I have a Between/Within subjects analysis to perform on SPSS and right at the beginning I get a significant Levene's test which I understand, prevents me from using the GLM mixed model. Which test should I use (I wanted to choose the post hoc options of Equal variances not assumed but SPSS does not allow me such)
I don't know your experiment, but when the variances are significantly different, we should correct the degree of freedom of denominator of the test F using the Satherthwaite’s approximation. We find some samples mainly in pages 325 to 329 of Snedecor’s book (SNEDECOR, G.W.; COCHRAN, W.G. Statistical Methods, 7ª ed. The Iowa State University Press, Iowa, 1980, 507p.). When using a statistics software (SPSS or SAS) sometimes it is necessary to correct manually or use the option it offers.
My understanding ( I am not an SPSS user )
https://www.researchgate.net/post/Has_anyone_used_SPSS_to_do_multilevel_analysis
is that you can in SPSS model complex level 1 heteroscedasticity according to a predictor if that predictor is categorical but not if it is continuous,
MLwin has specific facilities to do such complex level 1 modeling; see
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html
The ESRC has funded free access to MLwiN for all UK academics
http://www.cmm.bris.ac.uk/clients/reqform/
If you are using SPSS ANOVA for a split plot design then it should allow the unequal variance assumed post hoc test options for the between factors (options also prove Brown-Forthythe corrections for some tests). For the within factors the relevant assumption is sphericity. However, for post hoc tests you can sidestep this by computing a single df test with a non-pooled error term. This is easily done using paired t tests. You can then apply a suitable adjustment manually (e.g., Bonferroni or Holm) fairly trivially.
Under some circumstances you can use a multilevel model as Kelvyn suggests but this might not be sensible (depending on your sample size).
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