Statistical tests typically make simplifying assumptions about the data they operate on - for example, they may require it to be normally distributed. Most common tests are fairly robust in the face of minor deviations from these assumptions, however the results can be unreliable if the data are substantially different.
This often occurs if:
Non-parametric tests address this problem by making fewer assumptions about the data. Typically they consider the relative order (ranking) of the data points rather than the values themselves.
This allows them to model more general situations, however it sacrifices power. An equivalent parametric test will tend to give a stronger result, if its assumptions are satisfied.
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