I am running a two-way MANCOVA which needs to be adjusted by two covariates. Problem is, I am not entirely sure whether I clarified all assumptions correctly and how to finally deal with two covariates in combination.
I would appreciate if someone could clarify my situation by either confirming single steps, suggesting enhancements, or pointing out mistakes. As I did not find any exact resource(s) on the web myself, I’ll try to write in a way that someone else can follow in hope that this (together with your recommendations) might be useful for them as well.
Thank you for your support!
- Object: Online study about imagination.
- Research question: Does an imagery procedure have a certain effect?
- Factors: Gender (Male vs. Female) and Condition (Group1 vs. Group2).
- Covariates: Ability to imagine (Cov1), and imagery duration (Cov2).
- Dependent variables: Four DV’s (assessed by a questionnaire).
Covariate correlation: Both covariates are not correlated (r = .03). Covariate outliers: No outliers for Cov1. However, Cov2 has several outliers which I ignore. (Reason: these outliers followed instructions to spend 4 to 7 (and up to 10) minutes on the imagery procedure whereas most others followed the imagery instructions only superficial and skipped to the next part after 180 seconds (i.e., as soon as they were able to; median duration is 192 s).
Pearson correlation showed no evidence of multicollinearity (|r| < 0.9). Mahalanobis distance unveiled no multivariate outliers (p > .001; see Laerd Statistics for critical values). Few univariate outliers were found in some groups but weren’t considered crucial and kept in the sample; they would solely reduce statistical power. The observed covariance matrices of the DV’s were equal across groups; Box’s M value was not significant. Error variances were equal across groups for all DV’s; all Levene’s tests were not significant. All DV’s were normally distributed based on Shapiro-Wilk's tests (for this, p-value was Bonferroni adjusted; see Pituch & Stevens, 2016). The linear relationship between the DV's as assessed by scatterplots was considered acceptable (some were quite linear, others less so).
Calculations give me some solid results which I hope are based on legit assumptions. Cov1 is not significant what will let me skip it in a future study; Cov2 is significant for one DV what is a heavy support for my hypotheses (and unveils that the “outliers” were actually doing what they were supposed to while most others might just have been primed by what they were reading; that in particular is why I don’t want to skip any outliers here).
Anyway, do I miss something? For instance, any further assumption? Or, is this the way to go?
PS: The resources I use are Laerd Statistics (tutorials for a one-way MANCOVA and a two-way ANCOVA, both with one covariate plus the hint that there is more to consider when adding a second covariate), Tabachnick & Fidell - Using Multivariate Statistics (6th ed, 2012), and Pituch & Stevens - Applied Multivariate Statistics for the Social Sciences Analyses with SAS and IBM’s SPSS (6th ed, 2016). All three helped me a lot but did not give me my full final answer.
