Page:Biometrika - Volume 6, Issue 1.djvu/20

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The tables give the probability that the value of the mean, measured from the mean of the population, in terms of the standard deviation of the sample, will lie between $$-\infty$$ and $$z$$. Thus, to take the table for samples of six, the probability of the mean of the population lying between $$-\infty$$ and once the standard deviation of the sample is .9622 or the odds are about 24 to 1 that the mean of the population lies between these limits.

The probability is therefore .0378 that it is greater than once the standard deviation and .0756 that it lies outside ±1.0 times the standard deviation.

Illustration I. As an instance of the kind of use which may be made of the tables, I take the following figures from a table by A. R. Cushny and A. R. Peebles in the Journal of Physiology for 1904, showing the different effects of the optical isomers of hyoscyamine hydrobromide in producing sleep. The sleep of 10 patients was measured without hypnotic and after treatment (1) with D. hyoscyamine hydrobromide, (2) with L. hyoscyamine hydrobromide. The average number of hours’ sleep gained by the use of the drug is tabulated below.

The conclusion arrived at was that in the usual dose 2 was, but 1 was not, of value as a soporific.

First let us see what is the probability that 1 will on the average give increase of sleep; i.e. what is the chance that the mean of the population of which these experiments are a sample is positive. $$\frac{+.75}{1.70}=.44$$ and looking out $$z=.44$$ in the