SPSSX Discussion - Re: Shapiro-Wilks Statistic

Re: Shapiro-Wilks Statistic

Posted by Baker, Harley on
URL: http://spssx-discussion.165.s1.nabble.com/Shapiro-Wilks-Statistic-tp5739693p5739708.html

I have a number of religious identity labels that participants rate in terms of how well they fit. There are five response categories from ‘not at all’ to ‘very well.’ As is the case in most research like this, the distribution of responses is basically U-shaped. (Basically, a label either fits or it does not, very few in-between responses.) Mardia’s statistic shows a huge violation of multivariate normality, as one would expect. As such, univariate normality is not an issue, which is what I should have said originally. Pearson correlations underestimate the degree of linear relationship in these situations, and we often turn to polychoric correlations instead. (I am loathe to use nonparametric correlations when perfectly good parametric methods exist. When categorical data are well-behaved, I also prefer to use parametric models. I agree with one of my mentors, Fred Lord: the data don’t know where they came from. So, if they act parametric, treat them that way. If not, don’t.) Polychoric correlations provide a more accurate estimate of the true degree of linear association under these conditions. The matrix was then submitted to an EFA to see what patterns of self-labeling emerge, if any.

Hope this clarifies the situation a bit better.

Harley

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On Oct 1, 2020, at 10:52 AM, Rich Ulrich <[hidden email]> wrote:

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I'm a little confused. You say,

"The data are ordinal in nature, so the issue of normality doesn't even

apply to my situation."

"... the issue doesn't even apply ... "

That implies to me that you are doing analyses after rank-transform

("nonparametric") without considering ordinary ANOVA -- and the

reviewer asks you to justify abandoning the raw scores.

If I were reviewer, I might ask the same. I hope I would put the

request more clearly than what you seem to have received.

Bruce writes, unclear about the situation -

If it is to justify use of a parametric test, my advice would be, "Don't

bother!" Like me, Bruce is biased against non-parametric testing for

decently-behaved ordinal data.

--

Rich Ulrich

From: SPSSX(r) Discussion <[hidden email]> on behalf of Baker, Harley <[hidden email]>
Sent: Thursday, October 1, 2020 10:38 AM
To: [hidden email] <[hidden email]>
Subject: Re: Shapiro-Wilks Statistic

Hi Bruce,

An editorial reviewer is requiring me to do so. Otherwise, I would not. The data are ordinal in nature, so the issue of normality doesn't even apply to my situation. Regardless, I am complying . . .

Harley

Dr. Harley Baker

Professor Emeritus of Psychology

California State University Channel Islands

One University Drive

Camarillo, CA 93012

harley.baker@...

From: SPSSX(r) Discussion <[hidden email]> on behalf of Bruce Weaver <[hidden email]>
Sent: Thursday, October 1, 2020 5:26 AM
To: [hidden email] <[hidden email]>
Subject: Re: Shapiro-Wilks Statistic

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I'll repeat the question I asked earlier:

> Why do you [Harley & 3J LEMA] want to test for normality?

If it is to justify use of a parametric test, my advice would be, "Don't
bother!" ;-)

3J LEMA wrote
> Any tips on when to use the Shapiro-Wilk statistic over the
> Kolmogorov-Smirnov Statistic in testing normality?
>
> Thank you.

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