# Homoscedasticity violation: repeated-measures ANOVA

My study is a clinical trial with 2 treatment groups measured over 4 time points...with the outcomes assessed being blood levels.

So my independent variables are "treatment" (2 groups) and "time" (4 time points - with time being a within-subjects factor)...and my dependent variable is "blood levels".

So...I'm doing a repeated measures ANOVA (mixed model) in SPSS, but my assumption of homoscedasticity is not met.

My data meets the assumption of normality and sphericity...but not of homogeneity of variances/homoscedasticity.

I'm wondering what my best options are...given this limitation.

I've tried transformations and they haven't really helped.

I'd really appreciate any suggestions/help.

EDIT: I understand the possibility of options in my case such as: 1. repeated paired t-tests with a bonferroni correction (at the cost of loss of power) 2. non-parametric equivalents (i.e. Friedman test) to the rmANOVA ...but which is a more 'robust' test in lieu of the scientific design?

• It doesn't make a lot of sense to me that sphericity is OK but homogeneity of variance is violated. Can you elaborate on why you think so? – gung Jan 10 '14 at 17:52
• possible duplicate of Compare means - heterogeneous variance, non-normal, in respose to which @PeterFlom suggests a permutation test. I +1'd it :) – Nick Stauner Jan 10 '14 at 18:01
• @gung I'm really a beginner at stats, so please excuse any miscommunication, but my data exhibits normality (non-sigficant Shapiro-Wilk) and sphericity (non-significant Mauchly's test)...however, it is heteroscedastic (based on Levene's test). – elsa Jan 10 '14 at 18:09
• @NickStauner- just to clarify, would permutation tests be non-parametric alternatives to the ANOVA? In that case, I've mostly read mixed opinions suggesting that the loss of statistical power would not be worth it (if the deviation of variances is slight and the data exhibits normality). I guess I would require more insight on how we classify a "slight deviation" of variances of residuals. – elsa Jan 10 '14 at 18:16
• @NickStauner, these other questions are not quite identical, especially for an OP who is relatively new to stats. They aren't about rm ANOVA, or don't have quite the same mix of issues or don't have answers that address the OP's mix of issues. (The last one is more on point, though.) I think there may be room for an answer here that addresses rmANOVA as a special case of mixed-effects models, & the relations amongst its assumptions--particularly the nature of sphericity & homogeneity of variance. – gung Jan 10 '14 at 18:41