Chapter 15: Repeated Measures Designs

Question 1

repeated measures ANOVA

Answer 1

IVs or DVs have all been measured using the same participants in all conditions to control for individual differences

residuals are affected by both between participant factors and within-participant factors
- model within participant variability
- apply additional assumptions that allow a simpler, flexible model to be fit

Question 2

assumption of sphericity

Answer 2

the differences between variances for each condition are approximately equal

Question 3

assessing the severity of departures from sphericity

Answer 3

Mauchly’s test
Greenhouse Geisser estimate
Huynh Feldt estimate

Question 4

Mauchly’s Test

Answer 4

a significance test that assesses the hypothesis that the variance of the differences between conditions is equal
- if it is sig, then sphericity is not met
- if it is not sig, then sphericity is met
depends on sample size, advised not to use

Question 5

Greenhouse Geisser Estimate

Answer 5

estimate of the departure from sphericity

max value is 1 (0-1.00). values below 1 indicate departures from sphericity and are used to correct the df associated with the corresponding F

too conservative, overestimates the degree to which sphericity is violated

Question 6

Huynh Feldt estimate

Answer 6

estimate of the departure from sphericity

max value is 1 (0-1.00). values below 1 indicate departures from sphericity and are used to correct the df associated with the corresponding F

not strict enough

Question 7

effect of violating sphericity

Answer 7

creates a loss of power and an F statistic that doesn’t have the distribution it’s supposed to have

complications in post hoc tests/unreliable: use Bonferroni when sphericity is violated since it is the most robust power and controls type 1 error. use Tukey’s when sphericity is not violated

Question 8

what to do when sphericity is violated?

Answer 8

1. estimate the degree of violation and adjust the degrees of freedom accordingly for the affected F-test
2. use a multilevel model
3. use multivariate test statistics

Question 9

adjusting the df of any F affected

Answer 9

when you have sphericity: df doesnt change since you multiply by 1
when you dont have sphericity: df gets smaller since you multiply by less than 1
a greater violation of sphericity means a smaller estimate, smaller df. a smaller df = less sig pvalue associated w/ F

by adjusting df, F becomes more conservative, type 1 error is controlled

adjust using the GG of HF estimate
GG> 0.75: correction too conservative, use HF
GG< 0.75: nothing known about sphericity, use GG correction

Question 10

Partitioned variance for repeated measures

Answer 10

SSt (total variability) = SSb (between group variation) + SSw (within participant variation)

SSw = SSm (variation accounted for by model) + SSr (residual variance not explained by the model)

Question 11

Assumptions

Answer 11

1. additivity/linearity
2. normality
3. sphericity
4. independence