# Comparison of two rates

Command: | Tests Rates Comparison of two rates |

## Description

An incidence 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 incidence rates in two groups.

This test is not performed on data in the spreadsheet, but on data you enter in a dialog box.

## 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.

When all data have been entered click Test.

## Results

MedCalc reports:

- 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 and its 95% Confidence Interval. If the P-value is less than 0.05 it can be concluded that the ratio R1/R2 is significantly different from 1 (which is the case when the rates are equal).

For the confidence interval of the difference between two rates, MedCalc 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, MedCalc 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)

In the *Comment* input field you can enter a comment or conclusion that will be included on the printed report.

## 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.