Pardon a relative novice's question. I'm seeking a reference that describes, compares, and gives formulas for the standard error for ratios and the standard error for differences between means when small Ns are involved.
Here is the situation at hand:
- Multiple samples from two independent populations.
- The underlying variable is normally distributed in each population, but with somewhat different means and standard deviations.
- At least one sample will always be small, perhaps 3 to 15 cases, the other sample will generally be 50 or 100 cases, or even larger.
- Statistics of interest: ratio of means and difference between means.
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The variables are grades on multiple choice tests and such tests tend to be normally distributed. The p (i.e., probability of getting a question correct, AKA difficulty level) for the tests in question is around .7
Question: How will the standard errors of these two sample statistics compare?
Update based on comments
The specific question I have is whether the mean standardized difference between 2 groups will be a more or less stable measure (i.e., have a larger or smaller standard error) than the ratio of the means, when at least one of the groups is small.
