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Given an unbalanced completely randomized design with two treatment groups of unequal sizes and an appropriate one-way ANOVA parametric test, how can I properly check the validity of my model assumptions - namely, normally distributed errors, independence of the errors, homoscedasticity, and checking for outliers?

I started off checking for outliers by fitting a linear model to the data, and constructing a plot of the standardized residuals. To check for normality I inspected a normal probability plot, but I ran into trouble when checking for equal variances because I found that $s_{max}^2/s_{min}^2 > 3$. Then I realized that my two sample sizes were different - one is 90, and one is 95!

Hope my question isn't too basic. Thanks in advance.

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If you only have two samples, you're essentially just doing a t-test.

A small difference in sample sizes will be of almost no consequence (if the other assumptions hold, even quite different sample sizes is a non-issue, but equal sample sizes confers robustness to heteroskedasticity).

You should be able to deal with the variance issue by using the Welch adjustment (which I would recommend you do as a matter of course unless you have a good a priori reason to assert equal variances, rather than trying to assess the assumption), but since your sample sizes are very nearly equal that shouldn't matter much either.

The normal probability plot is a reasonable way to assess normality but unless the underlying distribution is pretty distinctly non-normal (likely enough that you would have known it before you collected the data) it will also likely have relatively small impact on your inference.

More detailed discussion of issues relating to the effects of the various assumptions can be found on site by searching.

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