For example, the skewness test statistic is based on averaging the x^3 of the data. If the distribution is symmetric, there will be similar number of positive x’s and negative x’s, thus x^3 and (-x)^3 roughly cancel each other with a small overall sum. However, if the distribution is not symmetric, say skewed to the right, there can be a lot of large positive x while not enough negative x-values to cancel the large x^3, thus the overall sum tends to be much larger than that of the normal distribution. If it’s skewed to the left, there can be a lot of large negative x values while not enough positive x-values to cancel the large -x^3, thus the overall sum tends to be much more negative than that of the normal distribution. I know that the kurtosis test tests for the shoulder of a distribution, but how does it do that?
Asked
Active
Viewed 111 times
1 Answers
0
Kurtosis does not test "shoulders"; that is (yet another) incorrect interpretation of kurtosis. Rather, kurtosis measures tail extremity. If the tails of the distribution are more or less extreme than the tails of the normal distribution, in excess of expected sampling variation given the sample size, then the kurtosis test will reject the normality hypothesis.
BigBendRegion
- 354