13 - Analysis Of Variance Techniques ANOVA Flashcards
ANOVA
Analysis of variance that enables us to test for significant differences between two or more means of groups as well as to look at the interaction of 2 independent variables on the dependent variable.
ANOVA assumptions
- normality
- homogeneity of variances
- independence of errors
ANOVA reduces Type I error
Wrap up a series of t test into one ANOVA which produce a single level of significance.
ANOVA reduces Type II error
More powerful than a series of t test because it considers all samples.
F ratio
Determine the total variability.
If F = 1 two variances are similar
F=between/within group variance = (TE + ID + EE)/(ID + EE)=MSbetween/MSwithin
Degrees of freedom within group
N-k
Degrees of freedom between group
k-1
To determine which of the 2 IV differs significantly we conduct
Post hoc tests
- Bonferroni: few comparisons (similar variances)
- Tukey: samples similar in size (similar variances)
- Game-Howell or Dunnett: variances differ
Types of ANOVA
- One-way between group ANOVA
- Related measure ANOVA
- Factorial ANOVA
- ANCOVA
- Kruskal-Wallis one way non-parametric ANCOVA
- Friedman two way non-parametric ANOVA
One way between groups ANOVA
- Independent groups
- 1 IV with different categories (country influence on performance)
- Partial Eta^2 is the proportion of the DV that is related to the factor
Partial Eta^2 = between group effect / total sum of squares
Related measure ANOVA
Repeated measure when the same subject is tested 2 or more times.
Assumption of sphericity.
Ex: Mauchey’s Test of Sphericity must be non significant to conduct ANOVA
Otherwise use the Greenhouse-Geisser values in the 2nd line
Factorial ANOVA
2 IV are examined at the same time
3 hypothesis:
- there are no statistically significant mean difference between levels of A (A main effect)
- there are no statistically significant mean difference between levels of B (B main effect)
- there is no statistically significant interaction between A and B
Interaction effect
When the effect of one IV is not the same under all the conditions
Main effect
Effect of a single factor on the scores in a factorial data set
ANCOVA
Covariance
Tells you whether your group differ on a dependent variable when you have removed the effects of another variable = hold constant the effect of a confounding variable.
