Analysis of covariance (groups at the same value of a control variable)

In brief

What for: The groups are compared while the influence of a number as a control variable (covariate) is removed. Typical: the post-test by teaching method, controlled for prior knowledge before the intervention. Statable shows adjusted means, the group means at the mean of the covariate. The control variable is chosen in the question "Do groups differ?" under "More options".

Requirements

• The covariate must not be influenced by the group. It is measured before the intervention, for example prior knowledge. Otherwise the analysis removes part of the effect of the group. Statable cannot check this.
• The covariate is linearly related to the outcome, and equally strongly in all groups (equal slopes). Statable reports a test for this.
• The outcome is a number; the observations are independent; each group has at least two people.

How to read the result

• First the test of the slopes (group × covariate). If it is significant (p < .05): "The covariate acts differently in the groups. The adjusted means can then be interpreted only to a limited extent."
• The group test (Type III) says whether the groups differ at the same value of the covariate; with ηp² and a 95% confidence interval.
• The adjusted means are shown with 95% confidence intervals next to the raw means. From three groups on, pairwise comparisons of the adjusted means follow, with Holm adjustment.
• The test of the covariate shows whether it explains anything beside the group; b is the common slope.

How to report

Group: F(2, 68) = 4.56, p = .014, ηp² = .12, 95% CI [.01, .26]; prior knowledge: F(1, 68) = 33.02, p < .001, ηp² = .33, 95% CI [.16, .48]; slopes (group × covariate): F(2, 66) = 0.45, p = .641

In the text, state at which value of the covariate the means are adjusted (the mean of all people) and report the result of the slopes test.

Limits

• One control variable. Statable does not calculate two groupings together with a control variable; a message appears instead of a result.
• Unequal slopes or a curved relationship make the adjusted means only partly interpretable. Statable does not switch the model by itself then.
• If the groups were not assigned at random, the analysis of covariance only evens out differences in the covariate, not in other characteristics.
• PSPP has no covariate in GLM; Statable runs four regressions with the same people and derives Type III tests from them (corresponds to car::Anova(lm(y ~ g + x, contrasts = list(g = contr.sum)), type = 3) in R).

Source

Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.), ch. 13. Maxwell, S. E., Delaney, H. D., & Kelley, K. (2018). Designing Experiments and Analyzing Data: A Model Comparison Perspective (3rd ed.). Routledge.