Hypothesis Testing

TL;DR

• Formulate a null hypothesis (default) and an alternative hypothesis (what you want to show).
• Collect a sample, compute a test statistic from the sample, and compare it to a critical value.
• If the test statistic is sufficiently different from the critical value, reject the null hypothesis in favor of the alternative.

Definition

Hypothesis testing is a statistical method used to determine whether or not a certain hypothesis about a population is true. It is used to make decisions about a population based on sample data.

Explanation

• The null hypothesis is a statement that assumes there is no difference between the population and the sample; it serves as the default assumption.
• The alternative hypothesis is the opposite of the null hypothesis and asserts that there is a difference between the population and the sample — it is what the analyst is trying to demonstrate.
• To perform a test, collect a sample from the population and compute a test statistic from the sample data.
• The test statistic is compared to a reference value called the critical value. If the test statistic is greater than (or otherwise sufficiently different from) the critical value, the null hypothesis is rejected and the alternative hypothesis is accepted.

Examples

Medical drug example

A medical researcher wants to determine if a new drug is effective at lowering blood pressure.

• Null hypothesis: the new drug has no effect on blood pressure.
• Alternative hypothesis: the new drug does lower blood pressure.
  The researcher randomly assigns patients to receive either the new drug or a placebo, measures their blood pressure after a certain period, computes a test statistic from the sample data, and compares it to the critical value. If the test statistic is greater than the critical value, the null hypothesis is rejected and the alternative hypothesis is accepted.

Psychology example

A researcher wants to determine if there is a difference in anxiety levels between men and women.

• Null hypothesis: there is no difference in anxiety levels between the two groups.
• Alternative hypothesis: there is a difference.
  The researcher collects a sample of men and women, administers a standardized anxiety test to each participant, calculates a test statistic (such as the difference in mean anxiety levels between the two groups), and compares it to the critical value. If the test statistic is significantly different from the critical value, the null hypothesis is rejected and the alternative hypothesis is accepted.

Related terms

• Null hypothesis
• Alternative hypothesis
• Test statistic
• Critical value