ARMS Week 2

Question 1

Simple (one-way) ANOVA

Answer 1

• used to detect differences between means (groups/conditions)
• 1 categorical predictor variable (factor)
• 1 continuous dependent variable
• Omnibus test

Question 2

Factorial ANOVA

Answer 2

ANOVA with more than one factor.
- Total number of groups: a * b -> Factor A with a levels and Factor B with b levels
- >1 categorical (nominal) predictor variables (‘factors’)
- 1 continuous dependent variable (interval/ratio)

Example: with Factor A (2 levels) and Factor B (2 levels), number of groups -> 2*2 = 4

Question 3

When do we use an independent samples t-test? And when do we use an ANOVA? Why do we not use multiple t-tests instead of the ANOVA?

Answer 3

Independent samples t-test: two independent groups
ANOVA: more than two independent groups

We don’t use multiple t-tests because this leads to Type-I error inflation. ANOVA compares all group means at once.

Question 4

Analysis of variance

Answer 4

Analysis that compares between-group variation and within-group variation

Question 5

Between-group variation

Answer 5

Variance explained by group differences

Question 6

Within-group variation

Answer 6

Unexplained/residual variance. Not explained by group differences.

Question 7

ANOVA assumptions

Answer 7

• Random sample
• Observations are independent
• Dependent variable is at least interval scale
• Dependent variable is normally distributed in each group
• Homogeneity of variances (equality of within-group variances)

Question 8

How do we interpret main and interaction effects of factors A and B?

Answer 8

• Main effect A: are the means equal for all levels of A? -> if yes, there is no main effect
• Main effect B: are the means equal for all levels of B? -> if yes, there is no main effect
• Interaction effects AxB: is the effect of A the same for all levels of B (and vice versa)? -> If yes, there is no interaction effect.

Question 9

Partial eta-squared

Answer 9

Effect size. Tells us for each effect what the influence is of this factor, while controlling for other factors
Rule of thumb: small effect -> 0.01, medium effect -> 0.06, large effect -> 0.14

Question 10

Partial eta-squared

Answer 10

Effect size. Tells us for each effect what the influence is of this factor, while controlling for other factors

Question 11

Simple main effects

Answer 11

Follow-up tests after a significant interaction

Question 12

Contrast testing

Answer 12

• Evaluating specific hypotheses in a frequentist approach. You do this after the omnibus test is significant.
• If you find where the difference is and the contrast is lineair, we can test the whole hypothesis at once -> bain

Question 13

Bonferroni correction

Answer 13

A correction for the post hoc tests. Lowers the alpha (decreases power) or p level. Prevents the increase of type-I error rate.
Formula -> a= a/c and p(bf)= comparisons x p

Question 14

Type I error formula

Answer 14

Error rate = 1 - (1- a) ^c