Pooled proportion

Definition

The pooled proportion is a weighted average of two sample proportions used when comparing two independent population proportions. It combines the data from both samples to provide a single estimate of the common population proportion.

5 Must Know Facts For Your Next Test

1. The formula for the pooled proportion is $\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}$, where $x_1$ and $x_2$ are the number of successes in each sample, and $n_1$ and $n_2$ are the sample sizes.
2. Pooled proportion assumes that the null hypothesis is true, meaning there is no difference between the population proportions.
3. It is mainly used in hypothesis testing for comparing two population proportions.
4. The pooled standard error incorporates the pooled proportion in its calculation: $SE_{pooled} = \sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}$.
5. Using a pooled proportion can increase statistical power by combining information from both samples.

Review Questions

• What is the formula for calculating the pooled proportion?
• Why do we use a pooled proportion when comparing two independent population proportions?
• How does the assumption of the null hypothesis influence the use of pooled proportion?

Related terms

Null Hypothesis: A statement that there is no effect or difference between groups or variables, often denoted as $H_0$. In this context, it posits that two population proportions are equal.

Standard Error: A measure of how much sample statistics (like means or proportions) deviate from actual population parameters. It decreases as sample size increases.

Two-sample Z-test: $A hypothesis test used to determine if there are differences between two population means or proportions. The test statistic follows a standard normal distribution under the null hypothesis.