Mann Whitney Test or Kolmogorov Smirnov Test

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11-02-2006 06:46 AM

mann whitney test or Kolmogorov smirnov test?

I'm working with nonparametric methods tocompare two samplesand detect diferencesbetween them. I usedthe mann-whitneytest and obtained, forall the variables, pvalues less than 0,05but when i used theKS test i found, fortwo of the fourvariables, p valueswith more than 0.05.I would like to knowwhich test is better?Or there some problemthat i'm not able tocapture?

Thank for any help? Marge.

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Marga

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11-02-2006 12:05 PM

These two tests serve entirely different purposes, so I'm not surewhat you're trying to do. The Mann-Whitney is a nonparametricversion of the t-test, checking for a significant difference in groupmedians. The K-S test is a goodness-of-fit test (i.e., is the sampledistribution a close approximation to the normal distribution).

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11-02-2006 12:23 PM

Hi!The KS test i refer in the initial question is the ks test for twoindependent samples. I wish to know if there exists differencesbetween two samples. In SPSS, for two independent samples, ihave choosen the mann-whitney test (location) and the KS test(shape) but for the first test all the variables have pvalues lessthan 0.05 and for the second test just two variables presentspvalues less than 0.05.

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Marga Originally Posted by JohnM

These two tests serve entirely different purposes, so I'm notsure what you're trying to do. The Mann-Whitney is anonparametric version of the t-test, checking for a significantdifference in group medians. The K-S test is a goodness-of-fittest (i.e., is the sample distribution a close approximation to thenormal distribution).


11-02-2006 12:57 PM

OK - it simply means that for all the variables, the two groups differon location, but only 2 of them differ on shape.

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11-02-2006 01:50 PM

THANKS! It´s really good to know that there's somebody to help!So i think i can use both tests and no one is preferable to another,or not?

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11-02-2006 02:12 PM #6



You can use both tests, but keep in mind that they test fordifferent things, one is for location, the other is for shape.

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11-02-2006 10:23 PM

Hellosorry , your answer is not true, please attend that k-s test is fortesting normality but mann whitney is for comparing twoindependent population.

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11-03-2006 08:56 AM

Yes, it is true. K-S can be used to compare the shapes of twodistributions - here's a link that proves it.

http://www.physics.csbsju.edu/stats/KS-test.html

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11-06-2006 11:48 PM

helloyour speeches is true if distribution of population exactly be known,but you know there is many density function that we dont knowthem , we know e.g : normal ,gamma,poisson , ...and k-s test do test for famouse distribution , but in campare meanproblems in nonparametric we dont know about type of density,that is free of distribution, then when we dont know about type ofdistribution , we should do nonparametric test not k-s test(we dok-s for limitary distribution )

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11-07-2006 12:11 PM

I'm sorry, but I have to disagree.

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11-08-2006 10:05 PM

no no no problem

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01-13-2007 09:38 AM

According to Siegel (1956), "the two-tailed test is sensitive to anykind of difference in the distributions from which the two sampleswere drawn" (p. 126).

The test compares the cumulative frequencies of the two samples.If there is a significant difference at any point, then the nullhypothesis will be rejected.

The M-W test focuses on central tendency while the K-S is anomnibus test. Like JohnM wrote, the test will be appropriatedepending on your research question(s).

Siegel, S. (1956). Nonparametric statistics for the behavioralsciences. New York: McGraw-Hill.

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01-18-2007 02:25 PM

Thanks for the reference!Really what i was trying to demonstrate is that it exists differencesbetween two small groups, regarding performance variables. Oneassumption of the Mann-whitney test is that the two distributionsmust be similar in shape. According instructions of the SPSS, theKS test for two independent samples can be useful to validate ornot that assumption.Am I right? Thanks for your help,Margue

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01-18-2007 10:43 PM

In the British Medical Journal, Hart (2001) states that "the Mann-Whitney test is a test of both location and shape" (see:http://www.bmj.com/cgi/content/full/323/7309/391).

For complicating the matter, the K-S tests both difference in size,dispersion and in central tendency. Some call it an omnibus test,because it compares different aspects of the distributions ofinterest. "The K-S test [...] is sensitive to any kind of distributionaldifference" (Sheskin, 2004, p. 453). This means central tendency,variability, skewness and kurtosis.

So, the K-S doesn't test only the difference in shape. Furthermore,a nonsignificant result could be be caused by a low power. This is acause of concern withe the K-S test.

I wonder if an exploratory analysis of the shape, along withreporting skewness and kurtosis could be sufficient to verify theassumption of similarity between distributions.

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01-19-2007 04:06 PM

Thanks! i use the box plots to explore tha shape as well as some

descriptive statistics, as you recomend!!!

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