Testing the Importance of Location Effects in the 2 k Design

This chapter illustrates the idea of an effect having a distribution of values. It shows that each and every location effect estimated from an orthogonal design will have the same standard deviation and a formula for estimating this standard deviation is derived. The chapter focuses on the construction of a simple student test and application of the ausforming process. It presents the test within the least squares framework of analysis. The chapter derives a simple graphical test and applied to both the high strength steel and the 2⁵ experiment of the ausforming process. It is important to realise that each of the estimated location effects, as a consequence of the way they are constructed, actually follow an approximate normal distribution. Probability plots are much easier to interpret in larger designs where there are likely to be more unimportant location effects that can be used to calculated the standard deviation of the distribution for location effects.