analysis of variance (ANOVA)

analysis of variance (ANOVA)

compares three or more groups using a variance ratio approach that does NOT rely on mean differences

- tests whether at least one sample mean is different from at least one other sample mean

(H0: μ1 = μ2 = μ3; H1: not H0)

familywise error

probability of making at least one type I error when conducting multiple hypothesis tests; inflated type 1 error

variance ratio

the ratio of the between-groups and within-groups variability

F-statistic (F = MSB / MSW)

variance ratio that balances how much the sample means vary from the grand mean (MSB) with how much variability there is within groups (MSW)

- as MSB increases, F increases (increases likelihood of rejecting null hypothesis)

- as MSW increases, F decreases (decreases likelihood of rejecting H0)

mean-square between (MSB; aka between-subjects variance)

variability among the group sample means (e.g., x̅1, x̅2, x̅3)

mean-square within (MSW; aka within-subjects variance)

variability of individuals within their respective groups (e.g., SS1, SS2, SS3)

partitioning of the variance

take the overall availability of all the scores and separate out pieces related to between- and within-subject variability

- done for both SS (SSTotal = SSB + SSW) and df (dfTotal = dfB + dfW)

ω2 (effect size for ANOVA)

proportion on variability in the dependent variability explained by the independent variable

- ω2 = .01 is small

- ω2 = .06 is medium

- ω2 = .14 is large