Non-parametric statistics is a branch of statistics that does not require data to be normally distributed. It can be used with ordinal or ranked data and does not assume a particular distribution shape or require parameters like the mean or standard deviation. Common non-parametric tests include rank sum tests like the Wilcoxon-Mann-Whitney U test and the Kruskal-Wallis H test, the chi-square test, and Spearman's rank correlation test. These tests make fewer assumptions about the underlying data distribution compared to parametric tests.

2. Non-parametric statistics test
Non-parametric statistics is the branch of statistics. It
refers to a statistical method in which the data is not required
to fit a normal distribution. Nonparametric statistics uses data
that is often ordinal, meaning it does not rely on numbers,
but rather a ranking or order of sorts.
For example: a survey conveying consumer preferences
ranging from like to dislike would be considered ordinal data.
Nonparametric statistics does not assume that data is
drawn from a normal distribution. Instead, the shape of the
distribution is estimated under this form of statistical
measurements like descriptive statistics, statistical test,
inference statistics and models. There is no assumption of
sample size because it’s observed data is quantitative.

3. This type of statistics can be used without the mean,
sample size, standard deviation or estimation of any other
parameters.
The non-parametric test are called as “distribution-free” test since
they make no assumptions regarding the population distribution.
It is test may be applied ranking test. They are easier to explain
and easier to understand but one should not forget the fact that
they usually less efficient/powerful as they are based on no
assumptions. Non-parametric test is always valid, but not always
efficient.
Types of Non-parametric statistics test
 Rank sum test
 Chi-square test
 Spearman’s rank correlation

4. Rank sum test
Rank sum tests are
U test (Wilcoxon-Mann-Whitney test)
H test (Kruskal-Wallis test)
U test: It is a non-parametric test. This test is
determine whether two independent samples have
been drawn from the same population. The data
that can be ranked i.e., order from lowest to highest
(ordinal data).

5. U test
For example
The values of one sample 53,
38, 69, 57, 46
The values of another sample
44, 40, 61, 53, 32
We assign the ranks to all
observations, adopting low to
high ranking process and
given items belong to a single
sample.
Size of sample in ascending
order
Rank
32 1
38 2
40 3
44 4
46 5
53 6.5
53 6.5
57 8
61 9
69 10

6. Kruskal-Wallis H test
 H test: The Kruskal-Wallis H test (also called as the “one-
Way ANOVA on ranks”) is a rank-based non parametric test
that can be used to determine if there are statistically
significant difference between two or more groups of an
independent variable on a continuous or ordinal
dependent variable.
For example: H test to understand whether exam
performance, measured on a continuous scale from 0-100,
differed based on test anxiety levels(i.e., dependent variable
would be “exam performance” and independent variable
would be “test axiety level”, which has three independent
groups: students with “low”, “medium” and “high” test
anxiety levels).

7. Chi square test
The chi-square test is a non-parametric test. It is used mainly when
dealing with a nominal variable. The chi-square test is mainly 2
methods.
 Goodness of fit: Goodness of fit refers to whether a significant
difference exists between an observed number and an expected
number of responses, people or other objects.
For example: suppose that we flip a coin 20 times and record the
frequency of occurrence of heads and tails. Then we should expect 10
heads and 10 tails.
Let us suppose our coin-flipping experiment yielded 12 heads and 8
tails. Our expected frequencies (10-10) and our observed frequencies
(12-8).
 Independence: the independence of test is difference between the
frequencies of occurrence in two or more categories with two or
more groups.

8. Spearman’s rank correlation test-In this method a measure of association that
is based on the ranks of the observations and not on the numerical values of the data.
It was developed by famous Charles spearman in the early 1990s and such it is also
known as spearman’s rank correlation co-efficient.
English (marks) Maths (marks) Rank (English) Rank (maths) Difference of
ranks
56 66 9 4 5
75 70 3 2 1
45 40 10 10 0
71 60 4 7 3
62 65 6 5 1
64 56 5 9 16
58 59 8 8 0
80 77 1 1 0
76 67 2 3 1
61 63 7 6 1