An Introduction to Modern Statistical Methods

An Introduction to Modern Statistical Methods

An Introduction to Modern Statistical Methods

An Introduction to Modern Statistical Methods

Excerpt

In the past three decades enormous advances have been made in the field of statistics. These advances have taken place so rapidly that it is not at all surprising that those employing statistical methods have found it difficult to keep pace with them, or that certain of the older methods, which are obsolete, and even in some cases erroneous--or, at the very best, crudely approximative in character--continue to be taught in the classroom and to be treated in textbooks which appear from time to time. A notable example is the use of the probable error or standard error in testing the significance of a correlation coefficient derived from a sample, although this method gives unreliable or incorrect results if there is a high degree of correlation in the population from which the sample is drawn, or if the number in the sample is small.

It is, of course, in the theory of small samples that the greatest progress has been made. The theory of sampling which assumes that the sample is composed of a large number of items is inadequate for many practical purposes. Biological, agricultural, and other scientific experiments frequently deal with comparatively few observations. Sometimes the cost of obtaining additional observations is prohibitive; sometimes, indeed, it is impossible to obtain more data, as might be true in the case of meteorological records. In manufacturing inspection, too, small samples are of frequent occurrence.

Most of this theory has been developed and unified by R. A. Fisher, who has shown how to make more accurate estimates and how to utilize the maximum amount of information contained in a set of data, and has provided exact tests of reliability and significance. Fisher's efficient methods, at first slow in taking hold, because not thoroughly understood, gradually began to gain momentum, and are now spreading rapidly.

In this book I have endeavored to explain the most widely used of these methods, illustrating their application by com-

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