Two-Proportion Test

Statistics · Axiom Academy

LESSON Two-Sample Proportion Test Comparing proportions between two independent groups to determine if there is a significant difference 1. Comparing Proportions Between Two Groups In a two-sample proportion test, we collect data from two independent groups and calculate the proportion of "successes" in each group. where x₁ and x₂ are the number of successes, and n₁ and n₂ are the sample sizes. Under the null hypothesis (that the two population proportions are equal), we calculate a pooled proportion that combines data from both samples. The pooled proportion combines all successes from both groups divided by the total sample size from both groups. We calculate a z-statistic to measure how many standard errors the difference in sample proportions is from zero. If the groups have equal proportions, we expect p̂₁ - p̂₂ to be close to zero. The standard error accounts for sample variability. 4. Conditions for a Valid Test Before conducting a two-sample proportion test, we must verify that certain conditions are met to ensure the test results are reliable. Independence: Observations within each group must be independent, and the two groups must be independent of each other Random Sampling: Data should come from random samples or randomized experiments Sample Size: For both groups, we need: n₁p̂ ≥ 10 and n₁(1-p̂) ≥ 10 10% Condition: If sampling without replacement, each sample size should be less than 10% of its population

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