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ISSUE

I have various samples, 97 in all, and they are of different sample sizes (n4...n100). All of these samples come from the same population data. The distribution of the population data is NOT normal.

Although the population data is not normally distributed, I want to determine which of these 97 samples is closest to representing a normal distribution. I have calcuated the skew & kurtosis for each sample. I then squared the results to make each value of skew & kurtosis a positive number, and then I ranked the skew from smallest to largest and I did the same for the kurtosis. I concluded that the sample with the smallest squared skew and the smallest squared kurtosis best represents the sample that most closely approximates a normal distribution. Something tells me, however, that this ranking system is inadequate because a skew of .01 where sample size equals 9 seems less significant than a skew of .07 where the sample size equals 66. Similarly, a kurtosis of 0 where sample size equals 12 seems like it might be less significant than where kurtosis is .09 and sample size equals 40.

Obviously, I'd like to come up with a way to rank the skew and kurtosis of each sample by weighting them somehow. How would you go about weighting them to determine which sample is the best relative representation of a normal distribution? Thank you in advance.

Kimberley

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# Skew & Kurtosis: Weighting Signficance

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