# Tests for equality of proportions (independent samples)

Tests for the equality of proportions of independent samples and their properties and assumptions.

Test | Purpose |
---|---|

Fisher exact | Test if the two proportions are equal. Assumes fixed marginal distributions. Although not naturally fixed in most studies, this test still applies by conditioning on the marginal totals. Uses hypergeometric distribution and computes an exact p-value. The exact p-value is conservative, that is, the actual rejection rate is below the nominal significance level. Recommended for small sample sizes or sparse data. |

Score Z | Test if the two proportions are equal. Uses the score statistic and computes an asymptotic p-value. Note that the two-sided Score Z test is equivalent to Pearson's X |

Pearson X² | Test if the proportions are equal in each category. Uses the score statistic and computes an asymptotic p-value. Note that the asymptotic distribution of the X |

**Related concepts**

**Available in Analyse-it Editions**

Standard edition

Method Validation edition

Quality Control & Improvement edition

Ultimate edition

- What is Analyse-it?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Contingency table
- Creating a contingency table
- Creating a contingency table (related data)
- Grouped frequency plot
- Effect size
- Estimators
- Estimating the odds ratio
- Estimating the odds ratio (related data)
- Relative risk
- Inferences about equality of proportions
- Equality of proportions hypothesis test
- Exact and asymptotic p-values
- Wald, Score, Likelihood ratio
- Tests for equality of proportions (independent samples)
- Testing equality of proportions (independent samples)
- Tests for equality of proportions (related samples)
- Testing equality of proportions (related samples)
- Inferences about independence
- Mosaic plot
- Creating a mosaic plot
- Study design
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 5.30

Published 15-Apr-2019