# What are the differences of the Student's T-Test, KS-Test and the MWW-Test?

I have got a question that

What are the differences of the Student's T-Test, Kolmogorov-Smirnov Test (KS-Test), and the Mann-Whitney-Wilcoxon Test (MWW-Test)?

In the case of the T-test, the null hypothesis is μ1 = μ2, indicating that the mean of feature values for class 1 is the same as the mean of the feature values for class 2. In the case of the KS-test, the null hypothesis is cdf(1) = cdf(2), meaning that feature values from both classes have an identical cumulative distribution. Both tests determine if the observed differences are statistically significant and return a score representing the probability that the null hypothesis is true (From Levner 2005).

How about the MWW-Test? Are there any assumptions of the distribution of the data for these tests?

When we want to test if there is significant difference between paired variables, which one or ones we should use?

• The t-test assumes normality and (generally) equal variance so that under the null distributions are identical, and tests against a location shift. The WMW is usually used to test a location shift with equality of distributions under the null (but without the normality assumption). However its sensitive to more general alternatives of the form $P(X>Y)\neq\frac{1}{2}$ (e.g. see Conover's Practical Nonparametric Statistics which discusses that kind of alternative). K-S also has a null of identical distributions, but its alternatives are completely general. Apr 5 '13 at 0:01
The t-test assumes normality and (generally) equal variance so that under the null distributions are identical, and tests against a location shift. The WMW is usually used to test a location shift with equality of distributions under the null (but without the normality assumption). However its sensitive to more general alternatives of the form $$P(X>Y)\not = 1/2$$ (e.g. see Conover's Practical Nonparametric Statistics which discusses that kind of alternative). K-S also has a null of identical distributions, but its alternatives are completely general. – Glen_b