# Inferences about the Difference between Two Proportions

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This Demonstration explores statistical inferences regarding the difference between two proportions of populations obeying a condition (or trait). It calculates the statistical significance and the confidence intervals for the difference and plots the confidence intervals versus -value. This is done for differing populations obeying a condition or without the condition and for differing -values for the estimation of the confidence intervals.

Contributed by: Theodora Chatzimichail and Aristides T. Hatjimihail (Aristeidis T. Chatzimichail) (August 2018)

(Hellenic Complex Systems Laboratory)

Open content licensed under CC BY-NC-SA

## Details

The statistical significance of the difference between the two proportions is assessed by means of the -score (or critical ratio statistic) [1]. The confidence interval for the difference between the proportions is calculated as in [2].

References

[1] J. L. Fleiss, B. Levin and M. C. Paik, "Methods for Generating a Fourfold Table," *Statistical Methods for Rates and Proportions*, 3rd ed., Hoboken, NJ: J. Wiley, 2003 pp. 51–52.

[2] J. L. Fleiss, B. Levin and M. C. Paik, "A Simple Confidence Interval for the Difference between Two Independent Proportions," *Statistical Methods for Rates and Proportions*, 3rd ed., Hoboken, NJ: J. Wiley, 2003 pp. 60–61.

## Snapshots

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