The Basis of Non-parametric Tests

Conceptual Understanding

These tests are also known as distribution-free tests as they do not rely on certain distributional assumptions.
They make minimal assumptions about the nature or parameters of the population distribution such as its mean or standard deviation.
Their aim is to test hypotheses which are not about specific parameters (i.e., non-parametric).

Non-parametric tests are applicable to ordinal, nominal, and ranked data.
They are not restricted to numeric data, and can also be used with categorical data.
However, they require that the data is measurable.

They are especially useful when the assumptions of parametric counterparts, like t-tests or ANOVA, are violated.
It’s suitable if the data isn’t normally distributed or if there’s non-constant variability.
They’re a good fit if there are outliers present in the data, as they’re less sensitive to them.
They also provide an avenue when the data is on a rank, score, or ordinal scale.

Non-parametric tests generally function by ranking the data from smallest to largest and evaluating the ranks.
These tests focus more on the order or ranking of data rather than the specific data values themselves.
They’re essentially comparing the median rather than the mean values, making them resistant to outliers.

A drawback is that non-parametric tests can be less powerful than their parametric counterparts. This means they are sometimes unable to detect a significant effect even if it truly exists.
Another limitation is that they cannot provide detailed insight into the differences between groups compared to parametric tests.
Lastly, while they avoid a few assumptions, they still require certain assumptions to be met (like homogeneous variance or independent observations), hence are not completely assumption-free.