Difference of Proportions Calculator

Step 1: Enter Your Data

For each group, provide:

• Group Name: Optional label for easier identification (e.g., "Control" vs "Treatment")
• Total Respondents (n): The total sample size for each group
• Positive Feedback Count (x): The number of successes or positive outcomes

Step 2: Set Hypothesis Parameters

• Hypothesized Difference: The expected difference under the null hypothesis (usually 0, meaning no difference)
• Significance Level (α): The threshold for determining statistical significance (commonly 0.05 for 95% confidence)

Step 3: Interpret Results

The calculator provides:

• Z-score: Measures how many standard deviations the observed difference is from the hypothesized difference
• P-value: The probability of observing this difference by chance. Lower values indicate stronger evidence against the null hypothesis
• Conclusion: Whether to reject or fail to reject the null hypothesis based on your significance level
• Confidence Intervals: The range where the true difference likely falls (95% and 99% levels)

📊 Example Use Case

Scenario: Testing if a new website design increases conversion rates

• Control Group: 1000 visitors, 80 conversions
• New Design: 1000 visitors, 110 conversions
• Result: Calculator determines if the 3% difference is statistically significant

💡 Key Assumptions

• Independent random samples from each population
• Sample sizes should be large enough (np ≥ 5 and n(1-p) ≥ 5 for normal approximation)
• The calculator uses a two-tailed test by default