Reed reported the chances of having test results outside of the normal reference range when a large number of tests is performed.
Rationale: The normal reference range usually assumes a binomial distribution of values, with the range including 95% of the reference population. About 5% will either be above or below the limits. If multiple tests are performed then there is a chance that 1 or more results will be "abnormal" without the presence of disease.
Method: binomial distribution (in excel BINOM.DIST.RANGE
Parameters:
(1) N for number of tests
(2) k, which equals the number of results outside the reference range (m) plus 1 = m+1
(3) p fpr probability of being outside a reference range, which is usually 0.05
probability of m results outside the reference ranges =
= BINOM.DIST.RANGE(N, p, k, N)
where:
• Why 1 is added to m is unclear.
• One would think that the probability that all tests would be normal is (0.95^N). Subtracting this from 1 gives you the same value as when k = m.
One caveat is that this does not describe how abnormal the outlying results are. The more abnormal the result, the more likely that it is not a random event.
