Half-normal probability plots

Normal probability plots or half normal probability plots (Bimbaun plots) [24,29] are graphical methods that help to decide which factors are significant. Effects that are normally distributed around zero are effects... 

Figure 3.2 b Example of a Birnbaun plot (half normal probability plot) (Reprinted from International Laboratory, volume 16, page 43, 1986. Copyright 1986 by International Scientific Communications Inc. [24])... 

The real power of the use of half-normal probability plots, however, comes with data that are likely to have embedded outliers. These data profoundly distort the half-normal plots, as illustrated with the data for methyl isobutyl ketone shown in Figure 9. The plot shows neither normal random error nor significant effects cleanly. Thus, this... 

Figure 7. Half-normal probability plot for methylene chloride.

Compound recovery data for duplicate runs differed by 2-15, depending on the compound. Half-normal probability plot analysis of the new data for the anomalous compounds indicated none of the distortion encountered earlier. Results for acetone and tetrachloroethylene now indicated only random variation with no significant outliers. Results for 2,4-dichlorophenol and 2,5-dichlorophenol indicated a significant pH effect. A significant interaction effect (AB) was detected between variables pH and primary column type for the dichlorophenols and also for methyl isobutyl ketone. This interaction effect indicates that at approximately low pH (pH 2), compound recoveries for dichlorophenols will be greater when a C18 phase is used as the primary column. The half-normal plot for 2,5-dichlorophenol is shown in Figure 10. In examining data for all the compounds from the 23 replicate factorials, this interaction consistently appears for phenolic compounds. 

Figure 3 shows a half-normal probability plot of the effect estimates obtained from the Design-Expert software package. Three main effects, A (pressure), B (power), and E (gap) are important. Because the main effects are aliased with three-factor interactions, this interpretation is probably correct. There are also two two-factor interaction alias chains that are important, AB = CE and AC = BE. Because AB is the interaction of two strong main effects, those of pressure and... 

Figure 3. Half-normal probability plot of the effect estimates from the plasma etching experiment in Table 3.

FIGURE 9 Half-normal probability plots for L-asparagine monohydrate (data from Verbist et alfigure from Abrahams see text). 

Finally, the warm happy feeling benefits strongly from indications of internal consistency and plausibility of the structural results themselves rational values for ordinary distances and angles, benzene rings that are regular and planar, etc. It does no harm to have more than one molecule per asymmetric unit and to show (by chi square testing or half-normal probability plots where appropriate) that the structural results are mutally consistent. 

As an alternative, the half normal probability plot [3] can be used to analyse the data. Figure 8.3 shows our half normal plot for the data in Kukovecz et al. (2005). In this analysis, we found that none of the factors is statistically significant at the 95% confidence level. 

The robustness-test of a quantitative off-line OPLC assay-procedure was recently reported (89). The test was performed by fractional factorial design and evaluated by half-normal probability plot. The effects of seven factors were investigated on two levels. The method was found to be robust. 

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