Efficiency

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The efficiency of a statistic is the degree to which the statistic is stable from sample to sample. That is, the less subject to sampling fluctuation a statistic is, the more efficient it is. The efficiency of statistics is measured relative to the efficiency of other statistics and is therefore often called the relative efficiency. If statistic A has a smaller standard error than statistic B, then statistic A is more efficient than statistic B.

The relative efficiency of two statistics may depend on the distribution involved. For instance, the mean is more efficient than the median for normal distributions but not for some extremely skewed distributions.

The efficiency of a statistic can also be thought of as the precision of the estimate: The more efficient the statistic, the more precise the statistic is as an estimator of the parameter.