PART III._THEORY OF SAMPLING.
CHAPTER XIII
SIMPLE SAMPLING OF ATTRIBUTES.
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 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
controlling the interpretation of statistical results.
1. ON several occasions in the preceding chapters it has been
pointed out that small differences between statistical measures like
percentages, averages, measures of dispersion and so forth cannot
in general be assumed to indicate the action of definite and assign-
able causes. Small differences may easily arise from indefinite
and highly complex causation such as determines the fluctuating
proportions of heads and tails in tossing a coin, of black balls in
drawing samples from a bag containing a mixture of black and
white balls, or of cards bearing measurements within some given
class-interval in drawing cards, say, from an anthropometric record.
In 100 throws of a coin, for example, we may have noted 56 heads
and only 44 tails, but we cannot conclude that the coin is biassed :
on repeating our throws we may get only 48 heads and 52 tails.
Similarly, if on measuring the statures of 1000 men in each of
two nations we find that the mean stature is slightly greater for
IB 4
