CONTENTS. 
PART IIL-THEORY OF SAMPLING. 
CHAPTER XIIL 
SIMPLE SAMPLING OF ATTRIBUTES. 
™ Ss 
1. The problem of the present Part—2. The two chief divisions of 
the theory of sampling—3. Limitation of the discussion to 
the case of simple sampling—4. Definition of the chance of 
success or failure of a given event—5. Determination of the 
mean and standard-deviation of the number of successes in 
n events—6. The same for the proportion of successes in n 
events : the standard-deviation of simple sampling as a 
measure of unreliability or its reciprocal as a measure of 
precision—7. Verification of the theoretical results by ex- 
periment—8. More detailed discussion of the assumptions 
on which the formula for the standard-deviation of simple 
sampling is based—9-10. Biological cases to which the 
theory is directly applicable—11, Standard-deviation of 
simple sampling when the numbers of observations in the 
samples vary—12. Approximate value of the standard- 
deviation of simple sampling, and relation between mean 
and standard-deviation, when the chance of success or 
failure is very small —13. Use of the standard-deviation of 
simple sampling, or standard error, for checking and con- 
trolling the interpretation of statistical results . . 254-275 
CHAPTER XIV. 
SIMPLE SAMPLING CONTINUED: EFFECT OF REMOV. 
ING THE LIMITATIONS OF SIMPLE SAMPLING. 
1. Warning as to the assumption that three times the standard 
error gives the range for the majority of fluctuations of’ 
simple sampling of either sign—2. Warning as to the use 
of the observed for the true value of p in the formula for 
the standard error—3. The inverse standard error, or 
standard error of the true proportion for a given observed 
proportion : equivalence of the direct and inverse standard 
errors when n is large—4-8. The importance of errors 
other than fluctuations of “simple sampling” in practice : 
unrepresentative or biassed sanples—9-10. Effect of diver- 
gences from the conditions of simple sampling: (a) effect 
of variation in p and gq for the several universes from which 
the samples are drawn—11-12. (b) Effect of variation in 
p and g from one sub-class to another within each universe— 
13-14. (c) Effect of a correlation between the results of the 
several events—15. Summary . 276-290 
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