In this article, I will teach you about Non-Parametric Tests. Types of non-parametric tests and Overview of Non-Parametric Tests.
A non-parametric test (sometimes called a distribution-free test) is a test that does not assume anything about the underlying
distribution.
They are
called distribution-free statistics because they are not constrained by assumptions
about the distribution of the population. Consequently, they can easily
accommodate data that have a wide range of variance.
·
When the word “non-parametric” is used in
stats, it doesn’t quite mean that we know nothing about the population. It usually
means that we know the population data does not have a normal distribution.
·
For example, one assumption for the one-way
ANOVA is that the data comes from a normal distribution. If your data isn’t
normally distributed, you can’t run an ANOVA, but you can run the non-parametric
alternative the ‘Kruskal Wallis test’.
·
Non-parametric tests can perform well with
non-normal continuous data, if we have a sufficiently large sample size
(generally 15-20 items in each group).
·
Non-parametric tests are used when your
data isn’t normal.
·
For nominal scales or ordinal scales,
we use non-parametric statistics.
Types of Non-Parametric Tests:
The main non-parametric tests are:
SignTest:
The Sign test is a non-parametric test that
is used to test whether two groups are equally sized. The sign test is used
when dependent samples are ordered in pairs.
Wilcoxon Signed-Rank Test:
The Wilcoxon test, which refers to either
the Rank Sum test or the Signed Rank test, is a non-parametric statistical test
that compares two paired groups. The test essentially calculates the difference
between each set of pairs and analyzes these differences.
For example, we can use a Wilcoxon signed-rank test to
understand whether there was a difference in smokers' daily cigarette
consumption before and after a 6-week hypnotherapy program.
Friedman Test:
This test is used to test for differences
between groups with ordinal dependent variables. It can also be used for
continuous data if the one-way ANOVA with repeated measures is inappropriate (i.e.,
some assumption has been violated).
Goodman Kruska’s Gamma:
Goodman Kruskal's gamma is a non-parametric
measure of the strength and direction of association that exists between two
variables measured on an ordinal scale. For example, Goodman Kruskal's
gamma is used to understand whether there is an association between test
anxiety and exam duration.
Kruskal-Wallis Test:
The Kruskal-Wallis H test (sometimes also
called the "one-way ANOVA on ranks") is a rank-based nonparametric
test that can be used to determine if there are statistically significant
differences between two or more groups of an independent variable on a continuous
or ordinal dependent variable. It is considered the non-parametric alternative
to the one-way ANOVA, and an extension of the Mann-Whitney U test to allow the
comparison of more than two independent groups. For example, we can use a
Kruskal-Wallis H test to understand whether exam performance, measured on a
continuous scale from 0-100, differed based on test anxiety levels.
Mann-Kendall Trend Test:
The Mann-Kendall trend test (sometimes
called the M-K Test) is used to analyze data collected over time
for consistently increasing or decreasing trends in Y values.
Mann-Whitney 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.
Mood’s Median test:
Mood’s median test is used to compare the medians
for two samples to find out if they are different. For example,
comparing the medians of the monthly satisfaction ratings (Y) of six customers
(X) over the last two years.
Spearman Rank Correlation:
Spearman's Rank Correlation is a
non-parametric test used to measure the strength of
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