ANOVA Flashcards
H0 ANOVA
H0: m1 = m2 = ….. = mi
HA: not all group means are equal
Or:
H0: alpha j = 0
SS partition in one way ANOVA
SST = SSE + SSG
SSE = within groups, unexplained part SSG = between groups, explained part
How is the F - test calculated in an one way ANOVA?
F = MSG/MSE
Assumptions ANOVA
- Independent observations
- In each group the scores are normally distributed
- In all groups equal variances
How to check the assumption of normally distributed scores in ANOVA?
Check via QQ plot or test on skewness and kurtosis or test via kolmogorov-Smirnov
How to check the assumption of equal variances in ANOVA
Rule of thumb: largest SD
3 characteristics of experiments
- random assignment
- manipulation
- control of extraneous variables
What is the difference between a p-value and an effect size?
P value: measures the significance of a factor
Effect size: measures the size of the difference
Why is an equal number of subjects per cell preferred?
Then the sum of squares of effects and interactions are orthogonal. Effects are completely separated and tests are independent
In case of unequal number of subjects per cell, which ways are there to decompose effects?
- Regression approach: adjust each effect for all other effects to obtain its unique contribution (type III SS)
- Experimental method: estimate the main effects ignoring the interaction, estimate the interaction adjusting for the main effects (type II SS)
- Hierarchical approach: use a theoretically based order in decomposing the effects (type I SS)
Purpose of an one way ANOVA
Comparison of group means (independent populations)
When is it possible to use a t test?
When you have two groups in the independent variable and one dependent variable
H0 and Ha t test
H0: m1 = m2
Ha: m1 is not equal to m2
Assumptions t test
- independent observations
- homoscedasticity(equal variances)
- normality
- no measurement error
What to do when the assumption of independent observations is violated?
Choose a model that accounts for dependency: multilevel modeling or RM-ANOVA
How to calculate degrees of freedom in an one way ANOVA?
DFG = i - 1 DFE = n - i DFT = n - 1
Name the standard contrasts
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
What is multicollinearity?
Correlation between multiple independent variables in a factorial ANOVA.
VIF = 1 / (1 - R2j)
VIF > 4 -> problem
3 types of SS
Type 1: hierarchical analysis, correlational design
Type II: experimental designs without an interaction
Type III: regression approach
How to calculate DF in factorial ANOVA?
DFA = i - 1 DFB = j - 1 DFAB = (i - 1) x (j - 1) DFE = n - (i x j) DFT = n - 1
Reasons to include a blocking variable
- to reduce error variance
- to eliminate systematic bias
What is an blocking variable?
By adding a categorical variable, you can control for this variable
