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Last updated on 2024年5月6日

What are the key differences between parametric and non-parametric tests?

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Understanding statistical tests is crucial for analyzing data effectively. Parametric and non-parametric tests are two broad categories of inferential statistics used to draw conclusions about a population based on sample data. The choice between these tests hinges on the nature of your data and the assumptions you can make about it. In this article, you'll learn the key differences that will help you decide when to use parametric tests and when to opt for non-parametric methods. This knowledge can empower you to make more informed decisions and interpret your statistical results with greater confidence.

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Travis Newton

Geospatial Analyst
Andrea Mafficini

Associate Professor at University of Verona

1 Parametric Basics

Parametric tests are the go-to choice when your data meets certain assumptions that allow for more powerful and precise conclusions. These tests assume that the underlying population from which the sample is drawn has a specific distribution, usually normal. They also presume that the variance is homogenous and that the data is measured on an interval or ratio scale, which provides meaningful numerical differences and ratios. Examples of parametric tests include the t-test for comparing means and the ANOVA for comparing means across multiple groups.

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Travis Newton

Geospatial Analyst
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Parametric is equally distributed data that's continuous, which can use anova and t-tests. For other data use non-parametric "fancy" stat testing.

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Andrea Mafficini

Associate Professor at University of Verona
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As obvious as it may seem, the first thing to do before choosing parametric vs. non-parametric tests is looking at your data on a graph to check whether they possibly follow a given distribution.

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2 Non-parametric Basics

Non-parametric tests, on the other hand, are used when your data doesn't meet the strict assumptions required for parametric tests. These tests don't assume a normal distribution and are less sensitive to outliers, making them more flexible and robust in dealing with ordinal data or data that's not normally distributed. They are ideal for small sample sizes or when the data's distribution is unknown. Common non-parametric tests include the Mann-Whitney U test for comparing two independent groups and the Kruskal-Wallis test for comparing more than two groups.

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Andrea Mafficini

Associate Professor at University of Verona
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I always prefer robust estimators and non-parametric tests for small datasets. Moreover, a lot of measurements from biological samples (and even from repeated experiments with cell lines) yield more robust assessments by avoiding pre-assumptions on data distribution if the number of data points is low.

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3 Assumption Differences

The assumptions underlying parametric and non-parametric tests are a key differentiator. Parametric tests rely on assumptions about the population distribution, the scale of measurement, and the equality of variances. If these assumptions are violated, the test may yield inaccurate results. Non-parametric tests have fewer and less stringent assumptions, which makes them more versatile but potentially less powerful when all parametric assumptions are met. Understanding these assumptions is essential to choose the correct test for your data.

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Andrea Mafficini

Associate Professor at University of Verona
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With several types of biological data you may rescue normal distribution and/or equal variance by transforming data points (e.g. using the logarithm or the squared root, or creating normalized scores). In that case it may be actually better to use a parametric test on transformed data, because it will yield more biologically meaningful results.

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Nathaniel GBENRO, Ing., Ph.D,

Statistique | Economie
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Les hypothèses sont cruciales dans les tests d'hypothèses paramétriques. En effet, un test très utilisé pour tester les valeurs aberrantes est celui de Grubbs qui repose sur la normalité des données. toutefois, l'article datant des années 1950, cette hypothèse est quelque fois oublié et le test est généralement utilisé sans fait mention de ses sous-jacent, ce qui peux conduire à des résultats erronés comme l'indique l'auteur.

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4 Data Requirements

Data requirements significantly influence whether you'll use a parametric or non-parametric test. Parametric tests require data to be normally distributed and often need larger sample sizes to ensure the validity of their results. In contrast, non-parametric tests do not require normal distribution and can be applied to smaller sample sizes, making them more suitable for preliminary studies or when data collection is challenging. The level of measurement also matters: parametric tests typically require interval or ratio data, while non-parametric tests can work with ordinal or nominal data.

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Andrea Mafficini

Associate Professor at University of Verona
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It's fairly difficult to apply parametric tests to scores obtained from histological or immunohistochemical analyses. Even when multiple parameters are incorporated in a single score, data tend to distribute in such a way that calls for using robust estimators and avoiding assumptions on the shape of the data.

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5 Test Power and Precision

When it comes to power and precision, parametric tests generally have the upper hand—if the data meets the necessary assumptions. They are more likely to detect a true effect when one exists because they make full use of data characteristics like mean and standard deviation. Non-parametric tests are less powerful in this regard but offer a safer alternative when parametric assumptions cannot be satisfied. The trade-off between power and flexibility is a crucial consideration in statistical testing.

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6 Choosing the Right Test

Choosing between parametric and non-parametric tests ultimately depends on your specific situation. If your data meets the assumptions for parametric tests and you're dealing with interval or ratio data, these tests can provide more precise results. However, if you're unsure about the distribution of your data, have outliers, or work with ordinal data, non-parametric tests may be more appropriate. It's important to carefully assess your data before deciding which statistical test to apply.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What are the key differences between parametric and non-parametric tests?

1

2

3

4

5

6

7

1 Parametric Basics

2 Non-parametric Basics

3 Assumption Differences

4 Data Requirements

5 Test Power and Precision

6 Choosing the Right Test

7 Here’s what else to consider

Statistics

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What are the key differences between parametric and non-parametric tests?

1

2

3

4

5

6

7

1 Parametric Basics

2 Non-parametric Basics

3 Assumption Differences

4 Data Requirements

5 Test Power and Precision

6 Choosing the Right Test

7 Here’s what else to consider

Statistics

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