table for ten experiment we find by interpolating between .8697 and .9161 that .44 corresponds to .8873, or the odds are .887 to .113 that the mean is positive.
That is about 8 to 1 and would correspond in the normal curve to about 1.8 times the probable error. It is then very likely that 1 gives an increase of sleep, but would occasion no surprise if the results were reversed by further experiments.
If now we consider the chance that 2 is actually a soporific we have the mean increase of sleep or 1.23 times the S.D. From the table the probability corresponding to this is .9974, i.e. the odds are nearly 400 to 1 that such is the ease. This corresponds to about 415 times the probable error in the normal curve. But I take it the real point of the authors was that 2 is better than 1. This we must test by making a new series, subtracting 1 from 2. The mean value of this series is +1.58 while the S.D. is 1.17, the mean value being +1.35 times the S.D. From the table the probability is .9985 or the odds are about 666 to 1 that 2 is the better soporific. The low value of the S.D. is probably due to the different drugs reacting similarly on the same patient, so that there is correlation between the results.
Of course odds of this kind make it almost certain that 2 is the better soporific, and in practical life such a high probability is in most matters considered as a certainty.
Illustration II. Cases where the tables will be useful are not uncommon in agricultural work, and they would be more numerous if the advantages of being able to apply statistical reasoning were borne in mind when planning the experiments. I take the following instances from the accounts of the Woburn farming experiments published yearly by Dr Voelcker in the Journal of the Agricultural Society.
A short series of pot culture experiments were conducted in order to determine the causes which lead to the production of Hard (glutinous) wheat or Soft (starchy) wheat. In three successive years a bulk of seed corn of one variety was picked over by hand and two samples were selected, one consisting of “hard” grains and the other of “soft.” Some of each of these were planted in both heavy and light soil and the resulting crops were weighed and examined for hard and soft corn.
The conclusion drawn was that the effect of selecting the seed was negligible compared with the influence of the soil.
This conclusion was thoroughly justified, the heavy soil producing in each case nearly 100 per cent. of hard corn, but still the effect of selecting the seed could just be traced in each year.
But a curious point, to which Dr Voelcker draws attention in the 2nd year’s report, is that the soft seeds produced the higher yield of both corn and straw. In
