## Significantly Different

An area's observed rate should be considered an estimate of the true underlying rate. The number of events (deaths, hospitalizations, etc.) in an area varies by chance, depending on the number of persons counted as residents there and the probability of the event. Thus, rates based on small numbers are particularly unstable.

Stability is especially important when comparing areas with each other. Therefore, we performed statistical significance tests to determine whether the differences between the county rates and the corresponding state rates were probably the result of chance factors.

On the Community Data Profiles, if an "H" or "L" is present in the Significantly Different column, there is 95 percent confidence that the true county rate is really higher ("H") or lower ("L") than the true state rate. That is, we estimate that there is only a 5 percent chance (1 in 20) that the difference between the county's rate and the corresponding state rate is due to random error or chance.

If "N/S" is noted, we cannot state with confidence that the difference between the county rate and the state rate is not due to random variations. That is, the difference is not statistically significant.

For example, in the case of death rates per 100,000 population, the significance of the difference between two rates is tested by:

((100,000) / (population X years)) X (1.96 X (square root of deaths))

If the result is less than the size (absolute value) of the difference between the rates (regardless of the direction of the difference), then the difference is significant.

The number of years is included in the denominator in order to annualize the rates.

Statistical significance is easier to obtain with larger populations. For indicators for which the number of events is less than 20, the observed rate may be very different from the true underlying rate, so that only a relatively large difference in rates would be considered significant. As the numbers grow larger, the chance component becomes less important and the observed rate is a better estimate of the true rate.