Parametric Test vs. Nonparametric Test: Know the Difference

By Shumaila Saeed || Published on January 29, 2024

Parametric tests assume underlying statistical distributions in the data; nonparametric tests do not, making them suitable for non-normal or unknown distributions.

Parametric Test vs. Nonparametric Test

Key Differences

Parametric tests are statistical tests that assume the data follow a certain distribution, typically the normal distribution. They are appropriate for hypotheses about the mean or variance of a normally distributed population. Parametric tests are powerful when their assumptions are met, as they can provide more accurate and reliable results. Examples include the t-test and ANOVA. These tests rely on parameters like mean and standard deviation and are less robust to deviations from normality.

Jan 29, 2024

Nonparametric tests, on the other hand, do not assume any specific distribution for the data. They are ideal for data that is not normally distributed or when the form of the distribution is unknown. Nonparametric tests are more flexible and can be used with ordinal data or non-numeric data. However, they may be less powerful than parametric tests when dealing with normally distributed data. Examples include the Mann-Whitney U test and the Kruskal-Wallis test. These tests are based on ranks and medians and are more robust to outliers and non-normality.

Jan 29, 2024

Comparison Chart

Assumption of Distribution

Assumes normal distribution of data.

Does not assume any specific distribution.

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Data Requirements

Requires interval or ratio data.

Can be used with ordinal or nominal data.

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Sensitivity to Outliers

Less robust to outliers.

More robust to outliers and non-normal data.

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Hypothesis about

Usually about means or variances.

Often about medians or distribution shapes.

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Examples

T-test, ANOVA.

Mann-Whitney U test, Kruskal-Wallis test.

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Parametric Test and Nonparametric Test Definitions

Parametric Test

It’s based on assumptions of the normality of data and known distribution parameters.

For normally distributed data, the ANOVA, a parametric test, is often the preferred choice.

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Nonparametric Test

Less powerful than parametric tests but more robust to outliers.

For skewed data, the nonparametric test was more appropriate due to its robustness.

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Parametric Test

Requires interval or ratio data for valid application.

Using the Pearson Correlation, a parametric test, required interval data for correlation analysis.

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Nonparametric Test

Often used when parametric test assumptions cannot be satisfied.

Given the unknown distribution, a nonparametric test was the best choice.

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Parametric Test

Parametric tests are suitable for hypothesis testing about population parameters.

The Z-test, another parametric test, was applied to assess the population mean.

Jan 05, 2024

Nonparametric Test

It’s based on ranks or medians rather than means and variances.

The Wilcoxon test, a nonparametric test, compared medians instead of means.

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Parametric Test

More powerful than nonparametric tests when assumptions are met.

Given the data's normal distribution, the parametric test provided more reliable results.

Jan 05, 2024

Nonparametric Test

A Nonparametric Test does not assume a specific distribution and is flexible.

The Mann-Whitney U test, a nonparametric test, was used for the ordinal data comparison.

Jan 05, 2024

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Parametric Test

A Parametric Test assumes a specific distribution and uses parameters like mean and variance.

The t-test, a parametric test, was used to compare the means of two groups.

Jan 05, 2024

Nonparametric Test

Suitable for ordinal or nominal data and non-normal distributions.

The Chi-square test, a nonparametric test, was ideal for the nominal data analysis.

Jan 05, 2024

Repeatedly Asked Queries

What is a Parametric Test?

A statistical test that assumes data follows a specific distribution, typically normal.

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When should I use a Parametric Test?

When your data is normally distributed and meets other parametric assumptions.

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In what situation is a Nonparametric Test preferred?

When data is not normally distributed or has an unknown distribution.

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What is an example of a Parametric Test?

The t-test is a common example.

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Are Nonparametric Tests useful for small sample sizes?

Yes, they can be particularly useful for small samples.

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Can Parametric Tests be used on ordinal data?

Typically no, they require interval or ratio data.

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Can I use a Nonparametric Test for ratio data?

Yes, nonparametric tests can be used for various data types, including ratio data.

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What assumptions do Parametric Tests make about variance?

They often assume homogeneity of variance.

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What is a Nonparametric Test?

A flexible statistical test that does not assume any specific data distribution.

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Are Nonparametric Tests less accurate than Parametric Tests?

Not necessarily less accurate, but sometimes less powerful if parametric assumptions are met.

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How do Parametric Tests handle outliers?

They are less robust to outliers compared to nonparametric tests.

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Is it easier to perform a Parametric Test?

Not necessarily, it depends on the data and the test requirements.

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What statistical information do Parametric Tests provide?

They provide insights like mean differences and variances.

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Which test is better for hypothesis testing about medians?

Nonparametric tests, as they focus on medians rather than means.

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Can a Parametric Test be used for skewed data?

Generally, no, as they assume normal distribution.

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Do Nonparametric Tests always involve ranks?

Many, like the Mann-Whitney U test, use ranks, but not all.

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How do Nonparametric Tests treat nominal data?

They can analyze nominal data effectively, unlike many parametric tests.

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Are Nonparametric Tests useful in clinical research?

Yes, especially when dealing with non-normal or ordinal data.

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Can Parametric Tests handle missing data?

Handling missing data can be complex and may affect test validity.

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Do Nonparametric Tests require data transformation?

Usually, they do not require transformation like normalizing data.

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About Author

Written by

Shumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.

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