One-Way Within-Subjects ANOVA

One-Way Within-Subjects ANOVA

1. Is like a two-way ANOVA where there is a subject factor (i.e., τ) and a treatment factor (i.e., α), and the interaction between factors (i.e., τα) is assumed to be zero

2. Slight of Hand. With one score per cell in this two0way design, there is no error variation. The error we use is actually the variation in the interaction term (which we have assumed to be zero so, if not 0 then it is error)

3. ·

4. Assumptions

   • Independence
   • Normality of Distribution
   • Homogeneity of Variance
   • Compound Symmetry
     • In assuming no interaction between treatment and individuals, we are assuming that correlations between pairs of variables are homogeneous
       • The off-diagonal entries in a intercorrelation matrix should be equal
       • Mauchly's Test of Sphericity (p > .05)
         • If compound symmetry is violated, it is possible that the F test is invalid.
           • We assume the worst and adjust F to be more conservative, by adjusting df of the F test (through the use of tests)
           • Use Huynh-Feldt if violation is slight, Greenhouse-Geisser if moderate, Lower-Bound if severe

5. For Post-hoc Pairwise Comparisons Consider

   • Pairwise or Setwise
   • How many means
   • Error rate
   • Compound Symmetry, if significant use df adjustments or MANOVA and paired t-tests

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