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MR. R. A. FISHER ON THE MATHEMATICAL 
expresses the proportion of the total available relevant information of which that 
statistic makes use. (4 and 10.) 
Efficiency ( Criterion). —The criterion of efficiency is satisfied by those statistics which, 
when derived from large samples, tend to a normal distribution with the least possible 
standard deviation. (4.) 
Estimation. —Problems of estimation are those in which it is required to estimate the 
value of one or more of the population parameters from a random sample of the 
population. (3.) 
Intrinsic Accuracy. —The intrinsic accuracy of an error curve is the weight in large 
samples, divided by the number in the sample, of that statistic of location which satisfies 
the criterion of sufficiency. (9.) 
Isostatistical Regions .—If each sample be represented in a generalized space of which 
the observations are the co-ordinates, then any region throughout which any set of 
statistics have identical values is termed an isostatistical region. 
Likelihood .—The likelihood that any parameter (or set of parameters) should have 
any assigned value (or set of values) is proportional to the probability that if this were 
so, the totality of observations should be that observed. 
Location .—The location of a frequency distribution of known form and scale is the 
process of estimation of its position with respect to each of the several variates. (8.) 
Optimum .—The optimum value of any parameter (or set of parameters) is that value 
(or set of values) of which the likelihood is greatest. (6.) 
Scaling .—The scaling of a frequency distribution of known form is the process of 
estimation of the magnitudes of the deviations of each of the several variates. (8.) 
Specification. —Problems of specification are those in which it is required to specify 
the mathematical form of the distribution of the hypothetical population from which 
a sample is to be regarded as drawn. (3.) 
Sufficiency. —A statistic satisfies the criterion of sufficiency when no other statistic 
which can be calculated from the same sample provides any additional information as 
to the value of the parameter to be estimated. (4.) 
Validity .—The region of validity of a statistic is the region comprised within its 
contour of zero efficiency. (10.) 
1. The Neglect of Theoretical Statistics. 
Several reasons have contributed to the prolonged neglect into which the study of 
statistics, in its theoretical aspects, has fallen. In spite of the immense amount of 
fruitful labour which has been expended in its practical applications, the basic principles 
of this organ of science are still in a state of obscurity, and it cannot be denied that, 
during the recent rapid development of practical methods, fundamental problems have 
been ignored and fundamental paradoxes left unresolved. This anomalous state of 
statistical science is strikingly exemplified by a recent paper (1) entitled “ The Funda- 
