ANOVA Multiple Regression Do the drug treatment affect differently mean activation in the amygdala ? Do the drug treatments relate to the mean activation in the amygdala? ____________________________________ Drug treatment (Factor A with p levels) ____________________________________ 1 2 3 4 ____________________________________ 2 3 6 5 1 4 8 5 3 3 7 5 3 5 4 3 1 0 10 2 Dependent variable = 1st level betas extracted from the amygdala 1st level betas Drug treatments 2 1 3 3 1 3 4 3 5 0 6 8 7 4 10 5 5 5 3 2 y x1 x2 x3 x4

  12. 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 One way ANOVA Multiple Regression Do the drug treatment affect differently mean activation in the amygdala ? Do the drug treatments relate to the mean activation in the amygdala? ____________________________________ Drug treatment (Factor A with p levels) ____________________________________ 1 2 3 4 ____________________________________ 2 3 6 5 1 4 8 5 3 3 7 5 3 5 4 3 1 0 10 2 Dependent variable = 1st level betas extracted from the amygdala 1st level betas Drug treatments 2 1 3 3 1 3 4 3 5 0 6 8 7 4 10 5 5 5 3 2 Y b1x1 b2x2 b3x3 b4x4 b0 = + + + +

  13. Multiple Regression One way ANOVA Do the drug treatment affect differently mean activation in the amygdala ? Do the drug treatments relate to the mean activation in the amygdala? ____________________________________ Teaching Methods (Factor A with p levels) ____________________________________ 1 2 3 4 ____________________________________ 2 3 6 5 1 4 8 5 3 3 7 5 3 5 4 3 1 0 10 2 Dependent variable = reading score 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 11 21 31 41 51 12 . . . . . . . . . . . . 44 54 b1 b2 b3 b4 b0 y = + *

  14. Repeated Measures Repeated ANOVA Single Measures Two-sample t-test Paired-sample-t-test ANOVA Repeated ANOVA between-subject ANOVA within-subject ANOVA F-test F-test • Assumptions • Homogeneity of Variance • Normality • Independence of observations • Assumptions • Homogeneity of Variance • Homogeneity of Correlations • Normality

  15. Grand mean Grand mean Subject effect Residual error Treatment effect (within-subject effect) Residual error One-way between-subject ANOVA One-way within-subject ANOVA An individual score is specified by An individual score is specified by Treatment effect

  16. Within subj. (SSwithin) Treatment effect (SStreat) Residual (SSres) Subj. x Treat & Error Total Variation (SStotal) Total Variation (SStotal) Partitions of Sums of Squares Between subj (SSbetween) Subject effects Treatment effect (SStreat) Error (SSerror)

  17. 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 11 21 31 41 51 12 . . . . . . . . . . . . 44 54 b1 b2 b3 b4 b0 y = + * Between Subjects Within subjects p1 p2 p3 p4 p5 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 11 21 31 41 51 12 . . . . . . . . . . . . 44 54 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 b1 b2 b3 b4 b0 y = + + *

  18. 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Between Subjects Within subjects

  19. 2 x 2 Repeated Measurement ANOVA Factor A Factor B Pooled Error Interaction between effect and subject Partitioned Error

  20. 1 2 3 4 Fear-implicit neutral-implicit fear-explicit neutral-explicit 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Within-Subjects Two-Way ANOVA

  21. Repeated Measurement ANOVA in SPM Pooled errors One way ANOVA = 1st level betas 2nd level + subjects effects Partitioned errors 2nd level (T-test for 2x2 ANOVA F-test for 3x3 ANOVA) Two way ANOVA = 1st level differential effects between levels of a factors for main effects differences of differential effects for interactions

  22. What contrast to take from 1st level? Two way ANOVA (2*2) with repeated measured Factor A Factor B

  23. What contrast to take from 1st level? Two way ANOVA (3*3) with repeated measured Factor A Factor B

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