## Key Concepts About Generating Geometric Means

In instances where the data are highly skewed, geometric means can be used. A geometric mean, unlike an arithmetic mean, minimizes the effect of very high or low values, which could bias the mean if a straight average (arithmetic mean) were calculated. The geometric mean is a log-transformation of the data and is expressed as the N-th root of the product of N numbers.

A highly skewed distribution is common in the measurement of environmental chemicals in blood or urine. The geometric mean is influenced less by high values than is the arithmetic mean. Geometric means are calculated by taking the log of each concentration and then computing the weighted mean of those log-transformed values. Ninety-five percent confidence intervals around this weighted mean are calculated by adding and subtracting an amount equal to the product of a Student’s t-statistic and the standard error of the weighted mean estimate. The degrees of freedom of the t-statistic are determined by subtracting the number of strata from the number of Primary Sampling Units (PSUs) according to the data available from the complex survey design. The weighted geometric mean and its confidence limits are then obtained by taking the antilogs of this weighted mean and its upper and lower confidence limits.