CPH Focus: Evidence-Based Approaches to Public Health: Hypothesis Testing: Null and Alternative Hypotheses

Understanding the concepts of null and alternative hypotheses is fundamental to the Certified in Public Health (CPH) exam. Hypothesis testing is a crucial statistical tool used in public health to make decisions based on sample data. In this tutorial, we will explore what null and alternative hypotheses are, how they are used in research, and their importance in hypothesis testing. We will also include practice questions with answers to reinforce your knowledge.

By the end of this tutorial, you will have a solid understanding of null and alternative hypotheses and how they apply in public health research. This knowledge is essential for public health professionals and for tackling questions related to hypothesis testing on the CPH exam.

Table of Contents:

• Introduction to Hypothesis Testing
• What Is a Null Hypothesis?
• What Is an Alternative Hypothesis?
• Types of Null and Alternative Hypotheses
• Steps in Hypothesis Testing
• Importance of Hypothesis Testing in Public Health
• Common Pitfalls in Hypothesis Testing
• Practice Questions
• Conclusion

1. Introduction to Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. Researchers start with two competing hypotheses: the null hypothesis and the alternative hypothesis. The goal of hypothesis testing is to determine whether the sample data provide enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

2. What Is a Null Hypothesis?

The null hypothesis (denoted as H₀) is a statement that there is no effect, no difference, or no relationship between variables. It assumes that any observed outcome is due to random chance or sampling error. In hypothesis testing, the null hypothesis represents the default or status quo assumption.

• Example: If a new vaccine is being tested, the null hypothesis might state that the vaccine has no effect on preventing disease (i.e., the vaccine is no better than a placebo).

Key Points about the Null Hypothesis:

• It is always assumed to be true until evidence suggests otherwise.
• The goal of hypothesis testing is to determine whether there is enough evidence to reject the null hypothesis.
• In most statistical tests, the null hypothesis is framed as an equality (e.g., mean difference = 0).

3. What Is an Alternative Hypothesis?

The alternative hypothesis (denoted as H₁ or Ha) is a statement that contradicts the null hypothesis. It suggests that there is an effect, a difference, or a relationship between variables. The alternative hypothesis is what the researcher aims to provide evidence for through hypothesis testing.

• Example: Continuing with the vaccine example, the alternative hypothesis might state that the vaccine is effective in preventing disease (i.e., the vaccine reduces the incidence of disease compared to a placebo).

Key Points about the Alternative Hypothesis:

• The alternative hypothesis is what researchers hope to demonstrate through their study.
• It is accepted if there is sufficient evidence to reject the null hypothesis.
• The alternative hypothesis can be one-sided (e.g., the vaccine is better than a placebo) or two-sided (e.g., the vaccine is either better or worse than a placebo).

4. Types of Null and Alternative Hypotheses

Hypotheses can be classified into two main types based on the direction of the effect being tested:

• Two-Tailed Hypothesis: In this case, the alternative hypothesis states that the value of interest is not equal to the value specified in the null hypothesis. The direction of the effect is not specified.
  Example: H₀: μ = 50 versus H₁: μ ≠ 50
• One-Tailed Hypothesis: The alternative hypothesis specifies a direction of the effect (either greater than or less than).
  Example: H₀: μ ≤ 50 versus H₁: μ > 50 (the mean is greater than 50).

5. Steps in Hypothesis Testing

The process of hypothesis testing involves several key steps:

1. State the Hypotheses: Formulate the null and alternative hypotheses based on the research question.
2. Select the Significance Level (α): The significance level is the threshold for deciding when to reject the null hypothesis. Commonly used values are 0.05 or 0.01.
3. Collect and Analyze Data: Gather sample data and calculate the appropriate test statistic (e.g., t-test, chi-square test).
4. Make a Decision: Compare the test statistic to a critical value or use a p-value to decide whether to reject or fail to reject the null hypothesis.
5. Draw a Conclusion: Based on the decision, draw conclusions about the population. If the null hypothesis is rejected, it suggests that there is evidence in favor of the alternative hypothesis.

6. Importance of Hypothesis Testing in Public Health

Hypothesis testing is critical in public health research because it allows researchers to make informed decisions about the effectiveness of interventions, the relationship between risk factors and health outcomes, and the impact of public health policies. It helps determine whether observed differences or associations are statistically significant, providing evidence to guide public health practice.

• Application: Hypothesis testing is often used in clinical trials, epidemiological studies, and health interventions to assess whether a new treatment is effective or whether there is a relationship between an exposure and an outcome.

7. Common Pitfalls in Hypothesis Testing

While hypothesis testing is a powerful tool, there are common pitfalls that researchers should be aware of:

• Type I Error: This occurs when the null hypothesis is incorrectly rejected. It means concluding that there is an effect when there is none. The probability of a Type I error is denoted by the significance level (α).
• Type II Error: This occurs when the null hypothesis is incorrectly accepted. It means failing to detect an effect when one actually exists. The probability of a Type II error is denoted by β.
• Over-reliance on p-values: A p-value alone does not provide the full picture. It is important to consider the effect size, confidence intervals, and the practical significance of the findings.

8. Practice Questions

Test your understanding of null and alternative hypotheses with these practice questions. Try answering them before checking the solutions.

Question 1:

A researcher wants to test whether a new drug lowers blood pressure. What is the null hypothesis and the alternative hypothesis?

Answer 1:

Question 2:

In a study comparing two diets, the researchers want to test whether there is any difference in weight loss between the diets. What are the null and alternative hypotheses?

Answer 2:

Question 3:

A study is conducted to determine whether a new public health campaign increases the rate of vaccination. What is the null hypothesis, and what is the alternative hypothesis?

Answer 3:

9. Conclusion

Hypothesis testing, with its focus on null and alternative hypotheses, is a foundational concept in public health research. It allows researchers to make evidence-based decisions about the effectiveness of interventions, relationships between variables, and public health outcomes. Here is a recap of the key points from this tutorial:

• The null hypothesis represents the assumption that there is no effect or difference, while the alternative hypothesis suggests that there is an effect or difference.
• Hypothesis testing involves comparing sample data to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
• Care must be taken to avoid errors in hypothesis testing, and p-values should be interpreted in the context of effect size and practical significance.

Humanities Moment

The featured work for this CPH Focus is Jaroslava Mucha by Alphonse Mucha (Czech, 1860-1939), a celebrated painter and graphic artist best known for helping define the Art Nouveau movement through his elegant posters and illustrations, especially those of Sarah Bernhardt. After achieving fame in Paris, Mucha returned to his homeland, where he devoted himself to The Slav Epic, a monumental series of canvases depicting Slavic history, which he regarded as his greatest legacy and gifted to the Czech nation.
By practicing the formulation of null and alternative hypotheses and understanding the importance of hypothesis testing in public health, you will be well-prepared for questions on the Certified in Public Health (CPH) exam and for applying these concepts in real-world public health research.