Wk 8 - ANOVA 3

Question 1

What is eta square? (x1)
And how is it interpreted/what is it’s limitation? (x1)
Calculated by… (x1)

Answer 1

Tells us the magnitude of experimental effect
Tells us only about the sample, as doesn’t account for sampling error
SStreat/SStotal

Question 2

What is omega-square? (X1)
It is beneficial because… (X1)
And how is it interpreted? (X1)

Answer 2

Estimate of proportion of variance in pop that is accounted for by treatment
More conservative than eta-square, as has larger denominator - MS error is in it
Through Cohens laws

Question 3

What are the advantages of using a RM ANOVA? (x2)

Answer 3

Removes overall variability by removing effects of individual diffs
So smaller error term = bigger F = more power than independent groups

Question 4

What are the disadvantages of using a RM ANOVA? (x3)

Answer 4

Order/practice/fatigue effects etc

Question 5

How does the partitioning of variance in RM ANOVA differ from in independent groups? (x1)

Answer 5

Also need to take out individual variability (SSsubjects) before comparing treatment and error

Question 6

What SSs are used in calculating the F ration for RM ANOVA>

Answer 6

SStotal
SStreat
SSsubjects
SSerror

Question 7

Explain the structural model underlying the independent groups ANOVA (x3)

Answer 7

Each score is a sum of 3 components…
Score for person i in condition j (Xij) = mu + tau + epsilon
The population mean + treatment effect for condition j + error associated with person i in condition j

Question 8

Explain the structural model underlying the RM ANOVA (x2)

Answer 8

Score for person i in condition j (Xij) = mu + pi + tau+ epsilon
Grand mean + additional variance for ith subject (SSsubject) + additional variance of being in jth treatment (SStreat) + experimental error associated with ith subject under jth treatment (SSerror)

Question 9

How is F related to t? (x2)

Which means that (x1)

Answer 9

t is based on diffs -
diff between means/diff expected by chance
F on squared diffs -
variability between treatments/var within
So for 2 levels of IV, F = t-squared

Question 10

Cohen’s rules for effect size (to interpret omega-square) (x3)

Answer 10

Small = .01
Medium = .06
Large = .15

Question 11

Three assumptions of an independent groups ANOVA (x6)

Answer 11

Independence of observations
Homogeneity of variances in treatments: same in different groups
Populations can be assumed symmetrical
Largest variance is no more than 4 times the smallest
Sample sizes are roughly equal
Normality of scores in treatments around their mean

Question 12

What needs to be calculated in RM ANOVA, but not independent groups?

Answer 12

SSsubjects

Sum of all possible people: number of conditions person was in times (person mean - grand mean) squared

Question 13

How to calculate df in RM ANOVA, if
N = number of data points
k = number of groups
n = number of participants

Answer 13

df-treatment = k - 1
df-subjects = n - 1 
df-error = (k - 1)(n - 1)
df-total = N - 1

Question 14

What are the three assumptions of RM ANOVA?

Pretty robust, but if violated too much, do…

Answer 14

Normality
Homogeneity of variance
Homogeneity of covariance (is new): refers to the degree that scores covary between different levels of the IV)
Factorial ANOVA