# Guidance for Health Outcome Data Review and Analysis Relating to NYSDEC Environmental Justice and Permitting

## Appendix B - Calculating Confidence Intervals

A basic spreadsheet such as Microsoft's Excel can be used to calculate confidence intervals using standard equations found in many epidemiology textbooks. This is especially useful if you will be repeating the calculation numerous times. There are also many web based statistical calculators which can calculate confidence intervals, although the results may vary slightly depending on which method is used. While Excel does have the capability to calculate a number of descriptive statistics and statistical functions itself, including confidence intervals, many of these assume you have access to the raw data needed to calculate the variance and standard deviation. Since we are only given the either the observed and expected cases or rates among the local and comparison populations, preprogrammed spread sheets with formulas that allow the user to calculate confidence intervals can be used without having all of the data points. Selection of the appropriate spreadsheet will depend on how your data are organized and the measure around which the confidence interval is being developed. So far there are two specific types of examples that have been given, asthma rates and cancer incidence. Each one needs to be approached slightly differently; however, the same general formula can be applied to both. The confidence limits are based on the Byar's approximation of the exact Poisson distribution which is extremely accurate even with small numbers (Breslow and Day, 1987).

SIR = Standardized Incidence Ratio
O = Observed number of cases
E = Expected number of cases
Za/2 = Value of the standard normal distribution for a given significance level (alpha).

(For a 95% confidence interval alpha = 0.05 and Za/2 =1.96)