I undertook a similar study, with the aim of proving a negative
(statistically). The sampling unit, as in Allen Dick's case, was an
individual hive.

The number of mite-infested hives follows a binomial distribution with the
following parameters (in the present case): n = 350 hives sampled (assuming
35 hives sampled in each of 10 yards); x = number of infested hives in the
sample; and p = probability of a hive being infested. To find the 99% upper
confidence limit on the prevalence of mite infestation, given negative
sampling results (i.e., no mites found), a simple formula can be used:
1-(alpha**(1/n)). Substituting the values: 1-(0.01**0.0029) = 0.0133.
Therefore, if the 350 hives represented a random sample of the total number
of hives managed, there would be a 99% probability that the unknown
prevalence of infestation would not exceed 1.33%.

However, the present example does not constitute a random sample. The sample
should include hives from each of the 66 yards, and the larger the sample
size, again assuming no mites found, the lower the theoretical prevalence of
infestation will be, lending more credence to the conclusion that the
population is mite-free.


Tom Culliney, Hawaii Dept. of Agriculture, Division of Plant Industry, 1428
South King St., Honolulu, HI 96814 U.S.A.
E-mail: [log in to unmask]
Telephone: 808-973-9528
Fax: 808-973-9533

"To a rough approximation and setting aside vertebrate chauvinism, it can be
said that essentially all organisms are insects."--R.M. May (1988)