PP Calculator (P-value & Proportion)

Calculate p-value, z-score, and statistical significance for proportion tests

Test Type
Proportion of successes in your sample
Total number of observations in sample
Theoretical or expected proportion
Frequently Asked Questions
What is a P-value?

A p-value (probability value) is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, suggesting that the observed effect is statistically significant.

How do I interpret the p-value?

p ≤ 0.05: Statistically significant - reject the null hypothesis
p > 0.05: Not statistically significant - fail to reject the null hypothesis
p ≤ 0.01: Highly statistically significant
p ≤ 0.001: Very highly statistically significant

What's the difference between one-tailed and two-tailed tests?

Two-tailed test: Tests for any difference (increase or decrease). Used when you're interested in whether the proportion is different from the hypothesized value in either direction.
One-tailed test (greater): Tests if the proportion is greater than the hypothesized value.
One-tailed test (less): Tests if the proportion is less than the hypothesized value.

What sample size do I need for a proportion test?

For a valid proportion test, your sample should satisfy:
- n × p ≥ 10 and n × (1-p) ≥ 10 (normal approximation condition)
- Random sampling from the population
- Independent observations
For small samples, consider using exact binomial tests instead.

What is a Z-score?

The Z-score (test statistic) measures how many standard deviations your sample proportion is from the hypothesized proportion. A larger absolute Z-score indicates stronger evidence against the null hypothesis. The p-value is derived from the Z-score using the standard normal distribution.

Can I use this calculator for A/B testing?

Yes! This calculator is perfect for A/B testing. Use the Two Proportion Test to compare conversion rates between control (A) and treatment (B) groups. Input the conversion rate (proportion) and sample size for each group to determine if the difference is statistically significant.

What does "statistically significant" mean?

Statistical significance (typically p < 0.05) means that the observed difference is unlikely to have occurred by random chance alone. It suggests that there is likely a real effect or difference. However, statistical significance doesn't necessarily mean practical significance - consider effect size and real-world importance as well.

What's the formula for the test statistic?

One Proportion Z-test: z = (p̂ - p₀) / √(p₀(1-p₀)/n)
Two Proportion Z-test: z = (p̂₁ - p̂₂) / √(p̂(1-p̂)(1/n₁ + 1/n₂))
where p̂ = (x₁ + x₂)/(n₁ + n₂) is the pooled proportion.

P-value Interpretation Guide
p ≤ 0.001 Very strong evidence against H₀ ***
0.001 < p ≤ 0.01 Strong evidence against H₀ **
0.01 < p ≤ 0.05 Moderate evidence against H₀ *
0.05 < p ≤ 0.10 Weak evidence against H₀ .
p > 0.10 Little to no evidence against H₀ ns