Hi everyone,
As part of my PhD project, I am conducting mixed ANOVA's in SPSS. I understand how to run the procedure and have been using the SPSS Survival Manual by Julie Pallant as my main reference. However, when I run some of the mixed ANOVA's, some of the Levene's tests of Equality of Error Variances are coming out as significant and are therefore violating the assumption of homogeneity of variances.
All my data is normally distributed. The only difference is that in some of these tests the subject groups vary but only by one less data point. However, from reading the below extract from the book this shouldn't be a problem as the difference is below 1.5.
"If you obtain a significance value of less than .05, this suggests
that variances for the two groups are not equal and you have therefore violated the assumption of homogeneity of variance. Don’t panic if you find this to be the case.Analysis of variance is reasonably robust to violations of this assumption, provided the size of your groups is reasonably similar (e.g. largest/smallest = 1.5; Stevens 1996, p. 249)"
Can I therefore proceed with the mixed ANOVA result or what is my best option?
Thank you in advance.
Hello Kiera. As the excerpt you quoted says, ANOVA is quite robust to heterogeneity of variance when the sample sizes are equal. To emphasize this point, George Box once said:
"To make the preliminary test on variances is rather like putting to sea in a rowing boat to find out whether conditions are sufficiently calm for an ocean liner to leave port." (http://garfield.library.upenn.edu/classics1982/A1982MX29400001.pdf)
It would help readers to advise you if you reported the following summary statistics for the analyses that have you concerned: means, SDs and sample sizes. Also, please clarify whether ANOVA means one-way (independent groups) ANOVA or some other model. HTH.
Are differences in variance something that is important for the theories you are investigating? Also, are the differences in variance roughly similar to the differences in means? An alternative is including differences in the variance in you r model. However, if only differences among the means are of interest then this is less important.
Hello Kiera. As the excerpt you quoted says, ANOVA is quite robust to heterogeneity of variance when the sample sizes are equal. To emphasize this point, George Box once said:
"To make the preliminary test on variances is rather like putting to sea in a rowing boat to find out whether conditions are sufficiently calm for an ocean liner to leave port." (http://garfield.library.upenn.edu/classics1982/A1982MX29400001.pdf)
It would help readers to advise you if you reported the following summary statistics for the analyses that have you concerned: means, SDs and sample sizes. Also, please clarify whether ANOVA means one-way (independent groups) ANOVA or some other model. HTH.
Worth adding to Bruce Weaver point (and nice quote), robust (in the sense of the .05 level is relatively well maintained when certain criteria are meet) should not be the only criterion to guide your statistical journey. As I said above, the first question should be are differences in variance interesting, and the second how can they be models, and then the way down in the questioning is how to estimate/interpret model fit. On Anova specifically, while robust in the sense above, it is not in the sense of power. A few large outliers can increase differences in variance and lower the p value (even if the outliers are in the hypothesized direction, e.g., try one-sample t-test [a simplel Anova] against a mean of 0 with 1,2,3,4,5, which has p = .01, and 1,2,3,4,15, which has p = .20). Wilcox has an article title that sums up his view: Article ANOVA: A Paradigm for Low Power and Misleading Measures of E...
For more details see Wilcox's textbooks and review articles on how robust these procedures are.
Thank you all very much for your informative suggestions. I will explore this further with the advice given and get back to you as soon as possible. Thank you again!
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