STATISTICS EXPERTS: How Do I Compare Means/Medians of Different Sample Sizes For...
...Relative Normality? I'm familiar with the JarqueBera Test which takes into account sample size, skew and kurtosis for determining the relative normality of different sample sizes. I'm looking to construct another test for this purpose. Does it make sense to determine the standard deviation between the Mean and Median of each sample, and multiply it by the square root of 1/n, and then concluding that the sample with the smallest result is most normally distributed?I'm basically looking for a formula that leads to the conclusion that the Mean and Median of one sample are relatively closer to each other than the Mean and Median of another sample. I need a way to take sample size into consideration because it seems biased to conclude that a sample size of 5 deserves the same weight as a sample size of 100, for having the same spread between Mean and Median. I'm not even sure this assumption makes sense, but viscerally it does. Any suggestions? Does my proposed backup test to Jarque Bera make sense?
