By D. J. Finney
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Extra resources for An Introduction To The Theory Of Experimental Design
Error . . . . 1- 1 1- 1 I- I I-I Total. . . ...... tX I GRECO-LATIN SQUARE Sum of quur .. n Square (1-1)(1 - 3) 1'- 1 letter of the new square occur once in each row and once in each column, but also it occurs once with each letter of the first square. 2 might have wi hed to test simultaneously inoculation by five different techniques Ca, (3, ... , E). 4. 3 also has no orthogonal square. 4 is both permissible and easily computed; thus the two 33 Randomized Blocks and Orthogonal Squares sets of treatments are examined simultaneously in the one experiment.
The normal error model is the simpler, in that if it is applicable the ratios of mean squares in the analysis of variance (for the completely randomized and for other designs) follow the variance ratio distribution when appropriate null hypotheses are true. Although the randomization moder has some theoretical advantages and involves more easily justified assumptions than does the normal, the difference between them has little relevance to the theme of this book and will seldom be mentioned. It is today fashionable to decry the normal error model as an improper basis for experimentation and statistical analysis, but this attitude appears to be somewhat pedantic.
3 3 6 646 . " . " "" , .. " . 15 2,545,75 . NTRATION IN MG. PER 100 CC. E. 8 54 , 2 ±2 . 83/ 4) . Underlying this analysis is the assumption that, for the general tXt Latin square, the yield J ijl: (i, j, k = 1, 2, ... 6) 31 Randomized Block. and Orthogo"al Square. 2). 6) is to be applicable. The expectations of the means squares are then t (12 + - - 2: r2 (3. 7) t- 1 for treatments, with similar expressions for columns and rows. 2. It is probably not unreasonable to think of the experimental animals as a random selection from a laboratory population.
An Introduction To The Theory Of Experimental Design by D. J. Finney