ANOVA

Question 1

H0 ANOVA

Answer 1

H0: m1 = m2 = ….. = mi
HA: not all group means are equal

Or:
H0: alpha j = 0

Question 2

SS partition in one way ANOVA

Answer 2

SST = SSE + SSG

SSE = within groups, unexplained part
SSG = between groups, explained part

Question 3

How is the F - test calculated in an one way ANOVA?

Answer 3

F = MSG/MSE

Question 4

Assumptions ANOVA

Answer 4

1. Independent observations
2. In each group the scores are normally distributed
3. In all groups equal variances

Question 5

How to check the assumption of normally distributed scores in ANOVA?

Answer 5

Check via QQ plot or test on skewness and kurtosis or test via kolmogorov-Smirnov

Question 6

How to check the assumption of equal variances in ANOVA

Answer 6

Rule of thumb: largest SD

Question 7

3 characteristics of experiments

Answer 7

• random assignment
• manipulation
• control of extraneous variables

Question 8

What is the difference between a p-value and an effect size?

Answer 8

P value: measures the significance of a factor

Effect size: measures the size of the difference

Question 9

Why is an equal number of subjects per cell preferred?

Answer 9

Then the sum of squares of effects and interactions are orthogonal. Effects are completely separated and tests are independent

Question 10

In case of unequal number of subjects per cell, which ways are there to decompose effects?

Answer 10

1. Regression approach: adjust each effect for all other effects to obtain its unique contribution (type III SS)
2. Experimental method: estimate the main effects ignoring the interaction, estimate the interaction adjusting for the main effects (type II SS)
3. Hierarchical approach: use a theoretically based order in decomposing the effects (type I SS)

Question 11

Purpose of an one way ANOVA

Answer 11

Comparison of group means (independent populations)

Question 12

When is it possible to use a t test?

Answer 12

When you have two groups in the independent variable and one dependent variable

Question 13

H0 and Ha t test

Answer 13

H0: m1 = m2
Ha: m1 is not equal to m2

Question 14

Assumptions t test

Answer 14

• independent observations
• homoscedasticity(equal variances)
• normality
• no measurement error

Question 15

What to do when the assumption of independent observations is violated?

Answer 15

Choose a model that accounts for dependency: multilevel modeling or RM-ANOVA

Question 16

How to calculate degrees of freedom in an one way ANOVA?

Answer 16

DFG = i - 1
DFE = n - i
DFT = n - 1

Question 17

Name the standard contrasts

Answer 17

Simple = compare all group means with the group mean of the reference group
Deviation = compare all group means with the overall mean
Helmert = compare all group means with all the following group means 
Difference = compare every group mean with all group means before
Repeated = compare every group mean with the next

Question 18

What is multicollinearity?

Answer 18

Correlation between multiple independent variables in a factorial ANOVA.
VIF = 1 / (1 - R2j)
VIF > 4 -> problem

Question 19

3 types of SS

Answer 19

Type 1: hierarchical analysis, correlational design
Type II: experimental designs without an interaction
Type III: regression approach

Question 20

How to calculate DF in factorial ANOVA?

Answer 20

DFA = i - 1
DFB = j - 1
DFAB = (i - 1) x (j - 1)
DFE = n - (i x j) 
DFT = n - 1

Question 21

Reasons to include a blocking variable

Answer 21

• to reduce error variance

- to eliminate systematic bias

Question 22

What is an blocking variable?

Answer 22

By adding a categorical variable, you can control for this variable