Two Sample Proportion Test Calculator

Two Sample Proportion Test Formula:

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

Proportion 1 (p1):

(0-1)

Sample Size 1 (n1):

samples

Proportion 2 (p2):

(0-1)

Sample Size 2 (n2):

samples

Z-Score:

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1. What Is The Two Sample Proportion Test?

The Two Sample Proportion Test is a statistical method used to determine whether there is a significant difference between two population proportions based on sample data. It calculates a z-score that measures how many standard deviations the observed difference is from the null hypothesis of no difference.

2. How Does The Calculator Work?

The calculator uses the Two Sample Proportion Test formula:

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

Where:

\( p_1 \) — Proportion from sample 1
\( p_2 \) — Proportion from 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 formula calculates a standardized score that indicates how far the difference between the two sample proportions is from zero, relative to the expected variability.

3. Importance Of Z-Score Calculation

Details: The z-score helps determine statistical significance. Typically, a z-score beyond ±1.96 indicates a statistically significant difference at the 0.05 level, suggesting the observed difference is unlikely due to random chance alone.

4. Using The Calculator

Tips: Enter proportions as values between 0 and 1, and sample sizes as positive integers. Ensure proportions are calculated as the number of successes divided by the sample size for each group.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a two sample proportion test?
A: Use this test when you want to compare proportions between two independent groups, such as comparing success rates between two treatments or response rates between two demographic groups.

Q2: What does the z-score tell me?
A: The z-score indicates how many standard errors the difference between proportions is from zero. Larger absolute values suggest stronger evidence against the null hypothesis of equal proportions.

Q3: What are the assumptions of this test?
A: The test assumes independent samples, random sampling, and sufficiently large sample sizes (typically n*p and n*(1-p) > 5 for each sample).

Q4: How do I interpret the results?
A: Compare the calculated z-score to critical values from the standard normal distribution. For α=0.05, if |z| > 1.96, the difference is statistically significant.

Q5: Can I use this test for small samples?
A: For small samples, consider using Fisher's exact test instead, as the normal approximation may not be accurate when sample sizes are small or proportions are extreme.