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I'm an undergraduate psychology student currently finishing up my dissertation, but a few days ago, while going through my SPSS output, I realized my Levene's test is significant, but my data is normally distributed. Is there any way I can justify that it is ok to still perform a two-way between-subjects ANOVA?

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    $\begingroup$ There is not enough information available here. How large is your data? Is it balanced? How large is the ratio of variances? If your data is unbalanced, does the larger group have larger or smaller variance? Generally speaking, balanced ANOVA is rather robust against heteroscedascity and the most problematic case is if the smaller group has larger variance. $\endgroup$ – Erik Apr 8 '13 at 12:30
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    $\begingroup$ Hey Erik, thank you for your reply. I'm really sorry if I'm coming across a bit naive on the stats, that's mainly because I am, It is definitely my weakest subject which is why I'm having such troubles with it. But, I'm pretty sure my data is unbalanced as I do not have equal sample sizes in each group. I have a sample of 121. Im testing cannabis use versus non-use and gender differences in self-reported schizotypy and social anxiety. I have 40 males and 81 females, where 53 are non-users and 68 are users. So, what do you think? Could I just ignore the heterogeneity? $\endgroup$ – Dominique Apr 8 '13 at 12:52
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    $\begingroup$ @Dominique rather yes. Actually one could argue that using the Levene test increases your overall alpha error and is a generally bad idea. But the overall answer rests however, on how different the variances are. If they are not grossly different (say one is more than 4 times larger than the smallest one), you should be fine. $\endgroup$ – Henrik Apr 8 '13 at 12:56
  • $\begingroup$ @Henrik, why not make that an official answer? $\endgroup$ – gung - Reinstate Monica Apr 8 '13 at 13:03
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As pointed out correctly by Erik, the question is how bad the deviations from the assumptions actually are. In other words, how big is the difference between the smallest and largest variance. In your case it sounds as if they are not that big. Then it is no problem. However, you have to take differences in the samples size into account. If I remember numbers for these issues can be found in the book on ANOVA by Tabachnik & Fidell.

Additionally, as I already said here, using the Levene test (or actually any null-hypothesis significance test on the assumptions) heightens your overall probability to commit an alpha error and is therefore not recommended. The other answers in the linked thread could also be interesting to you.

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  • $\begingroup$ Controlling alpha error across slightly unrelated tests may not be a big deal; I'm not sure that one shouldn't recommend using Levene's test just for this reason. Maybe a little additional info on why one would care about that problem would be useful here? +1 in any case! $\endgroup$ – Nick Stauner Jan 10 '14 at 18:24

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