A closed testing procedure for comparison between successive variances

ABSTRACT

For a sequence of $k$ independent normally distributed random samples from $k$ populations with different means and variances, it is common to know which successive populations differ significantly with respect to a parameter. In this article, a stepwise test procedure is proposed for simultaneously testing the difference between successive normal populations with respect to the variance. The proposed procedure controls the family-wise error rate strongly. Critical constants, obtained numerically, are tabulated for the use of the proposed procedure. An extension of the proposed procedure for detecting the difference between scale parameters of successive two-parameter exponential populations is given. A Monte Carlo simulation study of the power comparison of the proposed procedure with a single-step procedure revealed that the proposed stepwise procedure performs better than the single-step procedure. Finally, a numerical example is also given to illustrate the advantage of the proposed procedure in comparison to the single-step procedure.

KEYWORDS:

• Type I family-wise error rate
• power comparison
• single-step procedure
• step-wise procedure
• critical constant

Disclosure statement

No potential conflict of interest was reported by the authors.