Now suppose the lots of twelve tosses, each were lots of twelve hens, one Plymouth Rocks, the other Wyandottes, or one fed corn and the other wheat. The law of chance clearly proves that the larger number of unites, the nearer the theoretical truths will be the experimental results. Note, however, that small lots may by chance be as near the truth as large lots.
In practice two grave errors are made: First, conclusions are drawn from small lots compared with each other; second, conclusions are drawn from large lots compared with small lots. In the first case both may be off; in the latter case the small one may be off. Examples of the first error are to be found in the scores of contradicting breed and feed tests, that were published in the early days of poultry research. The second error is exemplified in the Ontario experiments in incubation, to which reference has already been made.
Here is a further example of this error. From the fifth egg laying competition at the Hawkesbury Agricultural College in Australia, I copy the following:
| No. of Hens. | Variety. | Ave. Egg Yield. |
| 6 | Cuckoo Leghorn | 190.16 |
| 30 | S.C. Brown Leghorn | 177.00 |
| 138 | S.C. White Leghorn | 174.93 |
| 12 | R.C. Brown Leghorn | 173.50 |
| 12 | R.C. White Leghorn | 172.66 |
| 18 | Buff Leghorn | 160.55 |
| 6 | Black Leghorn | 138.33 |
The ranking of Cuckoo Leghorns as first is a chance happening due to the small number; likewise the Black Leghorns had a streak of bad luck and received lowest place. To one not familiar with such work, the real significance of the table is that the S.C.W. Leghorns did the best work. A totaling of all other varieties gives 84 fowls with an average egg production of 170.5, which bears out the conclusion. As these birds were all kept in pens of six, we would expect to find the highest single pen to be White Leghorns, because, when compared with all other Leghorns, they have both the highest average and the greatest number. This accords with the fact that as the highest single pen is found to be White Leghorns with an egg yield of 239 eggs.
The above illustrates another important phase of the laws of chance, which says that not only is the average likely to be nearer the theoretical average sought when the number is increased, but that the individual extremes will be more removed.
Important Experimental Results at the Illinois Station.
From an Illinois Experiment Station report, the following is quoted:
"The stock used was Barred Plymouth Rock pullets. These pullets were a very uniform Barred Rock stock that had been bred as an individual strain for many years. They were practically the same age, and except for the factors mentioned were treated as uniformly as possible.
| First Year's Results. | ||||
| No. Hens. | Diet. | Ave. Egg Yield. | ||
| 10 | Nitrogenous Diet | 132.9 | ||
| 10 | Carbonaceous Diet | 128.4 | ||
| 10 | Wet Wash | 155.8 | ||
| 10 | Dry Wash | 111.4 | ||