14 Hypothesis Testing

What is Hypothesis Testing?

Hypothesis testing is a statistical method used to make inferences about population parameters based on sample data. It involves evaluating competing hypotheses about the population and making decisions using statistical evidence. The process typically follows these steps:

1. Formulating Hypotheses:
   • Null Hypothesis (H0): This is the default or status quo hypothesis. It often represents the absence of an effect or no difference between groups. For example, H0 might state that there is no difference in the mean test scores between two groups.
   • Alternative Hypothesis (Ha or H1): This is the hypothesis we want to test, typically suggesting the presence of an effect, difference, or relationship. It is often what researchers hope to find evidence for.
2. Collecting Data: Sample data is collected from the population of interest. This data is used to test the hypotheses.
3. Choosing a Significance Level (Alpha): The significance level (α) represents the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. Common choices for α include 0.05 (5%) or 0.01 (1%).
4. Selecting a Test Statistic: Depending on the type of data and the research question, a suitable statistical test is chosen. Common tests include t-tests, chi-square tests, and z-tests (although many others exist).
5. Calculating the Test Statistic: Using the sample data, the test statistic is computed based on the chosen statistical test. This statistic measures the degree to which the observed data deviates from what would be expected under the null hypothesis.
6. Determining the Critical Region (Rejection Region): Based on the significance level α and the chosen test, a critical value or range of values is established. If the test statistic falls into this critical region, the null hypothesis is not supported by the data. Instead, we say that the data support the alternative hypothesis.
7. Comparing the Test Statistic and Critical Region: The test statistic is compared to the critical value or range. If the test statistic falls within the critical region, the null hypothesis is rejected, indicating that there is enough evidence to support the alternative hypothesis. If the test statistic falls outside the critical region, the null hypothesis is not rejected, suggesting that there is not enough evidence to support the alternative hypothesis.
8. Drawing a Conclusion: Based on the comparison, a conclusion is drawn. This could be one of the following:
   • Reject the null hypothesis (if the test statistic falls in the critical region).
   • Fail to reject the null hypothesis (if the test statistic does not fall in the critical region).
9. Interpreting Results: The conclusion is interpreted in the context of the research question. Researchers consider the practical significance of their findings and whether the evidence supports their initial hypothesis.
10. Reporting Results: The results of the hypothesis test are typically reported along with the test statistic, p-value (the probability of observing the test statistic or more extreme values under the null hypothesis), and a clear statement about whether the null hypothesis was rejected or not.