The first general law that all experimenters should know and the ignorance of which has caused and still causes the waste of the major portion of experimental brains and money, we will call the “Law of Chance.”  Let the reader who is not familiar with such things take two pennies and toss them upon the table.  They are both heads up.  He tosses them again, one comes heads, the other tails.  The third time repeats the second.  The fourth both come tails.  The law of chance says this is correct.  Heads should appear 25 per cent., tails 25 per cent., and mixed 50 per cent. of the time.  Now let the reader try this in a lot of twelve tosses.  Does it prove the law?  Try it again.  Are all lots alike?  Now pitch a hundred times, then pitch pennies all day.  By night the law will be so near proven that the experimenter will be willing to concede its validity.

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.