I am not hard statistics student. I just want to know what is the underlying idea behind non-parametric test. Without assuming any distribution about the data,how can we perform various statistical test ? I just want to know how these test work and whats are their utilities ?
Please try to avoid unnecessary mathematics. Same example with parametric and non parametric test would be helpful.
Thanks
Your question is answered well, for one large class of tests, on this page. As long as you can rank-order observations, you can base tests on the probabilities of different rank-orderings. The resulting tests depend only on binomial or similar statistics based on things like pair-wise comparisons, rather than the specifics of the distributions from which the samples were taken. So for comparing two sets of measurements, say group A versus group B, you can examine the probability that each particular value in A is greater than a value in B, and vice versa. If groups A and B have the same distribution, then neither group should dominate the other. That's the basis of the Mann-Whitney test discussed on the page linked above.
Another approach is to accept the samples that you have as the best available estimates of the underlying distributions and to resample repeatedly (with replacement) to see how frequently, say, the mean of a new sample from group A exceeds that of a new sample from group B among hundreds to thousands of resamples. That's bootstrapping, frequently discussed on this site.
The fundamental construction of any frequentist test is to compare the estimated effect to its distribution under the null assumption.
Permutation tests compare the estimated effect to this null distribution in a particular class of events: those that have equal probability under the null. This is why you don't really need to assume the sampling distribution. You do however, need weaker assumptions on the symmetries of the sampling distribution, required to identify this set of events with equal probability under the null.
