Week 8 (ANCOVA)

Question 1

What does ANCOVA stand for

Answer 1

Analysis of Covariance

Question 2

What is an ANCOVA

Answer 2

-Type of linear model that combines the best abilities of linear regression with the best of ANOVA
-Includes one or more continuous variable (covariates) within the ANOVA
-Allows you to test differences in group means and interactions, just like ANOVA

Question 3

What is a covariate

Answer 3

-Other variables that might also influence the result
-These variables might also influence the DV are referred to as covariates in ANCOVA
-We include the covariates in the model to adjust for the influence they have on the DV

Question 4

How do covariates influence ANOVA results

Answer 4

-The error variance (F value equation) includes uncontrolled sources of variability
-Some of error variance may be caused by covariates

Question 5

F ratio equation

Answer 5

(Variance between conditions) divided by (Variance within conditions)

Question 6

Including variates to reduce error variance

Answer 6

-WITHOUT the covariate included in the analysis, it is part of the error variance (which is used to calculate F ratio)
-WITH the covariate included, error variance is reduced as variance due to the covariate is removed –> F ratio?

Question 7

Methods for controlling for covariation

Answer 7

-Random allocation: Of participants to conditions to minimise the influence
-Match participants: In different conditions to minimise the influence of covariates
-Statistically: Analysis of Covariance

Question 8

Reasons to include covariates in ANOVA

Answer 8

1. Reduces within group ‘error’ variance (the bottom half of the ratio/ unexplained variance)
2. Controls for the influence of the covariates on the DV (in other words, eliminating confounding effects from the covariates)

Question 9

Not everything can be a co-variate

Answer 9

1. Covariates should be continuous (e.g., not categorical)
2. There should be a theoretical reason for including a covariate (e.g., based on theories or previous literature)

Question 10

ANCOVA Assumptions

Answer 10

1. Linear relationship between the covariate and the DV at each level of the IV
2. Homogeneity of Regression Slopes
3. Independence of the covariate and experiment effect

Question 11

How can we test the assumption of a linear relationship between the covariate and the DV at each level of the IV

Answer 11

-Relationship can be positive or negative
-Check this by drawing scatterplots to show the relationships between the covariate and DV

Question 12

How can we test the assumption of Homogeneity of Regression Slopes

Answer 12

-Using plots
-Testing interaction between covariate and the IV
-We want regression slopes in the same direction and similar size (no interaction between IV and COV)

Question 13

What to do if homoegeneity of regression slope is violated

Answer 13

-We shouldn’t describe effect of the IV on the DV, without also including info about the COV
-You can still run the full model with the interaction, report the results in detail, and do not call it ANCOVA (instead call it GLM or regression)

Question 14

Assumption: Independence of the Covariate and the experimental treatments

Answer 14

-COV should be independent of the experimental treatments (IV)
-AKA, covariate does not differ systematically across all levels of the IV (i.e, it is not a confound)

Question 15

Ideal situation of the ANCOVA

Answer 15

The covariate shares its variance only with some of the DVs unexplained variance

Question 16

How can we test independence of covariate and experimental group

Answer 16

-Run an anova with covariate as DV with one of the IV’s, sees if IV effects covariate
-We don’t want this to be significant