Frequencies, Rates and Ratios

by

Adam J. McKee, Ph.D.

January, 2004

                The easiest way to present data is simply to count it and present the number of occurrences of the variable. These counts are referred to as frequencies (¦). Frequencies presented alone with no other information can be misleading.  This is especially true in dealing with populations of various sizes such as the FBI's Uniform Crime Report (UCR).  The UCR reports crime data by regions.  To present a more evenhanded view of things, crimes are often reported in rates.   Rates present data controlled for population size differences, functioning like a percent in that respect.    The FBI has chosen to express rates as incidents per 100,000 people.  This is referred to as standardizing.  This is the most common format.  The rate is calculated as follows:

Rate =

To calculate the standardized rate, we multiply the rate by 100,000 (or whatever base we are using).  Rates can be calculated for subpopulations in this manner, such as the rates of males and females. 

Ratios

                Ratios show the relationship between two numbers and indicate their size relative to each other.  A ratio is simply one number divided by another.  For example, given that the rate of murder in New Orleans is 100 and the rate of murder in Hattiesburg is 10, we can calculate the ratio as follows:

From this we can say:

·         For every one murder committed in Hattiesburg, 10 are committed in New Orleans.

·         Ten times more homicides were committed in New Orleans than in Hattiesburg.

Percents and Proportions

                A proportion (also called a relative frequency) is a ratio of cases with a specific value and the number in the sample.  If we want to know the proportion of whites in our sample, we divide the number of whites (¦) by the number in the sample (N).  For example, we draw a sample of 100 and 85 of those are white.

                A percentage reflects the number of cases that have our specified value per 100 cases.  We obtain a percentage by multiplying our proportion by 100.  If we want to know the percentage of whites in our sample, we divide the number of whites (¦) by the number in the sample (N) to obtain a proportion, and multiply that proportion by 100.

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