**Key Points:**

- Non-parametric tests are statistical processes that do not rely on specific data distribution assumptions, making them more versatile and resilient than parametric tests.
- They may analyze variables measured on an ordinal, interval, or nominal scale. They are especially effective when data contradicts assumptions such as normality or equal variances.
- Non-parametric tests, such as the Mann-Whitney U Test, Kruskal-Wallis Test, Spearman's Rank-Order Correlation, and the Chi-Square Test, serve distinct objectives and analyze different data types.
- Non-parametric tests provide advantages such as applying to any data, being resistant to violations of distributional assumptions, and being trustworthy with small sample sizes.
- While non-parametric tests have less power than parametric tests when assumptions are satisfied, they give valuable insights into connections, group comparisons, and hypothesis testing without jeopardizing the analysis's integrity.

**Introduction to
Non-Parametric Tests**

Parametric tests in statistical analysis frequently rely on presumptions
about the data, including normality or equal variances. These presumptions
could, however, only seldom be true in practical situations this situation
Non-parametric testing is useful. Non-parametric tests provide alternative
statistical techniques without particular population distribution assumptions.
These tests are adaptable and reliable, making them appropriate for various
data types and research contexts.

#### Definition

Non-parametric tests, often distribution-free, are statistical techniques
that need fewer data assumptions than parametric tests. These tests use rank or
categorical data. They may do ordinal, interval, or nominal scale analysis on
variables. Unlike parametric tests, non-parametric tests do not presuppose a specific
distribution in the data, such as normal distribution or equal variances.

The phrase "non-parametric test" has recognized relevance in statistics.
It refers to a group of statistical approaches that make no assumptions about
the population distribution's characteristics. The dictionary definition of a non-parametric
test is consistent with the prior discussion, emphasizing the absence of
particular assumptions about the form or features of the population
distribution.

#### Statistics

Non-parametric tests are essential in statistical analysis, especially
when the data violates the assumptions of parametric tests, such as normality
or variance homogeneity. These tests include the Mann-Whitney U test, the
Wilcoxon signed-rank test, the Kruskal-Wallis test, and Spearman's rank
correlation coefficient. Non-parametric tests using ranks or distribution-free
procedures give alternatives to their parametric equivalents, such as the
independent t-test, paired t-test, analysis of variance (ANOVA), and Pearson's
correlation coefficient.

#### Psychology

Non-parametric tests are commonly used in psychology, particularly when
analyzing data from experiments or surveys. They are beneficial when dealing
with data measured on ordinal scales or not regularly distributed data. Psychologists
frequently use non-parametric tests to compare medians, test for differences
across groups, examine correlations between variables, or analyze ranked data.

### Understanding the Purpose of Non-Parametric Tests

Non-parametric tests are used for a variety of applications in statistical analysis. They are frequently used in the following contexts:

- Data violates parametric test assumptions, such as normality or variance homogeneity.
- Data is ordinal or nominal scale.
- Small Sample size.
- The data contains outliers.

In these cases, non-parametric tests provide a viable alternative,
allowing researchers to make legitimate results without jeopardizing the
correctness of their investigation.

### Types of Non-Parametric Tests

Non-parametric tests encompass various techniques, each designed for specific research scenarios. Here is a list of commonly used non-parametric tests:

- Mann-Whitney U test
- Wilcoxon signed-rank test
- Kruskal-Wallis test
- Friedman test
- Spearman's rank correlation coefficient
- Kendall's rank correlation coefficient
- Runs test
- McNemar's Test
- Kolmogorov-Smirnov test
- Chi-square test for independence
- McNemar's test
- Median test

#### 1. Mann-Whitney U Test

The Mann-Whitney U test, or the Wilcoxon rank-sum test, compares two
independent groups. It assesses whether the distributions of the two groups
differ significantly. The test uses the ranks of the observations to make the
comparison.

Consider
comparing the efficacy of two different weight loss programs. Participants can
be assigned to either Programme A or Programme B at random. You gather weight
loss data from both groups at the end of the trial. The Mann-Whitney U test can examine whether the two programs have a statistically significant
difference in weight reduction.

#### 2. Wilcoxon Signed-Rank Test

The Wilcoxon signed-rank test is used when analyzing paired data. It
determines whether the medians of two related groups are significantly different.
The test compares the differences between the paired observations using their
ranks.

Assume you're looking at the effect of a new teaching approach on
pupils' test results. You give the same set of pupils a pre-test and a
post-test. The Wilcoxon signed-rank test can assess whether there is a
significant change in the students' results before and after implementing the
new teaching approach.

#### 3. Kruskal-Wallis Test

The Kruskal-Wallis test is a non-parametric alternative to one-way
analysis of variance (ANOVA). It compares three or more independent groups to
determine if there are significant differences among the medians.

Assume you wish to compare the degrees of pain experienced by patients
who got one of three different pain management treatments: drug A, medication
B, and a placebo. You assess the pain levels of each group of patients and
apply the Kruskal-Wallis test to see if there are any significant variations in
pain reduction between the three therapies.

#### 4. Friedman Test

The Friedman test is a non-parametric alternative to repeated measures
ANOVA. It compares three or more related groups to determine if there are
significant differences in the distributions.

Consider the following scenario: you wish to assess participants'
preferences for three distinct flavors of ice cream: chocolate, vanilla, and
strawberry. You invite each participant to rate their favorite flavors in order
of importance. The Friedman test can assess whether there is a statistically
significant difference in preference rankings between the three flavors.

#### 5. Spearman's Rank-Order Correlation

Spearman's
rank-order correlation measures the degree and direction of a monotonic link
between two variables. It is employed when the data is ordinal, or Pearson's
correlation assumptions are unsatisfied.

Assume you're researching the association between students' study hours
and exam grades. You gather information on the number of study hours and exam
grades for a set of pupils. Regardless of the detailed quantitative data,
Spearman's rank correlation coefficient may assess if there is a significant
association between study hours and exam grades.

#### 6. Kendall's Rank Correlation

Kendall's rank correlation is another way to determine the relationship
between two variables. When the data contains ties, it determines the strength
and direction of the rank-order connection.

Consider analyzing consumer preference rankings for three smartphone
brands: Brand X, Brand Y, and Brand Z. Every consumer ranks their favorite
brand. Kendall's rank correlation coefficient may determine the degree of
agreement or relationship between customer ranks and smartphone brands.

#### 7. Chi-Square Test

The chi-square test is used to determine the independence of two categorical
variables. It examines the observed and predicted frequencies to see if there
is a meaningful link.

Assume you want to see if there is a link between smoking status
(smoker/nonsmoker) and the occurrence of lung cancer. You collect data from a
sample of people and apply the chi-square test for independence to see if there
is a link between smoking status and the prevalence of lung cancer.

#### 8. McNemar's Test

McNemar's test evaluates the proportional difference in paired nominal
data. It is frequently used when comparing data before and after an
intervention or therapy.

Consider the following scenario: you want to evaluate the success of a
new advertising campaign. You poll a group of customers before and after the drive
to see if they are familiar with the brand. McNemar's test can assess whether
there is a statistically significant difference in brand awareness before and
after the promotion.

#### 9. Sign test

The sign test is a basic non-parametric test that compares the medians
of two related samples. It is useful when the data is ordinal or highly skewed.

Assume you wish to assess the new medicine's effectiveness in lowering pain symptoms. You gather a group of patients and consider their pain levels before and after they take the drug. The Sign Test can detect whether there is a substantial improvement in pain levels following drug administration. When the data is paired and non-parametric, this test is ideal for circumstances when the data does not fit the assumptions of parametric tests.

#### 10. Runs test

The run test determines if data values are random or independent. It
controls whether the observations alternate or cluster non-randomly.

Assume you're looking at the incidence of "hot streaks" in a
basketball player's performance. During a series of games, you note whether the
player makes a successful shot or misses a shot. The run test can identify if
the player's performance has a strong pattern or streak.

#### 11. Median Test

The median test compares two or more independent groups' medians. It
assesses whether or not there are substantial differences in medians without
making any assumptions about the underlying distribution.

Consider comparing the median wages of two separate cities, City A and
City B. You collect income information from a random sample of people in each town.
The Median Test may be used to see if there is a statistically significant
difference in median income between the two cities. This test is especially
beneficial when the data is skewed or does not follow a normal distribution.

#### 12. Kolmogorov-Smirnov test

The Kolmogorov-Smirnov test is a non-parametric statistical test that
compares a sample's distribution to a known distribution or two independent
models. It is based on the most significant difference under the null
hypothesis between the empirical cumulative distribution function (ECDF) of the
sample(s) and the theoretical cumulative distribution function (CDF).

Assume you are a researcher looking into the heights of adult males in a
specific population. You may want to know if the height distribution is normally
distributed. You collect heights from a random sample of people and want to see
how well they fit a normal distribution.

### Example of Non-Parametric Test

Consider
the following scenario: a researcher wants to compare the effects of two
different teaching methods on student performance. Instead of assuming normally
distributed data and equal variances, the researcher can apply the
non-parametric Mann-Whitney U test to determine whether there is a significant
difference in median scores between the two groups.

### Examples of Parametric Tests

While non-parametric tests provide greater flexibility in statistical analysis, parametric tests must also be understood. Metric tests assume the distributional features of the data. Parametric testing includes the following:

- The t-test for students
- ANOVA (Analysis of Variance)
- Pearson's coefficient of correlation
- Regression linear
- The paired t-test

When the assumptions are satisfied, the Chi-square test for independence is used. Parametric tests are frequently employed, although they are sensitive to changes in underlying assumptions. Non-parametric tests give a credible alternative when the data violates these assumptions.

**You may want to read this post :**

### Difference between Parametric and Non-Parametric Tests

The primary distinction between parametric and non-parametric tests is
in their data assumptions. Specific distributions, such as the normal
distribution and equal variances, are assumed by parametric tests.
Non-parametric tests, on the other hand, depend on rankings or categorical data
and make fewer assumptions. When the premises are satisfied, non-parametric
tests are frequently regarded as more robust. However, they may have lower
power than parametric tests.

### Advantages and Limitations of Non-Parametric Tests

In statistical analysis, non-parametric tests have various advantages:

- Any kind of data, including ordinal and nominal scales.
- Normal distributional assumptions are being violated.
- Small sample numbers produce accurate findings.
- Adaptable and may be used in a variety of study domains.

Non-parametric tests, on the other hand, have limitations:

- Have less power than parametric tests when the latter's assumptions are satisfied.
- They may not give particular parameters or extensive information about the underlying distribution.
- They need higher sample numbers to get the same degree of power as parametric tests.

### Non-Parametric Test for ANOVA

The Kruskal-Wallis test is a non-parametric version
of one-way ANOVA that allows researchers to determine if there are significant
differences between groups based on rankings rather than averages.

### Softwares

Several software programs are regularly used for parametric testing and
statistical analysis. Here's a rundown of some prominent software solutions,
along with their benefits and drawbacks:

#### SPSS (Statistical Package for the Social Sciences)

SPSS is a popular
statistical software program noted for its user-friendly interface and broad
statistical features. It includes a variety of parametric tests and data
analysis processes, making it appropriate for fundamental and sophisticated
statistical analysis. SPSS also includes data visualization and reporting
tools.

**Limitations**: SPSS
can be costly, particularly for individual users. The learning curve may be
longer for users new to statistical software. Furthermore, specific complex
statistical approaches may necessitate extra modules or programming abilities.

#### R or Rstudio, R Langauge

R is a statistical
programming language and software environment that is free and open source. It
includes many tools and libraries for performing parametric tests and
sophisticated statistical analysis. R is adaptable, allowing users to customize
and increase its features. It has a large and active user base and is
frequently utilized in academics and research.

**Limitations**: R needs
some programming skills, which may be difficult for people who have never coded.
Compared to other software programs, it may have a higher learning curve.
Furthermore, its graphical user interface (GUI) may need to be more user-friendly than other
specialist statistical tools.

#### Stata

Stata is a
sophisticated statistical software program noted for its simplicity and
user-friendly interface. It offers a diverse set of parametric tests and
statistical models. Stata facilitates repeatable research and has high-quality
graphical capabilities. It is frequently utilized in various domains, such as
social sciences, epidemiology, and economics.

Limitations: Stata
can be costly, especially for individual users or small research projects. Some
complex statistical approaches may necessitate the purchase of extra modules or
licenses. Stata's programming language may have a significantly higher learning
curve when compared to similar tools.

#### Conclusion

Non-parametric tests are valuable tools in statistical analysis because
they give researchers flexibility and resilience when data violates parametric
assumptions. Understanding the purpose, kinds, and differences between
parametric and non-parametric tests allows researchers to select the best
statistical strategy depending on their data characteristics and research aims.
Using non-parametric tests broadens the statistical analysis toolbox, enabling
accurate findings and valuable insights even when stringent assumptions are not
used.

### Frequently Asked Questions (FAQs)

**Can
non-parametric tests be used with continuous data?**

Yes,
non-parametric tests can be used with continuous data. They rely on ranks or
transformations of the data and are not limited to specific types of variables.

**Are
non-parametric tests less potent than parametric tests?**

Non-parametric
tests may have lower power when the latter's assumptions are met. However, they
offer robustness in situations where the premises are violated.

**How
do I choose between a parametric and a non-parametric test?**

The
choice between parametric and non-parametric tests depends on the data's nature
and the tests' assumptions. Suppose the data violate the assumptions of parametric tests or are measured on
ordinal/nominal scales. In that case, non-parametric tests are a suitable
choice.

**Can
non-parametric tests be used for hypothesis testing?**

Yes,
non-parametric tests can be used for hypothesis testing. They provide p-values
and test statistics, allowing researchers to draw inferences.

**What
are the 4 non-parametric tests?**

The
four common non-parametric tests are:

1. Mann-Whitney U test

2. Wilcoxon signed-rank test

3. Kruskal-Wallis test

4. Friedman test

**What
is an example of a non-parametric t-test?**

A
non-parametric equivalent of the t-test is the Wilcoxon signed-rank test. It is
used when comparing two related groups or paired observations.

**Is
chi-square a non-parametric test?**

The
chi-square test is a non-parametric test commonly used to assess the
association between categorical variables.

**Is
ANOVA a non-parametric test?**

No,
ANOVA (Analysis of Variance) is a parametric test that compares the means of
three or more groups.

**Is
Kruskal-Wallis a non-parametric test?**

The
Kruskal-Wallis test is a non-parametric test used to compare three or more
independent groups.

**Is
ANOVA a parametric test?**

Yes,
ANOVA is a parametric test used to compare the means of three or more groups
based on the assumption of normality and equal variances.

**How
do you know if a test is non-parametric?**

A
test is considered non-parametric if it does not assume a specific probability
distribution for the population or if it makes fewer distributional
assumptions.

**Is an
independent t-test a non-parametric test?**

The
independent t-test is a parametric test used to compare means between two separate
groups.

**What
makes a test non-parametric?**

A
test is considered non-parametric if it does not assume a specific probability
distribution or makes fewer distributional assumptions than parametric tests.

**What
is the most common non-parametric test?**

The
Mann-Whitney U test, or the Wilcoxon rank-sum test, is one of the most common
non-parametric tests used to compare two independent groups.

**What
is the most commonly used non-parametric test?**

The
chi-square test is one of the most commonly used non-parametric tests to
analyze categorical data.

**What
is an example of non-parametric data?**

Non-parametric
data refers to data that do not have a specific distributional assumption.
Examples include rankings, categorical data, or data measured on an ordinal
scale.

**Is
ANOVA a parametric or non-parametric test?**

ANOVA
is a parametric test that compares the means of three or more groups, making
assumptions about normality and equal variances.

**Is
regression a non-parametric test?**

Regression
analysis is a parametric method used to model the relationship between a
dependent variable and one or more independent variables.

**Is the
Mann-Whitney test non-parametric?**

Yes,
the Mann-Whitney U test is a non-parametric test used to compare two
independent groups when the assumptions of parametric tests are not met.

**What
is the simplest non-parametric test?**

The
sign test is considered one of the simplest non-parametric tests. It is used to
assess whether the median of a single sample differs from a hypothesized value.

**What
data type is a non-parametric test?**

Non-parametric
tests can be applied to both continuous and categorical data types. However,
they are more commonly used with ordinal or categorical data.

**What
is a one-sample non-parametric test?**

One-sample
non-parametric tests compare a sample distribution against a known or
hypothesized distribution without assuming a specific underlying population distribution.

**What
are the two kinds of non-parametric tests?**

The
two main non-parametric tests are tests for independent samples and tests for
related or paired samples.

**Why
not use the chi-square test?**

The
chi-square test is unsuitable for specific situations, such as small sample
sizes or low expected cell counts. In such cases, alternative non-parametric
tests may be more appropriate.

**What
is the difference between parametric and non-parametric tests?**

Parametric
tests assume specific population distributions and make assumptions about
parameters, such as means and variances. Non-parametric tests do not rely on
these assumptions. They are more flexible in analyzing data that do not meet
parametric assumptions.

**Is
Spearman's test non-parametric?**

Yes,
Spearman's rank correlation coefficient is a non-parametric test used to assess
the strength and direction of the monotonic relationship between two variables.

**Is
Pearson's test non-parametric?**

No,
Pearson's correlation coefficient is a parametric test used to measure the
linear relationship between two continuous variables.

**Can
I use ANOVA for non-parametric data?**

No,
ANOVA assumes normality and equal variances, so it is inappropriate for
non-parametric data. Non-parametric alternatives like the Kruskal-Wallis test
can be used instead.

**What
is a non-parametric substitute for the t-test?**

The
non-parametric substitute for the t-test is the Wilcoxon rank-sum test
(Mann-Whitney U test) for independent samples and the Wilcoxon signed-rank test
for related samples.

**When
should you use a non-parametric test?**

Non-parametric
tests should be used when the data do not meet the assumptions of parametric
tests, such as normality or equal variances, or when dealing with categorical
or ordinal data.

**Why
are non-parametric tests less powerful?**

Non-parametric
tests are less potent because they make fewer population and data distribution
assumptions. However, they are more robust and can be used in a broader range
of scenarios.

**Non-parametric
vs. parametric**

The distinction
between non-parametric and parametric tests lies in the assumptions about the
underlying population and the data distribution. Parametric tests assume
specific distributions and parameters, while non-parametric tests are
distribution-free or have fewer assumptions.

**Non-parametric
statistics**

Non-parametric
statistics refer to statistical methods and tests that do not rely on specific
population assumptions or parameters, making them more flexible and robust in
various situations.

**Parametric
and non-parametric test examples**

Examples
of parametric tests include t-tests, ANOVA, and regression analysis.
Non-parametric tests include the Mann-Whitney U test, the Kruskal-Wallis test,
and the chi-square test.

**Non-parametric
data**

Non-parametric data refers to data that do not adhere to a specific
distributional assumption or do not have fixed parameters. Examples include
rankings, categorical data, and data measured on an ordinal scale.

**Where
can I learn more about non-parametric tests?**

In our upcoming blog post, we will in detail explore this topic. Follow us and stay updated.