repeated measures ANOVA Flashcards
F ratio
MSA Γ· MSSxA
partial omega squared
excludes the variability due to differences between subjects (MSs)
W^2 <a>= ((a-1) (FA-1) Γ· ((a-1)(FA-1) + an)</a>
what is sphericity
assumption that the variance of a differences of a pair of observation is the same across all pairs
we assume that the relationship between pairs of experimental conditions is similar
replaces the assumption of homogeneity of variance
what happens if the assumption of sphericity is not met
then compound symmetry is also violated and the omnibus F tests in one way repeated measures ANOVA tend to be inflated, leading to more false rejections of H0 (Type 1 error)
how do we partition variation in one way repeated measures anova
SST (total sum of squares)
SS(A): variation between group means (IV)
SS(S): variation between row means (subject means)
SS (AxS): variation between cell means
which quanitities in the ANOVA summary table need to be adjusted if the assumption of sphericity is not met?
degree of freedoms
we reduce df in order to create a more conservative critical valye
DF(B)= π(k-1) and DF(BS)= π(k-1)(n-1)
π (epsilon) measures the extent to which sphericity was violated
when is repeated measures ANOVA appropriate for a research question
when we have 1 independent variable with at least 3 or more level and we want to know whether there are differences in the mean scores of the dependent variable across groups/conditions
Mauchlyβs test
test for violations of sphericity
H0: variances of differences between conditions are equal
if p<.05 the assumption of sphericity is violate
π=1
sphericity holds
π<1
sphericity is violated - reduces both DF(B) and DF(BS) and gives a larger critical value for F
what are three possible ways to calculate π
greenhouse-geisser approach
huynh-feldt approach
minimum possible value π an attain β π=1/(a-1)
