2 Sample Proportion Test Calculator

2 Sample Proportion Test Formula:

\[ Z = \frac{p_1 - p_2}{\sqrt{p(1-p)(\frac{1}{n_1} + \frac{1}{n_2})}} \]

Proportion 1 (p1):

(0-1)

Sample Size 1 (n1):

count

Proportion 2 (p2):

(0-1)

Sample Size 2 (n2):

count

Pooled Proportion (p):

Z-Score:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the 2 Sample Proportion Test?

The 2 Sample Proportion Test is a statistical method used to determine whether two population proportions are significantly different from each other. It's commonly used in A/B testing, medical research, and social sciences to compare success rates between two groups.

2. How Does the Calculator Work?

The calculator uses the Z-test formula for two proportions:

\[ Z = \frac{p_1 - p_2}{\sqrt{p(1-p)(\frac{1}{n_1} + \frac{1}{n_2})}} \]

Where:

\( p_1 \) — Proportion of success in sample 1
\( p_2 \) — Proportion of success in sample 2
\( n_1 \) — Size of sample 1
\( n_2 \) — Size of sample 2
\( p \) — Pooled proportion: \( \frac{p_1n_1 + p_2n_2}{n_1 + n_2} \)

Explanation: The Z-score measures how many standard deviations the difference between the two proportions is from zero (no difference).

3. Importance of Proportion Testing

Details: This test helps researchers determine if observed differences between groups are statistically significant or due to random chance. It's essential for making data-driven decisions in various fields including marketing, healthcare, and social research.

4. Using the Calculator

Tips: Enter proportions as decimals between 0 and 1. Sample sizes must be positive integers. The calculator will compute the pooled proportion and Z-score, which can be used to determine statistical significance.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this test?
A: Use when comparing proportions from two independent groups, such as conversion rates between two website versions or success rates between two treatment groups.

Q2: What does the Z-score mean?
A: A Z-score beyond ±1.96 (for 95% confidence) indicates statistical significance. The further from zero, the more significant the difference.

Q3: What are the assumptions of this test?
A: The test assumes independent samples, normal distribution approximation (n*p and n*(1-p) > 5 for each group), and random sampling.

Q4: How do I interpret the results?
A: Compare the calculated Z-score to critical values from the standard normal distribution. Typically, |Z| > 1.96 indicates significance at α=0.05 level.

Q5: What if my sample sizes are small?
A: For small samples, consider using Fisher's exact test instead, as the normal approximation may not hold well.