ANCOVA

Question 1

ANCOVA is ANOVA with ____

Answer 1

discrete IV and Continuous variable used as regressors

Covariate: a variable that cannot be experimentally manipulated and related to dependent variable

Question 2

How do we use covariate to reduce error variance

Answer 2

take away the variability in DV that is explained by the covariate CV using simple linear regression
(plot CV as x-axis, DV as y-axis and different level of IV representing different line on the graph)
use regression lines to estimate mean DV when CV is the same (grand mean)

Question 3

ANCOVA add the _____ of the regression of the date on the covariate

Answer 3

slope

Question 4

what is sources of variance (sums of Aquares) in Between subjects ANOVA and Between subjects ANCOVA

Answer 4

Between subjects ANOVA: DV score = grand mean + factor effect + Noise (indiv diff+ predict indiv diff + random error)

Between SS ANCOVA: DV score == grand mean + factor effect+ predict indiv diff + Noise (indiv diff+ random error)

Question 5

what is sources of variance (sums of Aquares) in Within subjects ANOVA and Within subjects ANCOVA

Answer 5

Between subjects ANOVA: DV score = grand mean + factor effect + indiv diff+Noise ( predict indiv diff + random error)

Between SS ANCOVA: DV score == grand mean + factor effect+ indiv diff+predict indiv diff + Noise ( random error)

Question 6

What are the advantage of ANCOVA compared to ANOVA

Answer 6

ANCOVA accounts for more variability, ‘controls for’ other variable, quantifies which subject characteristics (regressors) are important

Question 7

what are the assumptions of ANCOVA

Answer 7

1. Has the assumptions of ANOVA
   1) normality of error distributions (Absence of outliers, etc)
   2) Homogeneity of error variance
   3) Independence of ‘error term’ (each sample)
2. Has the assumptions of Covariates
   1) covariate is interval / ratio scale, or at least ordinal but central to interpretation of results
   2) covariate is independent of factors
   3) linearity of relationship between CV and DV
   4) No co-linearity between the covariates

Question 8

What are the issues with ANCOVA

Answer 8

1) precision of covariate measure: ANCOVA uses standard regression which assumes that there is no error in the measurement of the covariate: this is ok for directly measurable CVs but not good with likely psychological measures (since does not give accurate IQ or mood score)
2) Interpretation difficult when different slopes (Heterogeneous slopes), i.e. what is true at one level of CV is not true for all levels of CV

Question 9

How do we interpretate when heterogeneous slope of CV occur

Answer 9

1. Evaluate by looking at the interaction term between the covariate and the factors.
2. significant interaction between covariate and factor means interpretation is difficult. When ‘controlling for’, use the mean of the covariate, but assume the same applies across all values of the covariate
3. significant interaction does- by definition- indicate a significant effect
   the relationship between your CV and DV varies with the level of the factor