Normal probability plot of effects

Figure 3 Normal probability plot of effects on burn.

Figure 3.3 Normal probability plot of the normalized effects for the resolution between epianhydrotetracycline and tetracycline obtainedfrom the fractional factorial design...

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 3. Fialf-normal probability plot of the factor effects from the 2s factorial experiment on hue.

Box and Meyer did not present any formal inference procedures for using this statistic to identify dispersion effects. The use seems to be informal for screening factors with large effects from those with no or small effects on dispersion, for example, by making a normal probability plot of the statistics see Montgomery (1990) for an application of this idea. 

The are a number of ways of doing this. If the experiments have been replicated, ANOVA will reveal which effects are statistically significant. Otherwise, we rely on the fact that most of the effects are probably small and distributed randomly about zero. Thus, we look for the effects with the largest absolute values that stand out from the others. Making a normal probability plot of the distribution of their values is a widely used method. 

A normal probability plot of the estimated effects is shown in Fig. 6.13. 

A normal probability plot of the estimated coefficients is shown in Fig.17.2. It is seen that variables Xj and are significant, and that they also show a significant interaction effect. These are the same conclusions as were reached in the original report, where five derived responses were anaylzed one at a time. 

Fig. 3.10. Normal probability plot of the values in Table 3.9. Only the 1, 2, 3 and 12 effects appear to be significant.

Fig. 3A.13. Normal probability plot of the blocked 2 factorial effect values.

Fig. 4.2 Normal probability plot of parameters (effects) for a 2" experiment with significant points highlighted and labelled...

Plot a normal probability plot of the effects. Which effects are significant Which factor does not seem to influence the results at all ... 

A normal probability plot of the effects is shown in Fig. 4.3. The effects that lie far from the expected normal distribution values are those that are significant because they are not chance values. The most significant effects have been circled and labelled. It should be noted that in this particular example, some of the effects have the same value and so will appear at the same location in die plot, for example, both AD and BD are denoted by the same point. Furthermore, the circled point representing the two values AD and BD is borderline. It could be included or not. In this analysis, since the point lies much closer the straight line than any of the other points, it will not be considered in the final analysis. Therefore, the significant effects are those denoted as A, C, D, and AC. The effect due to B is negligible. 

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. 

Figure 4 Normal probability plot of the effects for the example described in Table I...

For the subplot analysis it appears that the effects due to A, and the interaction between B and Humidity are real, with some evidence of an interaction between B and Temperature. It is possible to split the two degrees of freedom for Temperature and Humidity into linear and quadratic contrasts and to construct a normal probability plot for the whole plot contrasts. This would reveal important effects due to the linear components of both Temperature and Humidity. 

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... 

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. 

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