Archive:ANCOVA

File:Wikademia.logo.png Resource type: this resource contains a tutorial or tutorial notes. Template:0%done This tutorial teaches use of analysis of covariance (ANCOVA) techniques, with practical exercises based on using SPSS.

Overview

• An ANCOVA evaluates whether population means on the DV, adjusted for differences on the covariate(s) (or 'nuisance variables'), differ across the levels of the IVs. Thus, the question being tested is whether the adjusted group means vary significantly from each other?
• ANCOVA is exactly like ANOVA, except the effects of a third variable are statistically “controlled out”.

Covariates

• Typically included in an experimental design to remove extraneous influences from the DV, thus decreasing the within-group variance
• Including covariates is appropriate in order to:
  1. Eliminate some systematic variance outside the control of the researcher that can bias the results.
  2. Account for differences in response due to unique characteristics of the respondents.

  This is usually achieved in experimental designs by random assignment to groups, however, in quasi-experimental designs problems related to non-random assignment can be minimised by statistically controlling for the effects of covariates.

Example

If you are interested in testing the effect of computer experience on the attitude towards use of internet shopping, and you suspect that those with more positive attitudes toward shopping in general are more likely to have positive attitudes towards internet shopping, you may include attitude toward shopping as a covariate so as to remove its influence from the attitude towards internet shopping measure.

Assumptions

Assumptions to be met are those for ANOVA, plus:

1. Covariates must be linearly related to the DV. The stronger the correlation, the more useful the CV will be. If there is no correlation, then the inclusion of the CV will have no effect.
2. Covariates must have a homogeneity of regression (or homogeneity of slopes) effect (equal effects on the DV across the IV groups) - if there is a significant interaction between the covariate and the factor – you cannot use this procedure.
3. The covariate should be unrelated to the IV.

The first two criteria can be checked via a scatterplot of the DV and the CV, with the IV as control variable (to check for equal slopes)

The third criteria depends on experimental design, e.g., if the CV is measured prior to the IV, then it cannot be affected by the IV.

Example write-up

A one-way analysis of covariance (ANCOVA) was conducted. The independent variable, vitamin C, involved three levels: placebo, low dose, and high dose. The dependent variable was the number of days with cold symptoms during treatment and the covariate was the number of days with cold symptoms before treatment. The assumptions for ANCOVA were met. In particular, the homogeneity of the regression effect was evident for the covariate, and the covariate was linearly related to the dependent measure.

The ANCOVA was significant, F (2,26) = 6.45, p = .005. The strength of the relationship between vitamin C treatment and the dependent variable was very strong, as assessed by <math>\eta</math><math>_p^2</math>, with the vitamin C factor accounting for 33 percent of the variance in dependent measure holding constant the number of days with pretreatment cold symptoms. The mean number of days with cold symptoms adjusted for initial differences were ordered as expected across the three vitamin C groups. The placebo group had the largest adjusted mean (M = 12.01), the low dose vitamin C group had a smaller adjusted mean (M = 7.71) and the high dose vitamin C group had the smallest adjusted mean (M = 6.67). Follow-up tests were conducted to evaluate pairwise differences among the adjusted means. The Holm’s sequential Bonferroni procedure was used to control for Type I error across the three pairwise comparisons. There were significant differences in the adjusted means between both groups that received vitamin C and the placebo, but no significant difference between the two vitamin C groups.

Francis exercise

In a hypothetical educational psychology experiment, participants were randomly divided into two groups. One group was taught conventionally, and the other were taught using an innovative method. Prior to allocation to the groups, learning motivation was assessed. Improvements in academic achievement were measured as the DV.

• Motiv.sav (p. 129; Section 5.2)
  • Achievement (achieve) (DV)
  • Teaching Method (teach) (IV)
  • Motivation (motiv) (CV)

See also

• ANCOVA (Wikipedia)

External links

• ANCOVA (ucspace)
  • ANCOVA Notes (Handout)