On Some Useful “Inefficient” Statistics

Summary

Several statistical techniques are proposed for economically analyzing large masses of data by means of punched-card equipment; most of these techniques require only a counting sorter. The methods proposed are designed especially for situations where data are inexpensive compared to the cost of analysis by means of statistically “efficient” or “most powerful” procedures. The principal technique is the use of functions of order statistics, which we call systematic statistics.

It is demonstrated that certain order statistics are asymptotically jointly distributed according to the normal multivariate law.

For large samples drawn from normally distributed variables we describe and give the efficiencies of rapid methods:

• i) for estimating the mean by using 1, 2, …, 10 suitably chosen order statistics;

• ii) for estimating the standard deviation by using 2, 4, or 8 suitably chosen order statistics;

• iii) for estimating the correlation coefficient whether other parameters of the normal bivariate distribution are known or not (three sorting and three counting operations are involved).

The efficiencies of procedures ii) and iii) are compared with the efficiencies of other estimates which do not involve sums of squares or products.