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Hypothesis Testing for Two Proportions

Jul 12, 2025

Overview

The lecture discusses how to set up a hypothesis test comparing the rates of death or disability in premature infants given caffeine therapy versus a placebo, focusing on two population proportions.

Identifying Groups in the Study

  • There are two groups: infants given caffeine therapy (treatment group) and infants given a placebo (control group).
  • Each group's outcome is whether infants suffered from death or disability (categorical variable: yes/no).

Recognizing the Type of Study

  • This is a controlled experiment with a treatment and a control group.
  • The main research question is whether caffeine therapy lowers the rate of death or disability compared to placebo.

Setting Up the Hypothesis Test

  • Hypothesis testing is suitable because the question compares two populations using the word "lower."
  • The letter P is used in hypotheses because the outcome is categorical (proportion of infants affected).
  • This is a test of two population proportions (P1 for caffeine group, P2 for placebo group).

Writing Hypotheses

  • The null hypothesis (H0): P1 = P2 (proportion affected is the same in both groups).
  • The alternative hypothesis (Ha): P1 < P2 (proportion affected is lower in caffeine group due to the word "lower").

Key Terms & Definitions

  • Treatment group — infants who receive caffeine therapy.
  • Control group — infants who receive a placebo.
  • Categorical variable — a variable with categories, e.g., suffered or did not suffer death/disability.
  • Population proportion (P) — the proportion of a group with a certain characteristic, such as death or disability.
  • Null hypothesis (H0) — the default assumption that proportions are equal.
  • Alternative hypothesis (Ha) — the assumption being tested; that the treatment changes the outcome.

Action Items / Next Steps

  • Practice setting up hypothesis tests for two proportions using similar study scenarios.