20 
The Prohahle Error of a Mean 
Section VIII. Ea:pla nation of Tables. 
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 — oo and z. Thus, to take the table for samples of six, the probability 
of the mean of the population lying between — oo 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 '0S78 that it is greater than once the standard 
deviation and "0756 that it lies outside + I'O times the standard deviation. 
Section IX. Ilhistrations of Method. 
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 Pliysiology 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 
hydrobi-omide, (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. 
Additional hours' sleep gained by the use of hyoscyamine hydrobromide. 
Patient 
1 (Dextro-) 
2 (Laevo-) 
Difference (2-1) 
1. 
+ -7 
+ 1-9 
+ 1-2 
2. 
-1-6 
+ -8 
+ 2-4 
3. 
— -2 
+ 11 
+ 1-3 
4. 
-1-2 
+ -1 
+ 1-3 
5. 
- 1 
- 1 
0 
6. 
+ 3-4 
+ 4-4 
+ 1-0 
7. 
+ 3-7 
+ 5-5 " 
+ 1-8 
8. 
+ -8 
+ 1-6 
+ -8 
9. 
0 
+ 4-6 
+ 4-6 
10. 
+ 2-0 
+ 3-4 
+ 1-4 
Mean + -7.5 
Mean +2-33 
Mean +1-58 
S. D. 1-70 
S. D. 1-90 
S. D. 117 
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 
+ •75 
experiments are a sample is positive. = "44 and looking out z = "44 in the 
