I have a simple an common question.
In summary, I have a data which has a variable named "A1" and a "group" with two categories.
The "A1" variable is not normal in total, nor in the group levels (please assume that this is non-normal variable).
I should compare the average of A1 in the two level of groups. (I know I should use non-parametric methods such as Mann-Whitney test, However, the doctor who gave me the data does not understand the mean of ranks or median. He only needs to compare the "mean" of two category).
How can I compare the "mean of A1" in two categories? Just the mean.
Do you really mean "comparing the means" or "testing a hypothesis about a mean difference"?
Comparing the means is simple: calculate the means and the differences or the ratio of the means (whatever makes more sense, practically).
Testing a hypothesis about a mean difference is relatively simple when your sample size is large (>30, say). If the distribution is not too skewed, you can rely on the central limit theorem and use a t-test. You can also bootstrap the p-value.
If the sample size is small, both t-test and bootstrapping may not be a good choice (t-test because the lack of convergence, bootstrap because a small sample might not be representative). If you can apply a monotone transformation so that the distribution of the transformed data is sufficiently symmetric (within the groups), you can use a t-test on the transformend data. If you can scho a significant difference there, the significance also includes the hypothesis about the untransformed data (if the transformation is monotone, like log or sqrt or 1/x).
Jochen Wilhelm Thank you Jochen. I mean testing the hypothesis about the mean. I know Central Limit Theorem. Based on this theorem "the mean of sample means have normal distribution", however, we have just one sample. I agree with you about bootstrapping.
We have just one sample, can this be considered normal?
Please read the CLT in a good MATH stats book. You have not stated it correctly. David Booth
You wrote that there are two groups. So you have a sample from each group, as I understood.
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