3

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?

elsa
  • 31
  • 1
  • 3
  • 1
    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 - Reinstate Monica Jan 10 '14 at 17:52
  • possible duplicate of [Compare means - heterogeneous variance, non-normal](http://stats.stackexchange.com/questions/67172/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
  • @NickStauner I've looked through both those threads (and many others on this site) but haven't really found any suggestions to guide my search further. – elsa Jan 10 '14 at 18:07
  • Have you ruled out a permutation test as a useful suggestion then? – Nick Stauner Jan 10 '14 at 18:08
  • 1
    @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
  • 1
    @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
  • Here's [another possible duplicate](http://stats.stackexchange.com/q/56971/32036). Yes, you may not need to do anything differently if the heteroscedasticity is minimal, according to @gung's answer here. BTW, to anyone who can provide a definitive answer here: there's also [another old question about heteroscedasticity in an ANCOVA](http://stats.stackexchange.com/q/68532/32036) that has been languishing without an answer! ;) – Nick Stauner Jan 10 '14 at 18:19
  • And [another](http://stats.stackexchange.com/q/55473/32036): same answer as gung's by @Henrik. BTW, forgot to confirm directly: permutation tests are non-parametric. – Nick Stauner Jan 10 '14 at 18:29
  • And [another](http://stats.stackexchange.com/q/43929/32036)! This is a classic question I guess! :) @ttnphns gives some helpful extra info here: group size matters..."SPSS' Explore procedure ('spread vs level plot')"..."power transformation"...and, "Linear Mixed procedure rather than ANOVA...is more flexible and generally does not require homogeneity of variances." – Nick Stauner Jan 10 '14 at 18:38
  • 1
    @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 - Reinstate Monica Jan 10 '14 at 18:41
  • Then I should've said "related question" instead of adopting the automated comment generator's use of "possible duplicate," which I also could've edited to avoid the unintended connotation that this is a complete clone. No objections from me to leaving this one open for a new, tailor-made answer! – Nick Stauner Jan 10 '14 at 18:47
  • @NickStauner- thanks for all the suggestions and useful related questions. I understand that the rmANOVA is pretty robust against minor deviations of normality and homoscedasticity (and is a better choice than non-parametric equivalents). But what if the deviation is *not minor* (i.e. largest variance is way more than 4x smallest variance)? – elsa Jan 13 '14 at 05:17

0 Answers0