Non-parametric Testing

We use non parametric testing if it is categorical or the mean is meaningless

Non parametric test make less assumptions, so more versatile but less powerful

Chi-square test

Relies on frequency

$$x^2 = \sum{\frac{(observedcount - expectedcount)^2}{expectedcount}}$$

DF on Contingency Table

df = (r-1) x (c-1)

Mann-Whitney U Test

Similar to T-test, instead of comparing the mean it compares the median

As the median is more robust to extreme values

Test statistic: U

When to use it:

• Your data are ordinal or continuous but not normally distributed, or sample sizes are small.

• The two samples are independent of each other.

But even if two samples have the same median, they can have a different distribution

Kolmogorov-Smirnov Test

No comparisons of means or medians. Tests whether the underlying distributions are the same (whatever they might be) Simply comparing the cumulative distribution function of samples. In that sense, the Kolmogorov-Smirnov (or KS) test is a goodness-of-fit test.