hypothesis tests on non-normal data

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• #29845

rko
Member

I have two sets of time study datas taken by two different groups.  They were done on the same workers, same condition (1st shifters), and same work.  I would like to see if there is a significant difference between the two results.  I was thinking of doing a paired t-test instead of 2 sample t-test.  I first check their variances and found that they have equal variances.  Later I found that both datas are not normal.  My question is, should I proceed doing paired t?  what type of hypo test is appropriate to non-normal data like mine?  Thanks.

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#77136

Ovidiu Contras
Participant

The Mood’s median test will tell you if there’s a statistically significant difference (p-value less than 0.05) between the medians of your two populations (distributions not normal) . If you have Minitab ,go to StatNonparametrics…
Good luck

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#77138

Sridhar
Member

Hi,
How many data points you have, if you have more than 30 points you may go for t – test, i am not sure whether this is correct or not.
The other way you can use not parametric tests like Anderson Darling, Man whiteny etc. which doesn’t depend on the kind of distribution.
thanks
A.Sridhar

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#77157

FGM
Participant

Rko:
For non-normal data you should use:
Levene’s test for equal variances, and:
Mann Whitney test to compare the medians (since your data is not normal, you can not compare means)
I Have never used the Moods test, but you can try both and compare the results.
In Minitab go to Stats-Nonparametric-Mann Whitney
Hope this helps,
FGM

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#77238

Kaushik
Participant

Hi Rko!
I assume that you tried normalizing your data , inspite of which the data is non normal. Hypothesis tests such as t and ANOVA assume normality of data and hence are not appropriate when  you have non normal data.
Mood’s Median test is what you could use to test the median value of your data before and after. This test does not assume normality of data and can be used to compare your sets of data. However your sample size before and after improvement should be same, to do this test.
Let me know, if this worked!
thanks
arun

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#77239

c.t.
Participant

Hi Rko,
I will also use Mann Whitely 2 Sample t test.
You may want to read up on non-normal data here:
https://www.isixsigma.com/library/content/c020121a.asp
Hope it helps.
Best Regards,
C.T.

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#77283

Erik L
Participant

RKO,
All of the responses are good to the question.  But, I wouldn’t completely throw out the t-test as a methodology.  The t-test has been shown, in many non-normal scenarios, to give good results.  It’s always preferred to use as much of the data as possible to base your hypothesis tests on.  Devolving to non-parametric means sacrifices hard won data.  My recommendation, in situtations like this, is to run the appropriate parametric tests and use the non-parametric as a sanity check for the results of the hypothesis test.
Regards,
Erik

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#77326

DrSeuss
Participant

Point of clairification –  Kruskal Wallis vs Mood’s median
If your data has outliers, the Mood’s median will handle the data better than Kruskal Wallis.  Otherwise ether test will work for testing median differences.

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