A nonparametric test or employing a transformation may result in a more powerful test. In particular, small or unbalanced sample sizes can increase vulnerability to assumption violations. If the data are in a particular order, consider the possibility of dependence. If you are unsure whether your samples are independent, you may wish to consult a statistician or someone who is knowledgeable about the data collection scheme you are using. Values may not be identically distributed because of the presence of outliers .
Outliers are anomalous values in the data.
They may be due to recording errors, which may be correctable, or they may be due to the sample not being entirely from the same population. Apparent outliers may also be due to the values being from the same, but nonnormal , population. The F statistic is based on the sample means and the sample variances, each of which is sensitive to outliers . In particular, a large outlier can inflate the overall variance, decreasing the F statistic and thus perhaps eliminating a significant difference. A nonparametric test may be a more powerful test in such a situation.