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 experiment—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 standarddeviation
 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 controlling
 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 divergences
 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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