Hypothesis Testing: How to interpret the metrics?

When conducting hypothesis tests, various metrics and measures help assess the validity and significance of the results. Here are some key metrics commonly used in hypothesis testing:

P-Value:

• The p-value is a crucial metric that indicates the probability of observing the data or more extreme results if the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis.

Level of Significance (α):

• The level of significance, denoted by α, is the predetermined threshold used to determine the statistical significance of the test. It represents the probability of committing a Type I error. Common choices include 0.05, 0.01, or 0.10.

Critical Value:

• The critical value is the boundary value beyond which the null hypothesis is rejected. It is derived from the chosen level of significance and the distribution of the test statistic.

Test Statistic:

• The test statistic is a numerical value calculated from the sample data that is used to assess the evidence against the null hypothesis. The choice of the test statistic depends on the type of hypothesis test being conducted.

Confidence Interval:

• For some tests, constructing a confidence interval is a valuable metric. It provides a range of plausible values for the population parameter and helps in understanding the precision of the estimate.

Effect Size:

• Effect size measures the magnitude of the difference or the strength of the relationship between variables. It helps interpret the practical significance of the results, especially when a test is statistically significant.

Power of the Test:

• The power of a test is the probability that it will correctly reject a false null hypothesis. It reflects the ability of the test to detect a true effect or difference. Power is influenced by factors such as sample size, effect size, and the chosen level of significance.

Type I Error Rate (False Positive Rate):

• The Type I error rate, denoted by α, is the probability of incorrectly rejecting a true null hypothesis. It is set by the researcher and is related to the level of significance.

Type II Error Rate (False Negative Rate):

• The Type II error rate, denoted by β, is the probability of failing to reject a false null hypothesis. Power of the test (1 — β) is the complement of the Type II error rate.

Degrees of Freedom:

• Degrees of freedom are a concept associated with certain statistical tests, such as t-tests or chi-square tests. The choice of degrees of freedom affects the critical values and the distribution of the test statistic.

In summary, when conducting hypothesis tests:

• The power of a test reflects its ability to correctly identify true effects.
• The p-value provides a measure of the strength of evidence against the null hypothesis.
• The level of significance (α) determines the threshold for rejecting the null hypothesis.
• Type I error (α) is the risk of falsely rejecting a true null hypothesis.
• Type II error (β) is the risk of failing to reject a false null hypothesis.

These metrics collectively provide a comprehensive understanding of the hypothesis testing process, from the statistical significance of results (p-value, level of significance) to the practical significance (effect size) and potential errors associated with the decision-making process (Type I and Type II errors). It’s important to consider these metrics in conjunction to make informed conclusions about the hypotheses being tested.