Normal probability plots, effects designs

As was discussed with arrangement (I), 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 environmental variable contrasts. This would reveal important effects due to the linear components of both Temperature and Humidity. A normal plot for the design contrasts would indicate that there appears to be a real effect due to A. The analysis of the design x environment interactions is obtained by pooling together higher-order interactions to obtain an... 

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... 

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. 

More convincing than that is the plot of the logarithms of these 45 data on the normal probability paper. Effectively the data are almost aligned along a straight line as shown in Fig. 4.20. The designer re-run all the statistics on these 45 tests and gets... 

Half normal plots give a visual indication of which factors are statistically significant. The technique is useful when there are few or no degrees of freedom available for a residual mean square in ANOVA or regression. Half normal plots are therefore useful when the experimental design is saturated and all effects are of interest. The half normal plot is a type of probability plot where a numerical value for the factor effects is plotted on the vertical axis against the expected normal order statistics on the horizontal axis (see Grove and Davis, 1997). 

Where Xe is the value to be codified, X is the average value of the defined limits for each variable and Xmax the maximum limit of the variable. From the results of these evaluations by use of the algorithm developed by Yates [6] employing the State-ease "Design Expert (5.0.9)" programme, the effects of each variable were calculated and plotted against a half normal percent probability, shown in Fig. 1 where those variables with little or no effect on the NO conversion value fall on the line. Variables that cause the greatest effect over the NO conversion are those that are located away from the line. 

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