Definition
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 Lexis ratio is sometimes also referred to as L.
Let there be k samples of size n1, n3, n3, ..., nk and these these samples have the proportion of the attribute being examined of p1, p2, p3, ..., pk respectively. Then the Lexis ratio is
If the Lexis ratio is significantly below 1, the sampling is referred to as Poissonian (or subnormal); it it is equal to 1 the sampling is referred to as Bernoullian (or normal); and if it is above 1 it is referred to as Lexian (or supranormal).
Chuprov showed in 1922 that in the case of statistical homogeneity
and
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
where 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.
Read more about this topic: Lexis Ratio
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