Two-way within-subjects ANOVA

Question 1

when is 2-way w-s anova used?

Answer 1

repeated measures design
used to increases statistical power

Question 2

SPSS outputs

Answer 2

• within-subjects factors (levels of factors)
• descriptive stats (means and SD)
• Mauchly’s test of sphericity (factors with only 2 levels - sphericity not calculated)
• tests of within-subjects effects (main effects in ‘sphericity assumed row’)
• estimated marginal means for factor A
• estimated marginal means for factor B
• profile plots (graph of the interaction)

Question 3

interpreting the ANOVA table

Answer 3

• tests of within-subjects effects displays stats needed to report main effects
• each main effect and interaction is tested against its own error term

Question 4

interpreting estimated marginal means

Answer 4

estimates table

shows means

Question 5

formally reporting ANOVA

Answer 5

• state anova type, effect of factor on DV
• present means and SD in table or text
• mention assumptions
• report ANOVA results giving df, f ratio and p value
• report effect size and what it means (for all effects/interactions)
• report comparisons

interpret

Question 6

what to do if the main effect is significant and there was a specified hypothesis being tested

Answer 6

planned comparisons; paired samples t-test/planned contrasts

Question 7

what to do if the main effect is significant and there was no specified hypothesis being tested

Answer 7

run unplanned comparisons; Bonferroni post-hoc tests

Question 8

what to do if the main effect is not significant and there was a specified hypothesis being tested

Answer 8

planned comparisons; paired samples t-tests/planned comparisons

Question 9

what to do if the main effect is not significant and there was no specified hypothesis being tested

Answer 9

no further action

Question 10

when are planned comparisons run?

Answer 10

either…

when the main effect is significant and there was a specified hypothesis

or

when the main effect is not significant and there was a specified hypothesis

Question 11

when are unplanned comparisons run?

Answer 11

when the main effect is significant but there was no specified hypothesis being tested