Editing Analysis of covariance (section)

==Conducting an ANCOVA ==
===Test [[multicollinearity]]===
If a CV is highly related to another CV (at a correlation of 0.5 or more), then it will not adjust the DV over and above the other CV. One or the other should be removed since they are statistically redundant.

===Test the homogeneity of variance assumption===
Tested by [[Levene's test]] of equality of error variances.
This is most important after adjustments have been made, but if you have it before adjustment you are likely to have it afterwards.

===Test the homogeneity of regression slopes assumption===
To see if the CV significantly interacts with the categorical IV, run an ANCOVA model including both the IV and the CVxIV interaction term. 
If the CVxIV interaction is significant, ANCOVA should not be performed. Instead, Green & Salkind<ref name="Green">Green, S. B., & Salkind, N. J. (2011). ''Using SPSS for Windows and Macintosh: Analyzing and Understanding Data'' (6th ed.). Upper Saddle River, NJ: Prentice Hall.</ref> suggest assessing group differences on the DV at particular levels of the CV. Also consider using a [[Moderation (statistics)|moderated regression analysis]], treating the CV and its interaction as another IV. Alternatively, one could use [[Mediation (statistics)|mediation analyses]] to determine if the CV accounts for the IV's effect on the DV{{Citation needed|date=December 2022}}.

===Run ANCOVA analysis===
If the CV×IV interaction is not significant, rerun the ANCOVA without the CV×IV interaction term.  
In this analysis, you need to use the adjusted means and adjusted [[mean squared error]]. The adjusted means (also referred to as least squares means, LS means, estimated marginal means, or EMM) refer to the group means after controlling for the influence of the CV on the DV.
[[File:Main Effects.jpg|thumb|Simple main effects plot showing a small Interaction between the two levels of the independent variable.]]

===Follow-up analyses===
If there was a significant [[main effect]], it means that there is a significant difference between the levels of one categorical IV, ignoring all other factors.<ref name="Howell">Howell, D. C. (2009) ''Statistical methods for psychology'' (7th ed.). Belmont: Cengage Wadsworth.</ref> To find exactly which levels are significantly different from one another, one can use the same follow-up tests as for the ANOVA.
If there are two or more IVs, there may be a [[Interaction (statistics)|significant interaction]], which means that the effect of one IV on the DV changes depending on the level of another factor. One can investigate the simple main effects using the same methods as in a [[Factor analysis|factorial ANOVA]].