[R] Use of geometric mean .. in good data analysis

[Simon, Stephen D.]

Sorry to prolong a thread on something that is clearly off topic, but when Michael Meyer wrote

 >by using the geometric mean all asymptotic results no longer apply.

that is flat our wrong. It's true that the geometric mean converges to something different that E[X], but it does indeed have an asymptotic distribution and one that makes sense in some contexts. There is no reason that converging to E[X] is desirable over other alternatives.

Reasons you might prefer the geometric mean.

1. You are interested in ratios instead of differences. A confidence interval for a ratio of geometric means is much simpler than a confidence interval for a ratio of arithmetic means.

2. Your data has issues with unequal variances caused by groups with larger means tending to have larger standard deviations.

3. You want to reduce the influence of outliers.

4. If your data follows a log normal distribution, then exp(E[log(X)]) is very good estimate of the population median.

An analysis using geometric means is different than an analysis using arithmetic means, but different does not mean inferior.