Contents
- Index
Skewness-Kurtosis Specific Normality Test (Heavy Tails Towards Spec)
The Skewness-Kurtosis Specific test for normality is not a general test for normality designed to detect all departures for normality like the other tests. This test is designed to only reject specific departures from normality that invalidate the confidence statements associated with variables sampling plans and normal tolerance intervals. It is designed to answer the question: "Is it OK to use a variables sampling plan or normal tolerance interval?" Passing this test is sufficient justification to use a variables sampling plan or normal tolerance interval, even if the other three tests fail.
The confidence statements are valid so long as the tails of the distribution are no larger than the tails of the normal distribution. This means the normal distribution bounds the tails of the distribution rather than exactly fit it. This test rejects when the tails are longer than the normal distribution, which occurs when there is a positive kurtosis or skewness in the direction of a spec limit. Depending on the type of specification involved, the Skewness-Kurtosis Specific test rejects when:
Lower Spec Limit Only: Rejects if negative skewness or a positive kurtosis.
Upper Spec Limit Only: Rejects if positive skewness or a positive kurtosis.
Two-Sided Spec Limit Only: Rejects if either positive or negative skewness or a positive kurtosis.
The Skewness-Kurtosis test does not give a p-value but instead just indicates pass/fail. If you fail, you can state with 95% confidence the data is not from the normal distribution as before.
The risk of proceeding if you pass the Skewness-Kurtosis Specific test is that of a false rejection. The tails may be less than the normal distribution. The confidence statements associated with the variables sampling plan or normal tolerance interval may overestimate the defect rate or range of the distribution resulting in failing a set of data that deserves to pass. If the Skewness-Kurtosis Specific test passes, but the other normality test fails, consider going ahead and transforming the data to avoid a false rejection. This will result in more accurate statements. However, it the Skewness-Kurtosis Specific test passes and the confidence statements meet the acceptance criteria, then the data clearly passes making a transformation unnecessary.