By Oscar Kempthorne
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Examples will be given as they arise. REFERENCES 1. Mood, A. M. Introduction to the theory of statistics. McGraw-Hill, New York. 1950. 2. Hoel, P. G. Introduction lo mathematical statistics. John Wiley & Sons, New York. 1947. org/access_use#pd-google 3. Wald, A. Sequential analysis. John Wiley & Sons, New York. 1947. 1 INTRODUCTION In this chapter we shall give an elementary discussion of least squares theory. This theory is basic to the subject of the design of experiments, and the material of this chapter is given with the hope that readers who are not mathematically minded will obtain sufficient insight into the process to appreciate the two succeeding chapters.
Alternatively he may claim that he will be correct in a proportion P of cases. org/access_use#pd-google we may examine whether the results he has obtained after a particular number of trials are in reasonable agreement with his claims. 96\/p(l - P)/n, unless he has been unlucky to the extent of a l-in-20 chance event happening. ) We note that the probable range within which the actual result will be depends on the true proportion and on the number of trials. The relation to the true proportion is not of particular interest at this stage of the discussion, though in other cases it is of fundamental importance, and so we will con- cern ourselves only with n, the number of trials.
Parametric es- timates are, of course, obtainable only when the form of the distribu- tion is known, in distinction to non-parametric estimates for which this is not the case. Most of the methods of estimation in current use are parametric, but increasing use is being made of non-parametric methods, because less specification or none at all of the parent distri- bution is necessary for their use. We shall be concerned mainly with parametric methods based dn distributions of assumed form, or speci- fied sufficiently to allow a solution.