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Analysis of Covariance - ANCOVA Cheat Sheet (DRAFT) by

ANCOVA Assumptions, Theory, Test Design and Analysis

This is a draft cheat sheet. It is a work in progress and is not finished yet.

When to use ANCOVA in place of ANOVA

To reduce within­-group error variance
Elimin­ation of confounds
Reducing SSresidual through covariates
Variables known to influence DV (and not IV)

ASSUMP­TIONS

Additivity and Linearity
 
Is the relati­onship linear?
Normally Distri­buted Sampling Distri­bution of Means
S-W and K-S tests
Q-Q plots and histograms
Homoge­neity of Variance
Levene's Test
Indepe­ndence of scores
 
Are the groups indepe­ndent?
No Univariate Outliers
Tested with Z-score conversion
Above or below +/- 3.29 (Field, 2013)
Indepe­ndence of Covariate (CV) and Treatment Effect
Tested using ANOVA or t-test for Covariate and Treatment
CV should not share variance with treatment IV
Homoge­neity of Regression Slopes
Tested using custom model, including intera­ction for CV and DV
Does the relati­onship CV and outcome apply to all treatment groups
 

Effect Size

Partial Eta Squared
= SSeffect/ (SSeffect + SSresidual)
= variance explained/ (variance explained + error variance)
Eta Squared uses SStotal in place of (SSeffect + SSresidual). Partial eta squared removes the variance explained by the covariate from SStotal

Contrasts

SPSS: Contrasts button in Univariate dialog box
Several possib­ilities

Post hoc Tests

Options button. Display Means for IV.
Tick Compare main effects
Confidence interval adjustment
Bonferroni (recom­men­ded); Sidak is conser­vative; LSD liberal (not recomm­ended).

Contrast Effect Sizes

Contrasts are effect­ively t-tests
Can calculate r
rcontrast = Square root [t2/ (t2 +df)]