By D. J. Finney
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Extra info for An Introduction To The Theory Of Experimental Design
76, so that differences between rabbits and differences between doses are statistically significant. The former is perhaps of no intrinsic interest, but it confirms the wisdom of using individual rabbits as block constraints. Although the mean square for days is not significantly greater than error, it is sufficiently large to suggest that there may have been genuine differences and to make the experimenter glad that he adopted a design with balance over days as well as over animals. £. Source of Varia li on Square 215 ,4 72 ,4 521 , 1 19 .
3 A LATIN SQUARE EXPERIMENT ON THE EFFECT Ol" I NSULIN ON BLOOD SUGAR IN RABBITS (Results Are mg. Glucose per 100 cc. of Blood) DAY No. RABBIT No. r II III IV 1 ..... . 2 .... . . 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.
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.