摘要：The traditional Behrens–Fisher (B-F) problem is to test the equality of the means µ1
and µ2 of two normal populations using two independent samples, when the quotient of
the population variances is unknown. Welch [43] developed a frequentist approximate
solution using a fractional number of degrees of freedom t-distribution. We make a
a comprehensive review of the existing procedures, propose new procedures, evaluate
these for size and power, and make recommendation for the B-F and its analogous
problems for non-normal populations. On the other hand, we investigate and answer
a question: does the same size fit all all, i.e. is the t-test with Welch’s degree of
freedom correction robust enough for the B-F problem analogs, and what sample size
is appropriate to use a normal approximation to the Welch statistic.
关键词：the Behrens;Fisher problem; the beta;binomial model; the negative binomial model;
the Weibull model;
