Selected Works of E. L. Lehmann pp 575-593 | Cite as

# Deficiency

## Introduction and summary

Consider a statistical procedure (Method A) which is based on n observations, and a less effective procedure (Method B) which requires a larger number k_{n} of observations to give equally good performance. Comparison of the two methods involves the comparison of k_{n} with n_{9} and this can be carried out in various ways. Perhaps the most natural quantity to examine is the difference k_{n} — n, the number of additional observations required by the less effective method. Such difference comparisons have been performed from time to time. (See, for example, Fisher (1925), Walsh (1949) and Pearson (1950).) Historically, however, comparisons have been based mainly on the ratio k_{n} */*n. Thus, Fisher (1920), in comparing the mean absolute deviation with the mean squared deviation as estimates of a normal scale, found this ratio to be 1/1.14. Similarly in 1925 he found a large-sample ratio of *2/π* for median compared with mean for estimating normal location, and the same value was found by Cochran (1937) for the sign test relative to the *t*-test in the normal case.

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Covariance### References

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