Hello Esra,

Goodness of fit tests, like the Kolmogorov-Smirnov (usually, with Lilliefors' correction) or the Shapiro--Wilk test, are (at least conceptually), testing all of the moments of the observed distribution vs. the target distribution. On the other hand, testing the computed skewness is evaluating just one such moment (ditto for kurtosis).

So, it's possible that the two methods (G-O-F vs. single moments) might not always agree.

Do note that, for your data set, the K-S and S-W give congruent results for all 6 comparisons. I'd be comfortable making judgments based on those results.

Good luck with your work.

Hello Esra,

Goodness of fit tests, like the Kolmogorov-Smirnov (usually, with Lilliefors' correction) or the Shapiro--Wilk test, are (at least conceptually), testing all of the moments of the observed distribution vs. the target distribution. On the other hand, testing the computed skewness is evaluating just one such moment (ditto for kurtosis).

So, it's possible that the two methods (G-O-F vs. single moments) might not always agree.

Do note that, for your data set, the K-S and S-W give congruent results for all 6 comparisons. I'd be comfortable making judgments based on those results.

Good luck with your work.

David's opinion on whether he can use Mardia kurtosis per instrument for multivariate distribution

Hello Esra Bagdere. Why are you testing for departures from normality? What is it that you ultimately want to do? Thanks for clarifying.

Since skewness uses a third power and kurtosis a fourth, these are greatly influenced by outliers and perform poorly if there are some (in the population distribution). See Article Problematic standard errors and confidence intervals for ske...

(and as others say, these and the Shapiro are testing different things so you shouldn't expect them to show the same results).

Thank you all for your answers!

Bruce Weaver I need to test for normality since I'm conducting an independent samples t-test and this is one of the assumptions I have to test before conducting the analysis.

Daniel Wright I already removed the extreme outliers, as assessed by inspection of a box plot for values greater than 1.5 box-lengths from the edge of the box. So I wonder if the outliers have anything to do with this.

David Morse , thank you. This seems very logical. But what confuses me more is that If I take a look at the normal Q-Q Plots, I only see an obvious non-normality in the applicant trait importance rating for the non-Western candidate (just as I found in the , z- value calculation of the skewness and kurtosis)

Could you maybe look along?

Thanks again for all your input!

I'd think carefully whether to remove outliers just because they have large values. On the assumptions, remember it is the distribution of the residuals. If you are worried you could use a bootstrap.

I agree with Daniel Wright, although at the risk of being pedantic, I would say it is the distribution of errors, not residuals. Even so, normality of the errors is a sufficient but not a necessary condition. As n gets large, the sampling distributions of the parameters will be approximately normal even if the errors are not. ;-)

• https://en.wikipedia.org/wiki/Errors_and_residuals
• https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/files/OLS_regression_assumptions_Wooldridge.pdf

I would also say that testing for normality as a precursor to some t-tests, ANOVA, OLS regression etc is never a great idea. Here's a short conference presentation I gave on that topic. HTH.

Presentation Silly or Pointless Things People Do When Analyzing Data: 1. ...

+1 for the title Bruce Weaver !

Bruce Weaver what does the sampling distribution bring? Perhaps unbiased standard errors, but the bias in the parameters themselves will be there no matter how big the sample...

Hi Peter. If I follow, you are disputing Jeff Wooldridge's Theorem 3.1 (slide 4 in the regression assumption slides in my earlier post), is that right? Thanks for clarifying.

Thanks everyone for the answers. Unfortunately I have to follow the study books and according to them I have to test the assumptions prior to my t-test.

Basically, the only thing I need to know is in which cases I have violated the assumption of normality (according to Z-values and Q-Q plots only in 1 case, while according to Shapiro Wilk in 5 cases).

In my thesis I wrote the following about this: (this is the part I have doubts about whether I have used the correct method):

Various methods for normality testing were used to assess whether the applicant rating scores for each level of the candidate (Western and non-Western) were normally distributed. To assess normality within the total sample (N = > 50), Normal Q-Q Plots were visually inspected, and z-scores were calculated by dividing the skewness and kurtosis values by their respective standard errors. Mayers (2013) suggested that a cutoff of ±2.58 should be used for samples from 51 to 100 participants. Applicant rating scores for each level of the candidate (Western and non-Western) were normally distributed, except for the applicant trait importance rating of the non-Western applicants with a skewness of -.92 (SE = .28) and kurtosis of 1.68 (SE = .56).

So I only want to know whether I should write down the results like I did in the paragraph above. OR that I should say something like:

Within the total sample, all applicant rating scores for each level of the candidate (Western and non-Western) violated the assumption of normality, as assessed by Shapiro-Wilk’s test (p < .05), except for the credential rating of the non-Western candidate.

That's all I want to know. Thanks!

Attached are the examples I need to follow according to my text books.

Hello Esra Bagdere.Are those screenshots from this document?

• https://www.scribd.com/document/359501508/One-Way-Anova-docx

I get only a very limited view of it.

Hi Bruce Weaver no its From Laerd Statistics.

https://statistics.laerd.com/spss-tutorials/independent-t-test-using-spss-statistics.php?utm_expid=.W48sSL-4Q7SwV9tvQsA1jA.0&utm_referrer=https%3A%2F%2Fwww.google.nl%2F

I do have a premium version though. Thats why I have acces to all information . Also the information on the Laerd Statistics website is completely in line with (and completing) my own study book : J. Pallant. SPSS survival manual (4th edition). Which I have to use for my analyses.