Graphical comparison of means with a standard in the one-way layout

Abstract

Some simple test procedures are considered for comparing several group means with a standard value when the data are in a one-way layout. The underlying distributions are assumed to be normal with possibly unequal variances. The tests are based on a union-intersection formulation and can be applied in a form similar to a Shewhart control chart. Both two-sided and one-sided alternatives are considered. The power of the tests can be obtained from tables of a non-central t distribution. Implementation of the tests is illustrated with a numerical example. The tests help identify any group means different from the standard and might lead to a decision about rejecting the null hypothesis before all the group means are observed. The resulting savings in time and resources might be valuable in applications where the number of groups is large and the cost of acquiring data is high. For situations where the normality assumption is untenable, a non-parametric procedure, based on one-sample sign tests is considered.