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As a final example, then, consider some calculations that were done in
1983 of the percentage of women in the Fellowship in the United States and
Canada. The problem was to establish conditions under which any member in
that population was equally likely to be chosen for determination of their
sex. The approximate solution was to establish conditions under which
each group listed at G.S.O. was equally likely to be selected for survey.
in 1983 somewhat less than 2% of the groups listed at G.S.O. were selected
by a process in which each group in the population was (approximately!)
equally likely to turn up in the two percent. On the average, about 20
members per group are expected to be reached in that way, and in 1983 we
had responses from about 7,000 individuals.
A biased result would have been obtained if all these individuals had been
selected from one state, or one region, or by a number of people around
the country selecting the groups they thought were the best groups, or the
groups they thought were most typical, etc.
In the random sample actually used, the percentage of women in 1983 was
determined to be 31 percent. Because we did not determine the sex of
every member of the Fellowship, this result can only have approximate
validity when applied to the population. However, statistics allows
precise statements to be made about the extent of its validity, in terms
of probabilities.
Confidence Limits: If we have succeeded in establishing random
conditions, then mathematical statistics can give a table of the
relationship between (1) the probability that the percentage of women in
the entire population falls within certain limits around the percentage in
the sample, and (2) the width of those limits; for example:
Statement of Confidence in
the result the statement
31% +- 2% 99%
31% +- 1% 90%
31% +- 0.5% 75%
The meaning of the entries in the table is this: If I want to make a
statement that is 99% likely to be correct, I can only say that the
percentage of women in the population lies between 29 and 33 percent. If,
however, I am content to make a statement that is only 90% likely to be
correct, then I can say that the percentage of women lies between 30 and
32 percent. Statisticians usually attribute significance only to state-
ments made with more than 90% probability of being correct.
This table approximates the actual confidence one can have in the
statement of the 1983 survey about the percentage of women in the sample,
and, when corrected for frequency of attendance at meetings, in the
population sampled. However, the term "A.A. member" is very loosely
defined and includes many not in the population sampled. Whether such
members differ from the sampled population in other respects, and by how
much, is not known.
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