I am doing a two way ANOVA in spss 27. However, the homogeneity of variances assumption is violated. Thus, I considered doing a Welch's factorial Anova but I cannot seem to find the way to do this in spss. How can I do this? And is there anything else I can do in spss, as it is the only program available to me, to solve this problem? I tried transforming my DV with the square root method, it did not work.
Thank you
Welch's factorial anova ? That's not one I've heard of. There are ways to account for heterogeneity in a two-way design, usually by generalized least squares or weighted least squares. There's some SPSS information here: https://www.ibm.com/docs/en/spss-statistics/26.0.0?topic=wls-overview-command#syn_wls_overview
Sal Mangiafico Thank you for your answer. Can this still be done if my two IVs are categorical and my DV is continuous?
Sal Mangiafico Thank you for your help. I think I have found the solution through your answer!
Hello Constantinos Kaniklides. I have two questions.
1) How did you determine that the homogeneity of variance assumption was violated?
2) Can you share n, mean and SD for each cell of the design?
I ask the 2nd question because ANOVA is very robust to heterogeneity of variance when the sample sizes in all groups/cells are equal or nearly so.
Finally, if you have a recent enough version of SPSS, check out the ROBUST sub-command for UNIANOVA/GLM:
https://www.ibm.com/docs/en/spss-statistics/28.0.0?topic=unianova-robust-subcommand-command
HTH.
Bruce Weaver ,
The question is, How robust is "very robust" ? ...
For the ROBUST / UNIANOVA approach, my question is if you can use EMMEANS as a post-hoc here. R has a similar common approach, where the Sandwich, or related estimators, can be used for anova. But the problem there is that it's not the model that is estimated this way, it's just the anova table output. So, any statistics you generate afterwards (including emmeans) aren't based on the robust model. Dunno about SPSS.
Hi Sal Mangiafico. Re your first question, a pretty good rule of thumb, IMO, is that if ratio of largest variance to smallest variance is no greater than 4 or 5 (when all sample sizes are equal), the model will be pretty good. See Table 2 in Glass et al. (1972), for example.
Glass, G. V., Peckham, P. D., & Sanders, J. R. (1972). Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance. Review of Educational Research, 42(3), 237-288. https://doi.org/10.3102/00346543042003237
Re your second question, excellent point. It has been a while since I tinkered with the ROBUST option for UNIANOVA, but I just cobbled together a quick "toy" example to remind myself that the tables of EMMEANS are the same (including SEs and CIs) regardless of whether the ROBUST sub-command is included. The difference appears in the table of "parameter estimates" (i.e., coefficients). But some more tinkering tells me that when you include the ROBUST sub-command, contrasts carried out via LMATRIX use the robust covariance matrix.
https://www.ibm.com/docs/en/spss-statistics/28.0.0?topic=unianova-lmatrix-subcommand-command
But frankly, I find LMATRIX very fiddly and frustrating. So if I needed to do this sort of thing, I would do it via Stata instead of SPSS! ;-)
Another issue is whether differences in the variances are of substantial interest. Often they are. Other times they may result from issues with scale (e.g., when data are constrained to > 0, often sd of group ~ mean pf group) and sometimes transformations may be appropriate. A first question may be whether there are good reasons for the variances to differ, and then if appropriate model these.
My tortoise mind must have continued working on this, because I suddenly remembered that several years ago, I drafted a manuscript showing how one could use the MIXED command in SPSS to estimate models that do not assume homogeneity of variance. I think I intended to submit it somewhere, but that never happened. Section 5 (factorial ANOVA) has a relevant example, I think. See attached.
Bruce Weaver , interesting.... I'd have to digest it a bit... Maybe you didn't submit it because the abstract states "Blah blah blah. Yada yada yada." ? :)
Yes, Sal Mangiafico, it might have needed a little bit of tweaking & polishing before it was ready to submit. ;-)
This paper was suggested by D.M. Lane on another thread. Covers variance ratio in anova for both equal and unequal sample sizes: Article Effect of variance ratio on ANOVA robustness: Might 1.5 be the limit?
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