How does multifactorial ANOVA differ with within-participant factors?

How does multifactorial ANOVA differ with within-participant factors?



Same asssumptions as for between-subjects ANOVA, plus assumption of sphericty (ONLY IF MORE THAN TWO CONDITIONS FOR A WITHIN-SUBJECTS IV)

Constant source of error due to having same participants in different conditions is subtracted from the error variance, as a result reducing the error term ("partialling out"; we do this because one assumption of the statistical tests (not earlier covered) is that the data from each condition should be independent of all other conditions.

In order to do this, the consistent effects of participants across all conditions (e.g. those who tend to perform well will do so over all conditions) are removed statistically, so that the conditions will effectively be independent of each other and analysis can continue

Extra table: "Within Subjects Effects": because same participants in each condition, we are able to calculate the degree of error associated with each effect (main/interaction)
, whereas in the completely between-participants analysis we are able to calculate only the overall amount of error. Can test each main effect and interaction against its own error term.

In a within-participants design, ANOVA analyses each main effect as if it were a one-way ANOVA. Calculates overall amount of variability associated with the main effect (including all sources of variance, including error.) ANOVA then subtracts from this overall variance the amount of variability that can be attributed to the main effect, and the amount of variability that can be attributed to the constant effect of participants.
The error term= the remaining variability; the variance that is unaccounted for.

For follow up testing: WITHIN participants; use RELATED T-tests rather than independent T tests

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