A statistical test is a formal technique, for arriving at a decision about the reasonableness of a hypothesis, based on some probability distribution.
The test technique uses the values obtained from sample data to arrive at a probability statement about the hypothesis. But it also uses some assertions about the population from which the sample is drawn.
Some of the important assumptions are like:
Population is normally distributed
Sample drawn is a random sample
But in case of Non-parametric tests, no such assumptions are made.
In a Statistical Test, 2 kinds of assertions are involved. An assertion directly related to the purpose of investigation.
𝐻_0: There is no difference between the perceived quality of two samples.
𝐻_𝑎: There is difference between the perceived quality of two samples.
When we apply a test without a model, it is called as distribution-free test or non-parametric test. Non-parametric tests do not make an assumptions about the parameters of the population and thus do not use parameters of the distribution.
There is growing use of these non-parametric tests where normality assumption is open to doubt.
Many distribution-free tests have been developed that do not depend on the parameters of the population or shape of the distribution.
One of these non-parametric tests type is Rank Sum Tests.
Rank Sum tests are a whole family of tests, but only 2 such tests are commonly used.
U-Test (popularly known as Wilcoxon-Mann-Whitney Test)
H-Test (also known as Kruskal-Wallis Test)
Very popular test among Rank Sum Tests, to determine whether 2 independent samples have been drawn from the same population or not
Uses more information than Sign test or Fisher-Irwin Test, applies under very general conditions
To perform this test, rank the data jointly, taking them as single sample, in either increasing or decreasing order of magnitude.
Find sum of the ranks assigned to the values of 1st sample (denoted as...
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