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By D. J. Finney
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1 Here y .! = L i Yii. Y;, = L Ya . j y .. 1 is likely to be needed. 2), can be tested by comparison of the mean squares for "treatments" and "residual" in the analysis of variance, for which reason the latter is frequently termed simply "error"; standard errors of treatment means can be based upon this error mean square. 2 USE OF RANDOMIZED BLOCKS This design is perhaps the most commonly used of all, because of its adaptability and the ease with which it can be modified. Obviously it can be constructed whatever the values of rand t, and, unlike many designs to be considered later, its structure has no intrinsi interest.
2 leaves the residual for PQ, here by chance exactly zero. Thus the sum of squares for treatments obtained previously can be subdivided into three components with different meanings, which can be examined separately for significance; of course, the occurrence of 0 for the PQ square is an accident due to the grouping of the original observations to the nearest unit. 4. 1. Essentially the same type of analysis and computation can be adopted when factors have more than two lev I . 4 was mentioned an inve tigation in which a factory product was to be made experimentally at each of three temperatures for a certain stage of the pro e s, u ing each of four quantitie of a certain raw material, and maintaining the temperature for one of two alternative periods.
Write Yii (i = 1,2, . , t; j = 1, 2, ... 1 RANDOMIZED ARRANGEMENT FOR 6 BLO CKS OF 5 TREATMENTS IN A RANDOMIZED BLOCK DESIGN PLOT WITIlIN BLOC>: 1.... ..... 2 . . . ... " ... 3 .. ........ 4 ..... •. .. 5 . . ... .. .... BLOCX D E C A B . II III IV D A C V VI B E A D D B C A C A B D B E E D E C B E C A The treatments are denoted by the letters A, B, C, D, E . i, and (77 + f'Ji) is the average for all treatments on block j alone. The residual t ii is the amount by which Yii differs from a value predicted by adding average block and treatment "effects" to 77; it is compounded of any "interaction" between the relative effects of different treatments and the block classification (d.