Introduction-to-Parametric-and-Non-Parametric-Test

1. Introduction to Parametric
and Non-Parametric Tests
In the realm of statistical analysis, researchers often encounter situations
where they need to choose between parametric and non-parametric tests to
analyze their data. Parametric tests are a family of statistical methods that
make specific assumptions about the underlying distribution of the data, such
as normality, equal variances, and independence. On the other hand, non-
parametric tests do not rely on these assumptions and are often more robust
to violations of these assumptions. Understanding the differences between
these two types of tests is crucial for researchers to select the appropriate
analysis method for their research questions and data characteristics.
Sa
by Shriram Kargaonkar

2. Definition of Parametric Tests
Defined by
Underlying
Assumptions
Parametric tests are a class
of statistical tests that make
specific assumptions about
the underlying distribution of
the data. These
assumptions typically
include that the data follows
a normal distribution, has
equal variances across
groups, and has
independence between
observations. Parametric
tests are designed to be
more powerful and precise
when these assumptions
are met, as they can
leverage information about
the shape and parameters
of the underlying
distribution.
Rely on Population
Parameters
Parametric tests use
information about the
population parameters,
such as the mean and
standard deviation, to make
inferences about the data.
This allows them to provide
more detailed and robust
conclusions compared to
non-parametric tests, which
make fewer assumptions
about the underlying
distribution. Parametric
tests are often the preferred
choice when the necessary
assumptions can be
confidently met.
Widely Used in
Research
Parametric tests are widely
used across various fields
of research, including
psychology, biology, and
economics. They are a
fundamental part of the
statistical toolbox and are
often the starting point for
data analysis. Researchers
rely on parametric tests to
draw conclusions about
populations, test
hypotheses, and quantify
the strength of relationships
between variables.

3. Assumptions of Parametric Tests
Parametric tests are a class of statistical tests that make certain assumptions about the underlying
distribution of the data being analyzed. These assumptions are crucial for the validity and reliability of the test
results. The key assumptions of parametric tests include:
1. Normality: Parametric tests assume that the data is normally distributed, meaning that the distribution
of the variable follows a bell-shaped curve. This assumption is important because many statistical
methods, such as t-tests and ANOVA, rely on the normal distribution for their validity.
2. Homogeneity of Variance: Parametric tests also assume that the variance (or spread) of the data is
the same across the different groups or conditions being compared. This assumption is known as
homogeneity of variance or homoscedasticity.
3. Independence: Parametric tests require that the observations in the data set are independent of one
another. This means that the value of one observation should not depend on the value of another
observation.
4. Interval or Ratio Scale: Parametric tests assume that the data is measured on an interval or ratio
scale, meaning that the differences between the values are meaningful and can be interpreted
numerically.
If these assumptions are not met, the validity of the parametric test results may be compromised, and the
conclusions drawn from the analysis may be inaccurate or misleading. In such cases, it may be necessary to
use non-parametric tests, which have different assumptions and are more robust to violations of the
parametric test assumptions.

4. Understanding Non-
Parametric Tests
Non-parametric tests are a class of statistical methods that do not rely on
specific assumptions about the shape of the data distribution, such as the
normal distribution. These tests are used when the data does not meet the
requirements of parametric tests, such as when the data is not normally
distributed or when the variances are not equal.
Non-parametric tests are based on ranking or ordering the data rather than
using the actual data values directly. This approach makes them more robust
and less affected by outliers or violations of assumptions. Non-parametric
tests are often preferred when the sample size is small, the data is ordinal or
ranked, or when the distribution of the data is unknown or cannot be
assumed to be normal.

5. Assumptions of Non-Parametric Tests
No Assumption of Normality
Non-parametric tests do not assume that the data is normally distributed. This is a key
difference from parametric tests, which rely on the assumption of normality for their statistical
inferences. Non-parametric tests are more robust to deviations from normality, making them
suitable for analyzing data that does not meet the normality assumption.
No Assumption of Homogeneity of Variance
Unlike parametric tests, non-parametric tests do not require the assumption of homogeneity of
variance. This means that the variances of the populations being compared do not need to be
equal. This makes non-parametric tests more appropriate when the assumption of equal
variances is violated, as is often the case with real-world data.
No Assumption of Interval or Ratio Scales
Non-parametric tests can be used with ordinal, ranked, or even categorical data, as they do
not require the data to be on an interval or ratio scale. This flexibility allows non-parametric
tests to be applied to a wider range of research questions and data types, making them a
useful tool for researchers working with data that does not meet the assumptions of
parametric tests.

6. Advantages of Parametric Tests
Statistical Power
Parametric tests generally have higher
statistical power compared to non-parametric
tests when the data meets the necessary
assumptions. This means they are more likely
to detect an effect or difference if one truly
exists, reducing the risk of a false negative
result.
Precision and Sensitivity
Parametric tests can provide more precise
and sensitive measurements because they
make use of the full information contained in
the data, such as the means and variances.
This allows for more nuanced analyses and
the detection of smaller effects.
Familiarity and Interpretability
Parametric tests are widely used and well-
understood statistical methods, with a rich
body of literature and established
conventions. This familiarity makes the results
more interpretable and easier to communicate
to a broader audience.
Parametric Modeling
Parametric tests can be used to fit complex
statistical models that allow for the exploration
of relationships between multiple variables.
This flexibility is valuable in many research
and applied settings where understanding
these relationships is important.

7. Advantages of Non-Parametric Tests
Flexibility
Non-parametric tests
are more flexible than
parametric tests
because they do not
rely on strict
assumptions about the
underlying distribution
of the data. This
makes them well-
suited for analyzing
data that may not
follow a normal
distribution or have
equal variances, which
are common
assumptions of
parametric tests.
Robustness
Non-parametric tests
are more robust to
outliers and extreme
values in the data.
Parametric tests can
be heavily influenced
by outliers, which can
skew the results. Non-
parametric tests, on
the other hand, are
less sensitive to these
extreme values,
making them more
reliable for datasets
with unusual
distributions.
Ordinal Data
Non-parametric tests
are particularly useful
for analyzing ordinal
data, which are data
that can be ranked but
do not have a
meaningful numerical
scale. Parametric
tests, which rely on
numerical values, are
not well-suited for this
type of data, whereas
non-parametric tests
can effectively analyze
ordinal data.
Small Sample
Sizes
Non-parametric tests
can be more effective
than parametric tests
when the sample size
is small. Parametric
tests often require
larger sample sizes to
ensure the
assumptions are met,
whereas non-
parametric tests can
provide reliable results
even with smaller
datasets.

8. Situations Requiring Non-Parametric
Tests
1
Small Samples
When the sample size is small and the distribution of the data is unknown.
2
Non-Normal Distributions
When the data does not follow a normal distribution.
3
Ordinal Data
For data measured on an ordinal scale, such as ratings or
rankings.
4
Heterogeneous Variances
When the variances of the populations are not
equal.
Non-parametric tests are often required when the assumptions of parametric tests are violated. This can
occur in a variety of situations, such as when the sample size is small, the data does not follow a normal
distribution, the data is measured on an ordinal scale, or the variances of the populations are not equal. In
these cases, non-parametric tests can provide more robust and reliable results than their parametric
counterparts.
For example, if you're comparing the median income of two different neighborhoods, a non-parametric test
like the Mann-Whitney U test would be appropriate, as the income data may not follow a normal distribution.

9. Examples of Parametric and Non-
Parametric Tests
Parametric tests are widely used statistical
methods that make assumptions about the
underlying distribution of the data, such as
normality and equal variances. Some common
examples of parametric tests include:
1. t-test: Used to compare the means of
two groups, such as comparing the
average test scores of a control group
and an experimental group.
2. ANOVA (Analysis of Variance): Used to
compare the means of three or more
groups, such as comparing the
performance of different treatment
groups in a clinical trial.
3. Pearson's correlation: Used to measure
the linear relationship between two
continuous variables, such as the
relationship between income and
education level.
On the other hand, non-parametric tests are more
flexible and do not make assumptions about the
underlying data distribution. Some examples of
non-parametric tests include:
1. Mann-Whitney U test: Used to compare

10. Conclusion and Takeaways
In conclusion, the key differences between parametric and non-parametric tests lie in their underlying
assumptions and the type of data they can effectively analyze. Parametric tests, such as the t-test and
ANOVA, rely on specific assumptions about the distribution of the data, including normality and homogeneity
of variance. These tests are powerful when the assumptions are met, providing robust and precise results. In
contrast, non-parametric tests, like the Mann-Whitney U test and the Kruskal-Wallis test, make fewer
assumptions about the data distribution and are more flexible in their application. They are particularly useful
when the data is ordinal, skewed, or does not follow a normal distribution.
The choice between parametric and non-parametric tests ultimately depends on the characteristics of the
data and the research question at hand. Parametric tests are generally preferred when the assumptions are
met, as they offer greater statistical power and the ability to make more precise inferences. However, when
the assumptions are violated, non-parametric tests become the more appropriate choice, as they can provide
reliable and valid results without the need for strict distributional assumptions. Researchers should carefully
evaluate the assumptions of their data and select the most appropriate statistical test to ensure accurate and
meaningful conclusions.
In summary, understanding the differences between parametric and non-parametric tests, their assumptions,
and their respective strengths and weaknesses is crucial for researchers to select the most suitable analytical
approach for their specific research questions and data characteristics. By considering these factors,
researchers can ensure the validity and reliability of their findings and draw meaningful insights from their
data.