ANOVA effect size & repeated measures Flashcards
What is eta-square & omega square, & how do you interpret them?
Eta-square is based on a sample & tells us how much of the overall variability is attributable to treatment effects (ratio of SS treat relative to SS total); but doesn’t take sampling error into account so overestimates the effect; Omega square is an estimate of proportion of variance in the population that is accounted for by the treatment variable (weighted against the error & is more conservative); It’s interpreted using Cohen’s rule (small effect: .01, medium: .06, large: .15)
What are the advantages & disadvantages of using repeated measures ANOVA?
Advantages: generally more powerful than independent groups; because the same participants serve in each condition, individual differences won’t contribute to chance differences between means; results in smaller error term (larger F obt); Disadvantage: susceptible to sequencing & carryover effects (habituation, learning, fatigue, contrast, adaptation, sensitisation)
How does the partitioning of variance in repeated measures ANOVA differ from partitioning variance in independent groups ANOVA?
In independent groups we separate treatment effect (known) from total variability relative to error (unknown); in repeated measures, we take out the variability due to individual differences before comparing treatment & error
What are the assumptions of repeated measures ANOVA?
Normality; homogeneity of variance & homogeneity of covariance (degree that scores covary between different levels of IV); but violations do not have a dramatic effect on results (fairly robust)
Can you explain the structural models underlying the independent groups ANOVA & the repeated measures ANOVA?
In independent groups: score for person i in condition j = mu (population mean) + tau (treatment effect for condition j) + epsilon (error associated with person i in condition j); In repeated measures: score for person i in condition j = mu (grand mean) + pi (additional variance associated with ith subject) + tau (variance associated with jth treatment) + epsilon (experimental error associated with ith subject under jth treatment)
How is F related to t?
t = the difference between the means divided by the difference expected by chance; F = the variability between treatments divided by the variability within treatments; t is based on differences, F is based on squared differences (negative values become positive, so non-symmetrical & positively skewed)
What are the degrees of freedom used in repeated measures ANOVA?;
Which ones are used to find F crit?
df treat = k (groups) - 1; df subjects = n - 1; df error = (k - 1)(n - 1);
df treat & df error
What happens to the critical F value for our contrasts if we move from planned to post-hoc comparisons?
It increases
In a repeated measures ANOVA, the SS error can be due to what?
Experimental error
If you conducted a between groups experiment & then realised it was actually a within-groups design, what would happen to your data upon reanalysis?
F value would probably increase & degrees of freedom would decrease
What are the statistical hypotheses for repeated measures ANOVA?
Null: mew1 = mew2 = mew3, etc
Alternative: mew k /= mew k prime
What is the test statistic for repeated measures ANOVA?
F = MS treat / MS error
How do we calculate the effect size of the sample data in a between-participants design?;
How do we calculate the magnitude of the sample data in a within-participants design?
Using eta-squared: SS treatment / SS total;
Using eta-squared: SS treatment / SS total - SS subjects
How do we estimate the proportion of variability in the population that could be attributed to the treatment variable?
Using omega-squared: SS treatment - (k-1) x MS error, divided by SS total + MS error
