L14: Repeated Measures 2 and Effect Size

Sphericity: Repeated Measures Assumption

• The assumption that the differences between conditions is more or less the same

• About differences between the conditions, not the scores within the conditions

• Within-subjects factor must have at least three levels (for two comparisons)

What test is used to test the assumption: the variances of the differences between all possible levels of the within-subject variable must be equal

Mauchly’s test

What does it mean if Mauchly’s Test of Sphericity is significant in SPSS

The assumption of sphericity has NOT been met

What happens if calculation violates sphericity assumptions

Corrections have to be applied called Epsilon (Greenhouse-Geisser)

• Make correction by multiplying Epsilon by the df

• If sphericity assumption ISN’T violated use top line (Sphericity Assumed), if it IS then use second line (Greenhouse-Geisser)

How do you pick which study to use taking into account the F value and p value

DONT because the F value and p value are sensitive to samples

• The bigger the sample, the bigger the F, the lower the p value

Why is the p value sensitive to samples

Giving a yes or no answer, yes there is a difference between my groups but not saying about how much you are impacting Ps by using this specific treatment

• Not saying how much my IV is affecting my P’s

What can F not be used for as it is sample size dependent

CANNOT use F to compare effects across different studies

What do you have to use to know the impact your IV has on P’s (i.e. which is the best therapy treatment intervention)

Have to use the effect size

Understanding Effect Size

• Studies with different sample sizes but the same characteristics (distributions, means, SDs)

  • Will differ in their F statistics and statistical significance values BUT not in their effect size estimates

• Effect size indicates the strength of an effect

  • Magnitude of our experimental effect

  • Strength of association between two or more variables

What is practical significance of out study

Effect size (statistical significance is another thing entirely)

How to calculate effect size for ANOVA

Effect size = SS(effect) / SS(total)

Eta-squared ANOVA

n² = SS(effect) / SS(total)

• Varies between 0 and 1

• n² = 0: No variability explained (all means EQUAL)

• n² = 1: All variability explained (no error)

Problems with Eta-Squared (why we use Partial n²)

• Values for an effect are dependent on the number of other factors in the ANOVA and the magnitude of those other effects

  • THEREFORE effect sizes for an IV are always smaller in a multifactorial situation than in a single factor situation because the denominator is bigger

How does partial n² differ from n²

Because the variability associated with all other effects identified in the analysis is removed from consideration (only IV of interest considered)