Most suitable test to check homogeneity of variances I'd like to apply a t-student test to compare diferent samples to reference one using R but first I'm checking if my data meets the requirements for t-test so I removed outliers using the function rm.outlier() from Rcmdr R package and performed a Shapiro-Wilk test to check if replicates and the reference data are normaly distributed and now I should perform a test to check homogeneity of variance comparing each sample with the reference.
The samples has 3 replicates each one while reference has 11 replicates and samples and reference are independent.
I though about a Fisher Test but R says I need the same amount of replicates in the sample and reference. Then I though about Levene's Test and I tryed to run it in R using the built-int function in Rcmdr package according to this post
http://stats.stackexchange.com/questions/262026/most-suitable-test-to-check-homogeneity-of-variances
On the other side, I'm performing a Wilcoxon test which does not need so many assuptions and at the end compare the "possitives" from t-student and wilcoxon. Or if one sample or reference does not meet one of the t.test ssumtions use de results provided by wilcoxon test.
What would be your suggestion?
 A: You are planning to perform a t-test to compare mean differences of two groups, one with with 3 cases, one with 11 cases. You are aware that there are assumptions that have to be met (sample must be drawn from a normally distributed population homogenous in variance) for the t-test to be valid. You are unsure whether and how you can safeguard that these assumptions are met. Further, you performed some type of automated outlier-exclusion, which is likely to be based on further assumptions about the distribution of your data.
In short, given your very low sample size you cannot check these your assumptions reliably. Given your small sample size, the outlier exlusion procedure will have a tremendous impact on your results.
The solution to your problem: Stick to a test that does not make distributional assumptions (Mann-Whitney-U) and do not exclude outliers by data-driven methods.
Although t-tests at very low sample sizes may be valid if all assumptions are met, there is no way you can check this with the data at hand and therefore it is better to default to a non-parametric test, if you do not have a good (external) source showing that your samples is taken from a normal distribution with homogenous variances.
For an excellent discussion of the pro's and con's of testing normality see: Rochon, Gondan, & Kieser M, 2012.
