One-Sided Difference of Proportions Test
Enter the number of successes and sample sizes for two groups, and choose the one-sided alternative hypothesis.
* Note: This test uses the pooled proportion under the null hypothesis \( p_1=p_2 \).
Step 1: Enter Data
e.g., 30
e.g., 100
e.g., 25
e.g., 100
Choose the direction for the one-sided test.
How It Works
Under the null hypothesis that the two proportions are equal (\(p_1=p_2\)), the pooled proportion is calculated as: $$ \hat{p} = \frac{x_1+x_2}{n_1+n_2}. $$
The test statistic is then computed using: $$ z = \frac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}}, $$ where \( \hat{p}_1=\frac{x_1}{n_1} \) and \( \hat{p}_2=\frac{x_2}{n_2} \).
For a one-sided test:
– If testing \(p_1>p_2\): \( \text{p-value}=1-\Phi(z) \),
– If testing \(p_1