By D. J. Finney
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Extra info for An Introduction To The Theory Of Experimental Design
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Y:, i-I -rr By difference (r-l) (I - l ) 0" 2 + -t~tJ~ r - r i- I 2+ r~T 2i t- 1 0" 0-' ~ rl - l 1 L , Yij-rr 2 y .. , .. 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.
B: 47 D :46 A: 62 C: 76 C: 79 B: 63 D: 58 D : 50 A: 69 4 . .... . A: 90 C: 74 B: 61 D : 63 A: 87 B: 59 266 252 247 285 288 287 244 1050 3 . . . . Total .. 231 A Total.. 308 . B 230 TOTAL C: 66 c D 295 217 and rows corresponding to different days, enables both constraints to be incorporated. 3 shows such a square, chosen at random from the 576 possible squares, with the set of 16 "yields," here mg. glucose per 100 cc. of blood at a fixed time after the insulin injection. Totals by row and by column have been inserted for use in the analysis, and totals for the four treatments have been recorded.
TQ ................. TP ........ ..... QP ...... . TQP ........ l. Variation 3 X 2 Mean Square 5 2 3 1 6 2 3 6 Treatments . . . . . Error ...... .... " . 23 115 Total .... .... 1, the treatment component could be subdivid d into 23 separate squares for single and mutually orthogonal contrasts. 1 uffices. Yields are classified according to temperature, and totals of the groups of 48 formed irrespective of quantity of material and period. , the main effect of factor T. Analogous calculations are used on four totals of 36 yields classified by quantity and the two totals of 72 classified according to period.