3: One-Way ANOVA Flashcards
When is an ANOVA used?
When the IV has more than 2 levels.
How is an ANOVA an extension of the t-test?
F = t^2
Why do we use ANOVAs?
Reduces the rate of type I error.
Familywise error rate
The probability that at least one in a ‘family’ of comparisons will result in type I error.
How do we calculate familywise error?
a’ = 1 - (1 - a)^c. (1 - a) = Level of confidence. c = Number of comparisons.
Assumptions of ANOVA
Normality, homogeneity of variance, sample size, independence of observations.
What are Levene’s and Welch’s?
Levene’s tests for homogeneity of variance, Welch’s F corrects for this.
Variance between IV levels
Treatment effects, individual differences, and experimental error (random/constant).
Variance within IV levels
Individual differences and experimental error (random).
Model Sum of Squares (SSM)
Sum of squared differences between individual values and the grand mean - between IV level variance.
Residual Sum of Squares (SSR)
Sum of squared differences between individual values and corresponding IV level mean - within IV level variance.
How is SST calculated?
SSM + SSR
dfM =
k (number of IV levels) - 1
dfR =
N (total sample size) - k (number of IV levels)
Model Mean Square (MSM)
SSM
____
dfM
Residual Mean Square (MSR)
SSR
____
dfR
How can F be calculated?
F = MSM / MSR
Which post-hoc test is classed as ‘very conservative’?
Bonferroni (very low type I error risk, very high type II error risk).
Which post-hoc test is classed as ‘liberal’?
LSD (high type I error risk, low type II error risk).
Which post-hoc test is classed as ‘reasonably conservative’?
Tukey HSD (low type I error risk, high type II error risk).
Partial eta-squared
How much variance in the DV can be explained by manipulation of the IV overall.
What is a small partial eta-squared score?
< .01
What is a medium partial eta-squared score?
.01 - .06
What is a large partial eta-squared score?
> .14
How is partial eta-squared calculated?
SSM / (SSM + SSR)
