Calculator 2 Sample Proportion Test R

Two Sample Proportion Test Formula:

\[ z = \frac{p_1 - p_2}{\sqrt{\bar{p}(1 - \bar{p})(\frac{1}{n_1} + \frac{1}{n_2})}} \] \[ \text{where } \bar{p} = \frac{x_1 + x_2}{n_1 + n_2} \]

Successes in Group 1 (x1):

count

Sample Size Group 1 (n1):

count

Successes in Group 2 (x2):

count

Sample Size Group 2 (n2):

count

Z-Score:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Two Sample Proportion Test?

The two sample proportion test (z-test) compares proportions from two independent groups to determine if they are statistically significantly different from each other. This test is R-compatible and follows standard statistical methodology.

2. How Does the Calculator Work?

The calculator uses the two sample proportion test formula:

\[ z = \frac{p_1 - p_2}{\sqrt{\bar{p}(1 - \bar{p})(\frac{1}{n_1} + \frac{1}{n_2})}} \] \[ \text{where } \bar{p} = \frac{x_1 + x_2}{n_1 + n_2} \]

Where:

\( p_1 \) — Proportion of successes in group 1 (\(x_1/n_1\))
\( p_2 \) — Proportion of successes in group 2 (\(x_2/n_2\))
\( \bar{p} \) — Pooled proportion
\( n_1 \) — Sample size of group 1
\( n_2 \) — Sample size of group 2
\( x_1 \) — Number of successes in group 1
\( x_2 \) — Number of successes in group 2

Explanation: The z-score measures how many standard deviations the difference between proportions is away from zero under the null hypothesis of equal proportions.

3. Importance of Proportion Testing

Details: This test is crucial in research and data analysis for comparing success rates, conversion rates, or any proportional outcomes between two groups in fields like medicine, marketing, and social sciences.

4. Using the Calculator

Tips: Enter the number of successes (x1, x2) and sample sizes (n1, n2) for both groups. Ensure successes don't exceed sample sizes. All values must be non-negative integers.

5. Frequently Asked Questions (FAQ)

Q1: What does the z-score represent?
A: The z-score indicates how many standard deviations the observed difference is from the null hypothesis (no difference between proportions).

Q2: How do I interpret the z-score?
A: Typically, |z| > 1.96 suggests statistical significance at α = 0.05 level, meaning the proportions are likely different.

Q3: When should I use this test?
A: Use when comparing proportions from two independent groups with sufficiently large sample sizes (typically n > 30 per group).

Q4: What are the assumptions of this test?
A: The test assumes independent observations, random sampling, and sufficiently large sample sizes (np and n(1-p) > 5 for both groups).

Q5: Is this test R-compatible?
A: Yes, this calculation follows the same methodology used in R's prop.test function for two-sample proportion testing.