P Score Calculator 2 Prop Z Test Example

Two Proportion Z-Test Formula:

\[ P = 2 \times (1 - \text{normcdf}(|z|)) \] \[ z = \frac{p_1 - p_2}{\sqrt{p(1-p)(\frac{1}{n_1} + \frac{1}{n_2})}} \] \[ p = \frac{x_1 + x_2}{n_1 + n_2} \]

P-Value:

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1. What is the Two Proportion Z-Test?

The two proportion z-test is a statistical method used to determine whether two population proportions are significantly different from each other. It compares the proportions of successes in two independent groups.

2. How Does the Calculator Work?

The calculator uses the two proportion z-test formula:

\[ P = 2 \times (1 - \text{normcdf}(|z|)) \] \[ z = \frac{p_1 - p_2}{\sqrt{p(1-p)(\frac{1}{n_1} + \frac{1}{n_2})}} \] \[ p = \frac{x_1 + x_2}{n_1 + n_2} \]

Where:

\( p_1 \) — Proportion in group 1 (x1/n1)
\( p_2 \) — Proportion in group 2 (x2/n2)
\( p \) — Pooled proportion
\( n_1 \) — Sample size of group 1
\( n_2 \) — Sample size of group 2

Explanation: The test calculates a z-score which measures how many standard deviations the observed difference is from the null hypothesis (no difference). The p-value represents the probability of observing such a difference by chance.

3. Interpretation of Results

Details: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, suggesting a statistically significant difference between the two proportions.

4. Using the Calculator

Tips: Enter the number of successes (x1, x2) and total sample sizes (n1, n2) for both groups. The calculator will compute the two-tailed p-value.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this test?
A: Use when comparing proportions from two independent groups with sufficiently large sample sizes (n*p > 5 and n*(1-p) > 5 for both groups).

Q2: What's the difference between one-tailed and two-tailed tests?
A: Two-tailed tests detect any difference (default), while one-tailed tests detect differences in a specific direction.

Q3: What if my sample sizes are small?
A: For small samples, consider Fisher's exact test which doesn't rely on normal approximation.

Q4: How is this different from chi-square?
A: The two-proportion z-test is mathematically equivalent to a chi-square test for 2x2 tables, but z-tests can be one-tailed.

Q5: What assumptions does this test make?
A: Assumes independent samples, normal approximation to binomial distribution, and equal variances under the null.