# What are the best ways to express measures using two or more variables?

Efficiency, quality and outcome measures often consist of two or more variables.  These types of measures typically show a relationship or make a comparison, and should be expressed as proportions, percentages, rates or ratios.

## Proportions

A proportion is a pair of numeric values where the numerator must be contained within the denominator.  A proportion will identify the relative importance of an aspect in the population.  An example would be the number of driving while intoxicated arrests as a proportion of all traffic stops.  In a given period of time there are 80 traffic stops with 12 arrests for driving while intoxicated.  The measure is 12/80 = 0.15.

## Percentages

A percentage is a proportion multiplied by 100.  When measuring percentage the numerator is contained in the denominator.  An example would be where there are 100 clients and 69 are female.  The measure is 69/100 x 100 = 69%.

## Rates

A rate is commonly used to specify the frequency of a phenomenon in a specified group or population.  When calculating a rate, the numerator is also included in the denominator.  An example would be the number of calculation errors made on tax returns.  In a given period there are 45,000 tax returns filed with 6,300 calculation errors.  The error rate measure would be 6,300/45,000 = 0.14.  When expressed as a percentage the error rate measure would be 6,300/45,000 X 100 = 14%.

## Ratios

A ratio is a comparison of two values.  In a ratio, the numerator is not included with the denominator.  Ratios are used to compare a characteristic of a population with the portion of the population with the characteristic.  An example would be to compare the number of right-handed players to the number of left-handed players on a baseball team.  The team has 60 players.  45 players are right handed and 15 players are left-handed.  The ratio of right-handed players to left-handed players is 45 to 15.  Taken to the lowest common denominator, the ratio is 3 to 1.

Program Area Performance Management Performance Measures, Efficiency, Quality, Outcome, Proportions, Percentages, Rates, Ratios