What about normality and hogeneity?
I have 12 treatments (5 with 32 replicates, 7 with 31)
What about Kruskall-Wallis?
ANOVA has some desirable properties when the design is balanced (i.e., group sizes are equal), such as optimum power and reduced sensitivity to heteroscedasticity. However, the lack of balance you have is so small as to not be of particular concern.
You do need to assume that variances are homogenous across the treatments for a conventional oneway ANOVA fit by ordinary least squares (OLS). If this assumption is breached, the OLS estimates will not be efficient.
You do not need to make any normality assumptions for the OLS estimates to be unbiased, consistent, and efficient. Conventional confidence intervals and significance tests do, however, assume that the sampling distribution of the treatment group means is normal. This will be the case if the distribution of the response variable within each group is normal. However, even if the within-group distributions are not normal, the sampling distribution of the means will still converge to a normal distribution as the sample grows larger, provided the other assumptions are met. So the normality assumption is not particularly crucial in most contexts.
The attached paper discusses the assumptions of linear regression when fit by OLS (oneway ANOVA is just a special case of regression).
Article Assumptions of Multiple Regression: Correcting Two Misconceptions
You can use ANOVA with unequal replication also. However the analysis will be complex. You check the normality and homogeneity assumptions, if you want. If noraml, then no need to use Non Parametric test.
Thank you very much for your answer.
Rajiv Randey, you said "However the analysis will be complex", could you please explain it in more details?
What I have to do if 1) I have homogeneity but no normal distrubution, 2) I have normality but no homogeneity and 3) both assumptions are violated
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