CPH Focus: Evidence-Based Approaches to Public Health: Hypothesis Testing: Parametric and Non-parametric Tests

In this article, we will explore the differences between parametric and non-parametric tests, two types of statistical tests commonly used in hypothesis testing. Both types of tests have their own assumptions and applications, and public health professionals must understand when to use each type to analyze data correctly. Mastering parametric and non-parametric tests is essential for the Certified in Public Health (CPH) exam and for conducting research in public health settings.

By the end of this article, you will understand the key differences between parametric and non-parametric tests, when to use each, and how they apply to public health research. Practice questions are included to help reinforce your understanding.

Table of Contents:

1. Introduction to Hypothesis Testing
2. What Are Parametric Tests?
3. What Are Non-parametric Tests?
4. Differences Between Parametric and Non-parametric Tests
5. When to Use Parametric vs. Non-parametric Tests
6. Common Parametric Tests
7. Common Non-parametric Tests
8. Practice Questions
9. Conclusion

1. Introduction to Hypothesis Testing

Hypothesis testing is a statistical method used to determine whether there is enough evidence in a sample of data to infer that a certain condition holds true for the entire population. In public health research, hypothesis testing is widely used to compare groups, assess associations, and evaluate the effectiveness of interventions. Depending on the nature of the data and the assumptions that can be made about the population, researchers may use either parametric or non-parametric tests to analyze the data.

2. What Are Parametric Tests?

Parametric tests are statistical tests that rely on assumptions about the underlying population distribution, typically that the data follow a normal distribution. These tests use parameters such as the mean and standard deviation to make inferences about the population. Because parametric tests make more assumptions about the data, they tend to be more powerful (i.e., they have a higher likelihood of detecting a true effect) when the assumptions are met.

However, parametric tests are not suitable for all types of data, especially when the data do not meet the assumptions of normality or when the sample size is small.

Key Features of Parametric Tests:

– Assume the data follow a specific distribution, usually a normal distribution.
– Use population parameters (mean, standard deviation) to make inferences.
– Tend to be more powerful when assumptions are met.
– Require interval or ratio-level data.

3. What Are Non-parametric Tests?

Non-parametric tests, also known as distribution-free tests, do not assume that the data follow a specific distribution. These tests are often used when the sample size is small, when the data are not normally distributed, or when the data are ordinal or nominal. Non-parametric tests are more flexible than parametric tests because they make fewer assumptions about the data, but they are generally less powerful (i.e., they may require a larger sample size to detect a true effect).

Non-parametric tests are particularly useful in public health research when dealing with skewed data, small sample sizes, or data that do not meet the assumptions required for parametric tests.

Key Features of Non-parametric Tests:

– Do not assume a specific population distribution.
– Use ranks or medians instead of means.
– Suitable for ordinal, nominal, or non-normally distributed data.
– Less powerful than parametric tests but more robust when assumptions are violated.

4. Differences Between Parametric and Non-parametric Tests

5. When to Use Parametric vs. Non-parametric Tests

The decision to use a parametric or non-parametric test depends on several factors, including the distribution of the data, the level of measurement, and the sample size. Here are general guidelines for when to use each type of test:

• Use Parametric Tests When:
  • The data are normally distributed or approximately normally distributed.
  • The sample size is large enough to rely on the Central Limit Theorem (typically n > 30).
  • The data are measured at the interval or ratio level.
• Use Non-parametric Tests When:
  • The data are not normally distributed, and the sample size is small.
  • The data are ordinal or nominal.
  • The assumptions required for parametric tests are not met.

6. Common Parametric Tests

Here are some common parametric tests used in public health research:

• t-test: Used to compare the means of two groups (e.g., comparing the mean blood pressure between two groups).
• ANOVA (Analysis of Variance): Used to compare the means of three or more groups.
• Paired t-test: Used to compare means from the same group at different times (e.g., before and after an intervention).

7. Common Non-parametric Tests

Here are some common non-parametric tests used in public health research:

• Mann-Whitney U Test: Used to compare two independent groups when the data are not normally distributed (non-parametric alternative to the t-test).
• Kruskal-Wallis Test: Used to compare three or more independent groups (non-parametric alternative to ANOVA).
• Wilcoxon Signed-Rank Test: Used to compare two related samples or repeated measurements (non-parametric alternative to the paired t-test).
• Chi-Square Test: Used to test associations between categorical variables (e.g., smoking status and lung cancer diagnosis).

8. Practice Questions

Test your understanding of parametric and non-parametric tests with these practice questions. Try answering them before checking the solutions.

Question 1:

A researcher wants to compare the mean cholesterol levels between two groups of patients, but the data are not normally distributed. Which type of test should the researcher use?

Answer 1:

Question 2:

A study compares the blood pressure of patients before and after they undergo a new treatment. The data are normally distributed. What test should be used?

Answer 2:

Question 3:

A researcher is analyzing the effectiveness of three different diets on weight loss. The data are not normally distributed. What test should the researcher use?

Answer 3:

9. Conclusion

Both parametric and non-parametric tests are essential tools in public health research. Parametric tests are more powerful but require certain assumptions about the data, while non-parametric tests are more flexible and can be used when those assumptions are not met. Understanding when to use each type of test and how they differ is crucial for accurately analyzing data and making valid conclusions in public health research. Make sure you understand the assumptions behind parametric and non-parametric tests, and practice identifying which test is appropriate for different types of data and research scenarios. This knowledge will be essential not only for the Certified in Public Health (CPH) exam but also for conducting sound public health research.

Humanities Moment

The featured image for this CPH Focus is Olive Trees (1889) by Vincent van Gogh (Dutch, 1853–1890), a post-impressionist painter whose emotionally charged use of color and expressive brushwork helped lay the groundwork for modern art. Despite creating over 2,000 artworks in just a decade, van Gogh struggled with mental health and poverty throughout his life and achieved lasting fame only after his death. Today, his deeply personal paintings are celebrated worldwide and his legacy is preserved at the Van Gogh Museum in Amsterdam.