To a statistician, a parameter is a measurable characteristic of a population. The population characteristics that usually interest statisticians are the location and the shape. Non-parametric statistics are used when the parameters of the population are not measurable or do not meet certain standards. In cases when the data only orders the observations, so that the interval between the observations is unknown, neither a mean nor a variance can be meaningfully computed. In such cases you need to use non-parametric tests. Because your sample does not have cardinal, or interval, data you cannot use it to estimate the mean or variance of the population, though you can make other inferences. Even if your data is cardinal, the population must be normal before the shape of the many sampling distributions are known. Fortunately, even if the population is not normal, such sampling distributions are usually close to the known shape if large samples are used. In that case, using the usual techniques is acceptable. However, if the samples are small and the population is not normal, you have to use non-parametric statistics. As you know, "there is no such thing as a free lunch". If you want to make an inference about a population without having cardinal data, or without knowing that the population is normal, or with very small samples, you will have to give up something. In general, non-parametric statistics are less precise than parametric statistics. Because you know less about the population you are trying to learn about, the inferences you make are less exact.
When either (1) the population is not normal and the samples are small, or (2) when the data is not cardinal, the same non-parametric statistics are used. Most of these tests involve ranking the members of the sample, and most involve comparing the ranking of two or more samples. Because we cannot compute meaningful sample statistics to compare to a hypothesized standard, we end up comparing two samples.
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