Topic 8 - ANOVA & ANCOVA

Sphericity

indicates whether the variances and covariances across pairs of repeated measures groups are the same

Sphericity Test

Compares if the differences in co/variances differ between pairs of conditions in the repeated measures variable; can only be tested where there are more than 2 levels

Violation of Sphericity Causes

bias in the F statistic where it appears larger than it really is, increasing the risk of type 1 error

type 1 error

seeing an effect where there is none

Huynh-Feldt adjustment

Lowers the df and therefore makes it harder to find significance

Mauchley’s test

if p < .05, sphericity has been violated

variance

how much the different levels of the given IV vary

covariances

indicate the unstandardised correlations between each level

Normality

How representative the mean of the DV is to the population of interest

Floor effects

Most people score very low / zero

Ceiling effects

Most people score very high / the top score

Homogeneity of variance

Examines whether the variance within each group is the same

Levene’s test

p < .001 indicates homogeneity of variance has been violated

Square root transformation

Reduces the impacts of larger scores, therefore reducing variance. There is less adjustment for smaller scores

Sums of squares III

used when there is unequal n between groups, treats each group as independent so they arent combined when generating an error term

Effect sizes

A family of statistical indices that give a measure of the strength and magnitude of the treatment effect

Unstandardised effect example

years in school, raw test scores; used when they are meaningful on their own

Standardised effect example

Cohen’s d, beta, correlation; used if unstandardised effect is not directly interpretable, or to compare effect sizes across different units of measurement

variance accounted for example

R2, eta2, partial eta2; represent the percentage of variance accounted for by the model

adjusted variance accounted for example

adjusted R2, omega2, partial omega2

Eta2

The proportion of variance in the DV accounted for by the main effect and interaction term; ranges 0-100%

Partial eta2

Similar to eta2 but can add up across the various main effects and interactions to over 100%

Cohen’s d

Estimates the distance between means in standard deviation units – can only be calculated if there are 2 groups in the IV

covariates

variables that influence the dv but have no influence on the IV

use of covariates

reduce the variance unexplained in the DV, increasing the likelihood of finding a significant effect of the IV/s

requirements of a covariate

has a linear relationship with the DV at each level of the IV, and has a completely independent effect from the IV

error term in ANCOVA

the difference between the raw score and predicted score on the covariate based on the regression line

group means of the covariate

should be nearly identical

Homogeneity of regression slopes

display the same linear relationship between the covariate and DV should across all levels of the IV