By D. J. Finney
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Extra resources for An Introduction To The Theory Of Experimental Design
T - LY~' 1- 1 . 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.
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.
And error exa tly as for an ordinary randomized block design. S / Blocks .............. Temperatures (T) . . Quantities (Q) . . . . Periods (P) . . . . . 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.