Method of half normal plotting

The sets of contrast values have to be standardised so that they have the same standard deviation before they can be plotted in a half normal plot. Once the standardised contrasts have been found, they are placed in ascending order without regard to their sign. They are then plotted on the vertical axis against the expected half normal scores on the horizontal axis. Half normal scores are available in Minitab Statistical software or elsewhere, for example Grove and Davis (1997). 

The set of orthogonal contrasts in Table 18.4 applied to the results for mean time to spall (see Appendix I for data) were used to produce the half normal plot in Fig. 18.6. For example, the standardised contrast value for hot is 119. This is the vector product of the contrast for hot and the results column 

The plot is interpreted by drawing a straight line through the origin and the lower few points. All points above this line correspond to effects that are probably significant. The linear effect of temperature and hot dwell time are significant as the points appear off the line. A half normal plot can be constructed for any of the summary outputs. The plot in Fig. 18.7 is for Am. 

Trial Temp Hot Cold Env Qtemp Qdwell Errorl Error2 

In the plot of time to spall, the effects of hot dwell time and temperature are clearly significant as they are off the line. However, in the plot for Am none of the effects are off the line. This implies that none of the effects are significant as regards Am. 

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An alternative approach, which can be used when there are no or only one or two degrees of freedom, is to use the graphical method of half normal plotting to show which effects are statistically significant. The results for Alloy 800 are analysed by half normal plots instead of analysis of variance or regression as there are only two degrees of freedom for the experimental error variance. Similar to ANOVA and regression, analysis by half normal plots still requires that the data are independent, approximately normal and with constant variance. 

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