 Chuprov showed in 1922 that in the case of statistical homogeneity
and 

formula_6

where "E"() is the expectation and "var"() is the variance.The formula for the variance is approximate and holds only for large values of "n".An alternative definition is

here formula_8 is the (weighted) sample variance derived from the observed proportions of success in sets in "Lexis trials" and formula_3 is the variance computed from the expected Bernoulli distribution on the basis of the overall average proportion of success.