Compare Two Proportions Calculator

Use this free calculator to test whether two proportions (percentages) measured in independent samples differ significantly. Enter the proportion and sample size for each group; the calculator returns the absolute difference between the proportions, its 95% confidence interval, the chi-squared statistic, and the p-value.

Typical applications include comparing response or cure rates between a treatment and a control group in a clinical trial, checking whether a medical outcome differs between two patient populations, or analysing survey responses from two independent groups.

Example: Compare 45% (n=120) vs 60% (n=150).

Sample 1
Proportion (%):
Sample size:
Sample 2
Proportion (%):
Sample size:

Interpreting the results

Difference: the absolute difference in percentage points between the two proportions. A positive value means Sample 1 has the higher proportion.

95% confidence interval: the range within which the true difference in the population is likely to fall. If the interval does not include 0, the difference is statistically significant at the 5% level.

P-value: the probability of observing a difference at least this large by chance, assuming the two true proportions are equal. A p-value below 0.05 is conventionally considered statistically significant, though the actual threshold depends on the study context.

Computational notes

MedCalc uses the "N-1" Chi-squared test as recommended by Campbell (2007) and Richardson (2011).

The confidence interval is calculated according to the recommended method given by Altman et al. (2000).

Standardized Mean Difference (SMD)

A P-value tells you whether a difference is statistically significant; it does not tell you how large the effect is. The Standardized Mean Difference (SMD) is an effect size measure that expresses the difference between two proportions in units of standard deviation, making it independent of sample size and directly comparable across studies. As a rule of thumb (Cohen, 1988), an SMD around 0.2 is a small effect, 0.5 a medium effect, and 0.8 or more a large effect.

The SMD with a 95% confidence interval is available in the MedCalc desktop program, which uses the accurate noncentral t distribution method for the confidence interval. Download MedCalc — free 15-day trial.

Literature

Altman DG, Machin D, Bryant TN, Gardner MJ (Eds) (2000) Statistics with confidence, 2^nd ed. BMJ Books. (p. 49)
Campbell I (2007) Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations. Statistics in Medicine 26:3661-3675.
Richardson JTE (2011) The analysis of 2 x 2 contingency tables - Yet again. Statistics in Medicine 30:890.

How to cite this page

MedCalc Software Ltd. Compare Two Proportions Calculator. https://www.medcalc.org/en/calc/comparison_of_proportions.php (Version 24.0.3; accessed November 7, 2026)