tailieunhanh - A Course in Mathematical Statistics phần 9

Tham khảo tài liệu 'a course in mathematical statistics phần 9', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Chapter 17 Analysis of Variance The Analysis of Variance techniques discussed in this chapter can be used to study a great variety of problems of practical interest. Below we mention a few such problems. Crop yields corresponding to different soil treatment. Crop yields corresponding to different soils and fertilizers. Comparison of a certain brand of gasoline with and without an additive by using it in several cars. Comparison of different brands of gasoline by using them in several cars. Comparison of the wearing of different materials. Comparison of the effect of different types of oil on the wear of several piston rings etc. Comparison of the yields of a chemical substance by using different catalytic methods. Comparison of the strengths of certain objects made of different batches of some material. Identification of the melting point of a metal by using different thermometers. Comparison of test scores from different schools and different teachers etc. Below we discuss some statistical models which make the comparisons mentioned above possible. One-way Layout or One-way Classification with the Same Number of Observations Per Cell The models to be discussed in the present chapter are special cases of the general model which was studied in the previous chapter. In this section we consider what is known as a one-way layout or one-way classification which we introduce by means of a couple of examples. 440 One-way Layout or One-way Classification 441 EXAMPLE 1 Consider I machines each one of which is manufactured by I different companies but all intended for the same purpose. A purchaser who is interested in acquiring a number of these machines is then faced with the question as to which brand he should choose. Of course his decision is to be based on the productivity of each one of the I different machines. To this end let a worker run each one of the I machines for J days each and always under the same conditions and denote by Yy his output the jth day