﻿ A Graphical Method for Assessing Mean Squares in Saturated Fractional Designs - ASQ

# A Graphical Method for Assessing Mean Squares in Saturated Fractional Designs

A new graphical method, motivated by Bissell's iterative test, is proposed for assessing mean squares in saturated fractional designs. The method is illustrated using a number of examples.

Key Words: Exponential Plots, Fractional Factorial Designs, Half-Normal Plots, Normal Plots, Saturated Designs.

By JEFFREY H. DODGSON Napier University, Edinburgh, EH11 4BN UK

Introduction

A SIMPLE method for assessing mean squares in saturated fractional designs, i.e., designs in which all available degrees of freedom are associated with effects of potential interest, has been given by Bissell (1989, 1992). Suppose there are k factors each having degrees of freedom. Let m and s represent, respectively, the sample mean and standard deviation of the k mean squares (i.e., s has divisor k - 1). Under the null hypothesis of no real effects, we have Bissell (1992) determined percentage points for the coefficient of variation of the mean squares s/m under the null hypothesis of no e.ects and described an iterative procedure for assessing the significance of the effects. In brief, s/m is determined for all k factors and its significance assessed by reference to the table of percentage points. If deemed significant, the factor having the largest mean square is omitted, s/m is determined for the remaining k - 1 factors, and its significance is again determined (noting that k is reduced by 1). The procedure continues until no further factors are excluded.

At this point, those factors that have been excluded are identified as being of potential interest. It is suggested that the use of a significance level of approximately 25% provides a stopping rule corresponding to the visual impression gained from examining a probability plot. 