# How does software normally get the p value?

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• #28279

hoon
Participant

In almost every software, once the histogram or the normal probability plot are plotted, p-value is given. How does this value calculated from ? the normal mean or any other data is not provided. only a row of data is key in.
Thank you.

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#70201

Ken K.
Participant

You did not specify the test that the p-value is associated with. It sort of sounds like you are talking about a test of normality.
There are several goodness of fit tests for normality – probably the most common are the Shapiro-Wilke Test (the Ryan-Joiner Test in MINITAB), the Anderson-Darling A^2 Test, the Kolmogorov-Smirnov test, and the chi-square test.
The formulas are more complex than can be presented in this format, but they are all covered in Ralph B. D’Agostino & Michael A. Stephen’s book “Goodness -of-Fit Techniques”.
The Shapiro-Wilks test uses the correlation observed in the normal probability plot. The Anderson-Darling and Kolmogorov-Smirnov tests both compare the empirical cdf to that of the best fit normal curve. The Anderson-Darling test pays more attention to the tails than does the K-S test.
D’Agostino & Stephen’s recommendations are that the Shapiro-Wilks test and Anderson-Darling A^2 test are amoung the best to use. They indicate that the Shapiro-Wilks type tests are probably overall most powerful. MINITAB defaults to the Anderson-Darling test, but I don’t really know why.
D’Agostino & Stephens go on to say:
“For testing for normality, the Kolmogorov-Smirnov test is only a historical curiosity. It should never be used. It has poor power in comparison to the above procedures.”
and
“For tetsing for normality, when a complete sample is available the chi-square test should not be used. It does not have good power when compared to the above tests.”

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#70208

hoon
Participant

Dear Mr. Ken,
What I mean is that the p-value for the Anderson , K-S test or histogram is of the same formular? p-value is the probability that we would have obtained the sample if Ho is true.  What I understand is if we are testing for normality, to calculate the p-value, we should have either the nominal mean or standard deviation for the population or some else that we can use to get the z-value or t-value before getting the respective p-value from the tabulated z or t distribution data.
However in the software, what I did is I test a column of data with the normality test, either Anderson or K-S test, then the normal probability plot with the A squared or D-value and the p-value will be shown.  The A squared for Anderson Test and the D-value for the K-S test is calculated from the respective formulas but what about the p-value for these tests?
Thank you for your explaination.

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