Đây là một ví dụ đơn giản của một thử nghiệm giai thừa, sẽ được thảo luận nói chung trong § 9,3. Sự khác biệt giữa tình trạng này và ngăn chặn các thử nghiệm ngẫu nhiên là sau `khối phân loại 'được giới thiệu chủ yếu là để cung cấp thêm độ chính xác để so sánh điều trị | Two-way analysis of variance randomized blocks 239 combination of r periods of storage of plasma and c concentrations of adrenaline mixed with the plasma. This is a simple example of a factorial experiment to be discussed more generally in . The distinction between this situation and the randomized block experiment is that in the latter the block classification is introduced mainly to provide extra precision for treatment comparisons differences between blocks are usually of no intrinsic interest. Two-way classifications may arise also in non-experimental work either by classifying in this way data already collected in a survey or by arranging the data collection to fit a two-way classification. We consider first the situation in which there is just one observation at each combination of a row and a column for the zth row and th column the observation is yij. To represent the possible effect of the row and column classifications on the mean value of ytj let US consider an additive model by which E yy p a Py where Uj and Py are constants characterizing the rows and columns. By suitable choice of p we can arrange that r E a - 0 j l and c E py 0. 7 1 According to the effect of being in one row rather than another is to change the mean value by adding or subtracting a constant quantity irrespective of which column the observation is made in. Changing from one column to another has a similar additive or subtractive effect. Any observed value yy will in general vary randomly round its expectation given by . We suppose that yij E yy y where the ij are independently and normally distributed with a constant variance Ơ2. The assumptions are of course not necessarily true and we shall consider later some ways of testing their truth and of overcoming difficulties due to departures from the model. Denote the total and mean for the zth row by R and w those for the ýth column by Cj and ỹy and those for the whole group of N rc observations by T and y see .
