NON PARAMETRIC TEST IN RESEARCH METHODOLOGY

1. NON PARAMETRIC TEST IN
RESEARCH METHODOLOGY
BY:
GROUP 8
ARCK SRIVASTAVA
M MAHESHWARAN
E. SANJAI KUMAR
SHADAB AZIZ
S. THIYAGARAJAN

2. Introduction
Hypothesis testing is one of the most important concepts in Statistics which is heavily used by Statisticians, Machine
Learning Engineers, and Data Scientists.
In hypothesis testing, Statistical tests are used to check whether the null hypothesis is rejected or not
rejected. These Statistical tests assume a null hypothesis of no relationship or no difference between groups. The
statistical test for hypothesis testing including both parametric and non-parametric tests.

3. Non-parametric Tests
In Non-Parametric tests, we don’t make any assumption about the parameters for the given population or
the population we are studying. In fact, these tests don’t depend on the population.
Hence, there is no fixed set of parameters is available, and also there is no distribution (normal
distribution, etc.) of any kind is available for use.
This is also the reason that nonparametric tests are also referred to as distribution-free tests.
In modern days, Non-parametric tests are gaining popularity and an impact of influence some reasons
behind this fame is –
• The main reason is that there is no need to be mannered while using parametric tests.
• The second reason is that we do not require to make assumptions about the population given (or taken)
on which we are doing the analysis.
• Most of the nonparametric tests available are very easy to apply and to understand also i.e. the
complexity is very low.

4. Non-
parametric
Tests
Kolmogorov-
Smirnov (K-
S)
Chi Square
Mann-
Whitney U
test
Wilcoxon

5. Kolmogorov–Smirnov test
In statistics, the Kolmogorov–Smirnov test (K–S test or KS test) is
a nonparametric test of the equality of continuous one-dimensional probability
distributions that can be used to compare a sample with a reference probability
distribution (one-sample K–S test), or to compare two samples (two-sample K–S
test). In essence, the test answers the question "What is the probability that this
collection of samples could have been drawn from that probability distribution?" or,
in the second case, "What is the probability that these two sets of samples were
drawn from the same (but unknown) probability distribution?". It is named
after Andrey Kolmogorov and Nikolai Smirnov.

6. CHI SQUARE
A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test that is valid to perform when the
test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and
variants thereof. Pearson's chi-squared test is used to determine whether there is a statistically
significant difference between the expected frequencies and the observed frequencies in one or more categories
of a contingency table.
In the standard applications of this test, the observations are classified into mutually exclusive classes. If the null
hypothesis that there are no differences between the classes in the population is true, the test statistic computed
from the observations follows a χ2 frequency distribution. The purpose of the test is to evaluate how likely the
observed frequencies would be assuming the null hypothesis is true.
Test statistics that follow a χ2 distribution occur when the observations are independent. There are also χ2 tests
for testing the null hypothesis of independence of a pair of random variables based on observations of the pairs.
Chi-squared tests often refers to tests for which the distribution of the test statistic approaches
the χ2 distribution asymptotically, meaning that the sampling distribution (if the null hypothesis is true) of the
test statistic approximates a chi-squared distribution more and more closely as sample sizes increase.

7. Mann-Whitney U test
The Mann-Whitney U test is used to compare differences between two independent groups when the
dependent variable is either ordinal or continuous, but not normally distributed.
For example, you could use the Mann-Whitney U test to understand whether attitudes towards pay
discrimination, where attitudes are measured on an ordinal scale, differ based on gender (i.e., your
dependent variable would be "attitudes towards pay discrimination" and your independent variable
would be "gender", which has two groups: "male" and "female").
Alternately, you could use the Mann-Whitney U test to understand whether salaries, measured on a
continuous scale, differed based on educational level (i.e., your dependent variable would be "salary"
and your independent variable would be "educational level", which has two groups: "high school"
and "university").
The Mann-Whitney U test is often considered the nonparametric alternative to the independent t-test
although this is not always the case.

8. Wilcoxon
The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used either to
test the location of a population based on a sample of data, or to compare the locations of
two populations using two matched samples.
The one-sample version serves a purpose similar to that of the one-sample Student's t-
test. For two matched samples, it is a paired difference test like the paired Student's t-test
(also known as the "t-test for matched pairs" or "t-test for dependent samples").
The Wilcoxon test can be a good alternative to the t-test when population means are not of
interest; for example, when one wishes to test whether a population's median is nonzero, or
whether there is a better than 50% chance that a sample from one population is greater than
a sample from another population.

9. CONCLUSION
In statistics, nonparametric tests are methods of statistical analysis that do not require a distribution to
meet the required assumptions to be analyzed (especially if the data is not normally distributed). Due to
this reason, they are sometimes referred to as distribution-free tests.
Nonparametric tests serve as an alternative to parametric tests such as T-test or ANOVA that can be
employed only if the underlying data satisfies certain criteria and assumptions.
Note that nonparametric tests are used as an alternative method to parametric tests, not as their substitutes.
In other words, if the data meets the required assumptions for performing the parametric tests, the relevant
parametric test must be applied.
In addition, in some cases, even if the data do not meet the necessary assumptions but the sample size of
the data is large enough, we can still apply the parametric tests instead of the nonparametric tests

10. GROUP MEMBERS:
 ARCK SRIVASTAVA
 M MAHESHWARAN
 E. SANJAI KUMAR
 SHADAB AZIZ
 S. THIYAGARAJAN