Test of Normality (Shapiro-Wilk)

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Geograman
Posts: 2
Joined: Sat Jun 20, 2020 2:19 pm

Test of Normality (Shapiro-Wilk)

Post by Geograman »

Hello, I have a question about the Test of Normality (Shapiro-Wilk) in an Independent Samples T-Test. Normally you would check both groups for normal distribution as a requirement for the T-test. So you would get 2 results of the Shapiro-Wilk test. One result for each group. But I have seen that you can also do a test for normal distribution directly in the T-test. But this test seems to give only one result for both groups and not for each group separately. My question now is what exactly this result indicates.
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MAgojam
Posts: 421
Joined: Thu Jun 08, 2017 2:33 pm
Location: Parma (Italy)

Re: Test of Normality (Shapiro-Wilk)

Post by MAgojam »

Hi, @Geograman.

Some time ago, Jantonie posted here:
viewtopic.php?f=5&t=315
a problem with using the Shapiro-Wilk normality test.
Suggesting, when having two samples, to perform the normality test not on the scores, but rather on the differences within the group.

Here as a reminder for the jamovi team:
https://github.com/jamovi/jamovi/issues/488

I think Jonathon subsequently applied Jantonie's suggestion.

I am attaching a Screenshot, with a small script in the Rj module that applies this tip.
ScreenShot_S-W.PNG
ScreenShot_S-W.PNG (95.61 KiB) Viewed 11033 times
Cheers,
Maurizio
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jonathon
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Joined: Fri Jan 27, 2017 10:04 am

Re: Test of Normality (Shapiro-Wilk)

Post by jonathon »

hi geograman,

the shapiro-wilk test is performed on the residuals, and not on the groups themselves. i do occasionally bump into people who want to test the groups separately. if you want to do that, you can do that in descriptives.

but putting all the residuals together and testing is accepted practice.

(it follows that if the residuals from one group is not normally distributed, then the residuals from all the groups combined will not be normally distributed either).

cheers

jonathon
Geograman
Posts: 2
Joined: Sat Jun 20, 2020 2:19 pm

Re: Test of Normality (Shapiro-Wilk)

Post by Geograman »

Hi, thanks a lot, now I understand what jamovi is doing here. :)
Asmaryadi
Posts: 3
Joined: Wed Jun 24, 2020 12:32 pm

Re: Test of Normality (Shapiro-Wilk)

Post by Asmaryadi »

is x-mean(x), the residual formula ?
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jonathon
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Joined: Fri Jan 27, 2017 10:04 am

Re: Test of Normality (Shapiro-Wilk)

Post by jonathon »

yup.

jonathon
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