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- Re: Manual Calculation of the Shapiro-Wilk Test Statistic

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Jan 7, 2019 5:15 PM
(158 views)

Hello Everyone,

Does anyone know how to implement manual calculation of the Shapiro-Wilk test statistic in JMP?

Using JSL script and/ or column formulas?

I know that JMP natively does this calculation natively in Analyze>Distribution and then Continuous Fit>Normal>Goodness of Fit, but I'm trying to reproduce the calculated value of the test statistic in order to understand it's basis with greater depth.

There are a number of useful clues in references online, but I'm having some difficulty putting the pieces together:

https://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test#cite_note-8

Here's the basis for it summarized nicely from Wikepedia link above:

Also some helpful clues here using MS Excel.

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@PatrickGiuliano I am not sure why you would want to do this manually, when you have JMP that can produce the statistics and you can extract it from a report. A simulation where the sample size is the same so the weight coefficients are the same, meaning the weights are calculated once and used many times, might be a good scenario for doing this by hand/matrix.

That said, I found references for the coefficients and an algorithm to get them. The references are reported in the attached script. Here are the results of two tests with N=40.

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##### Re: Manual Calculation of the Shapiro-Wilk Test Statistic

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Jan 7, 2019 7:54 PM
(142 views)
| Posted in reply to message from PatrickGiuliano 01/07/2019 08:15 PM

Here is a link that does a step by step calculation that you might be able to use.

http://blog.excelmasterseries.com/2015/05/how-to-create-completely-automated_4.html

Jim

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Jan 9, 2019 10:41 AM
(114 views)
| Posted in reply to message from PatrickGiuliano 01/07/2019 08:15 PM

Ignore this...I did not read your request very closely...sorry

~~JMP calculates the Shapiro-Wilk's test.~~

~~Open a data table.~~~~Go to Help > Statistics Index> find Shapiro-Wilk test for normality on the left, then press launch~~~~Select which columns of your table to be tested~~

~~The test is available in JMP PRO 12 and higher.~~

~~ ~~

~~It is the Goodnes of Fit test for a Normal Fit. The JSL is~~

```
Distribution(
Continuous Distribution(
Column( :height ),
Fit Distribution( Normal( Goodness of Fit( 1 ) ) )
)
);
```

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@PatrickGiuliano I am not sure why you would want to do this manually, when you have JMP that can produce the statistics and you can extract it from a report. A simulation where the sample size is the same so the weight coefficients are the same, meaning the weights are calculated once and used many times, might be a good scenario for doing this by hand/matrix.

That said, I found references for the coefficients and an algorithm to get them. The references are reported in the attached script. Here are the results of two tests with N=40.

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Thank you this is excellent.