# Comparison of two rates

A rate is a ratio between a count and another measurement, for example the ratio of a number of events observed and the total number of person-years of observation.

This procedure allows to compare the rates in two groups.

This test is not performed on data in the data table, but on data you enter in a form.

## Required input

**Numerator**: the observed number of events in each group.**Denominator**: for example the total person-years for each group.- Option
**Express result as 1:X**: when this option is selected the rate R will be displayed as 1:(1/R), e.g. the rate 10/200 equals 0.05 and can be represented as 1:20.

## Results

The program displays:

- The (incidence) rate in the two groups with their Poisson 95% Confidence Interval.
- The difference between the two rates R2-R1 with its 95% Confidence Interval and associated P-value. If the P-value is less than 0.05 it can be concluded that there is a statistical significant difference between the two rates.
- The ratio of the two rates (the incidence rate ratio) R1/R2 with its 95% Confidence Interval and associated P-value. If the P-value is less than 0.05 it can be concluded that the ratio R1/R2 is not significantly different from 1 (which is the case when the rates are equal).

## Computational details

For the confidence interval of the difference between two rates, SciStat.com uses the "Test based Method" given on page 169 of Sahai H, Khurshid A (1996). The P-value is obtained using the Chi^{2}-statistic.

For the confidence interval of the incidence rate ratio, SciStat.com uses the "Exact Poisson Method" given on page 172-174 of Sahai H, Khurshid A (1996). The P-value is the exact mid-P double sided P-value (Hanley, 1986).

## Literature

- Hanley H (1986) Analysis of Crude Data. In: Modern Epidemiology, ed Rothman KJ. Boston: Little, Brown & Co.
- Sahai H, Khurshid A (1996) Statistics in epidemiology: methods, techniques, and applications. Boca Raton, FL: CRC Press, Inc.

## Link

Go to Comparison of two rates.