In the case of *K* *independent *samples,
the *Chi-square* statistic is essentially the sum of the *Chi-squares*
computed on independent samples. Consequently, most of what was stated
about the single sample estimation process remains true in the multiple
sample case.

Specifically, for each sample *k* having
sample size Nk,
one computes a discrepancy function Fk in the same
manner as with a single sample. These are then combined to produce an
overall discrepancy function of the form

(155)

where

(156)

This overall discrepancy function *F *is
minimized during the iterative process. The *Chi-square *statistic
is then computed as

(157)