# Thread: mann whitney test or Kolmogorov smirnov test?

1. ## mann whitney test or Kolmogorov smirnov test?

I'm working with non parametric methods to compare two samples and detect diferences between them. I used the mann-whitney test and obtained, for all the variables, p values less than 0,05 but when i used the KS test i found, for two of the four variables, p values with more than 0.05.
I would like to know which test is better? Or there some problem that i'm not able to capture?
Thank for any help?
Marge.

2. These two tests serve entirely different purposes, so I'm not sure what you're trying to do. The Mann-Whitney is a nonparametric version of the t-test, checking for a significant difference in group medians. The K-S test is a goodness-of-fit test (i.e., is the sample distribution a close approximation to the normal distribution).

3. Originally Posted by JohnM
These two tests serve entirely different purposes, so I'm not sure what you're trying to do. The Mann-Whitney is a nonparametric version of the t-test, checking for a significant difference in group medians. The K-S test is a goodness-of-fit test (i.e., is the sample distribution a close approximation to the normal distribution).
Hi!
The KS test i refer in the initial question is the ks test for two independent samples. I wish to know if there exists differences between two samples. In SPSS, for two independent samples, i have choosen the mann-whitney test (location) and the KS test (shape) but for the first test all the variables have pvalues less than 0.05 and for the second test just two variables presents pvalues less than 0.05.

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

5. 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?

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

7. Hello
sorry , your answer is not true, please attend that k-s test is for testing normality but mann whitney is for comparing two independent population.

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

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

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

10. I'm sorry, but I have to disagree.

11. no no
no problem

12. According to Siegel (1956), "the two-tailed test is sensitive to any kind of difference in the distributions from which the two samples were drawn" (p. 126).

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

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

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

13. Thanks for the reference!
Really what i was trying to demonstrate is that it exists differences between two small groups, regarding performance variables. One assumption of the Mann-whitney test is that the two distributions must be similar in shape. According instructions of the SPSS, the KS test for two independent samples can be useful to validate or not that assumption.
Am I right?
Margue

14. 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 of interest. "The K-S test [...] is sensitive to any kind of distributional difference" (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 a cause of concern withe the K-S test.

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

15. Thanks! i use the box plots to explore tha shape as well as some descriptive statistics, as you recomend!!!