===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARDThanks -I agree that univariate normality should not be at issue, and Iwonder anew at what your reviewer had in mind. Showing theextreme kurtosis should be enough (if there were any question).
From Bruce's citation - I have doubts that the assumptions ofunderlying bivariate normality are met, when it comes to polychoric.
If the polychoric r's are larger, then they also have larger standarderrors than the Pearson r's. I think I had one set of data that I everplayed with, testing polychoric for factoring, and I ended up using
Pearson's.
What also came to mind was Item (or Latent) Response Theory, whichuses logistic transformations. I know IRT from reading, too, rather thanhands-on experience. I don't know if they have examples with U-shapes.
(a) Underlying Logistic is shaped like Normal with slightly fatter tails, so
it might not meet assumptions any better for U shaped data. (b) If both
tails are always fat, the correlations won't change by much. (c) The
people who perform IRT have some interesting ancillary statistics.
--
Rich Ulrich
From: Baker, Harley <[hidden email]>
Sent: Thursday, October 1, 2020 2:36 PM
To: Rich Ulrich <[hidden email]>
Cc: [hidden email] <[hidden email]>
Subject: Re: Shapiro-Wilks StatisticI 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 thereviewer asks you to justify abandoning the raw scores.
If I were reviewer, I might ask the same. I hope I would put therequest 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 fordecently-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 StatisticHi 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 BakerProfessor Emeritus of PsychologyCalifornia State University Channel IslandsOne University DriveCamarillo, CA 93012===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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 StatisticCAUTION: This email originated from outside of CSUCI. Do not click links or open attachments unless you validate the sender and know the content is safe. Please forward this email to [hidden email] if you believe this email is suspicious. For more information on how to detect Phishing scams, please visit https://www.csuci.edu/its/security/phishing.htm
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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Bruce Weaver
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