Thus the measure is used to evaluate how data compares to a fixed-probability-of-success Bernoulli distribution.
is the (weighted) sample variance derived from the observed proportions of success in sets in "Lexis trials" and
is the variance computed from the expected Bernoulli distribution on the basis of the overall average proportion of success.
This ratio ( Q ) is a measure that can be used to distinguish between three types of variation in sampling for attributes: Bernoullian, Lexian and Poissonian.
The formula for the variance is approximate and holds only for large values of n. An alternative definition is here
is the (weighted) sample variance derived from the observed proportions of success in sets in "Lexis trials" and
is the variance computed from the expected Bernoulli distribution on the basis of the overall average proportion of success.
Wilhelm Lexis introduced this statistic to test the then commonly held assumption that sampling data could be regarded as homogeneous.