Main effect plots

FIGURE 15 An example of a main effect plot.The average responses at low level and high level of the factors are plotted. 

FIGURE 15 Example of a main effect plot (for the critical resolution) clearly showing the extent of the effects relative to each other. Factor temperature appears to be the most important factor on the resolution. Reprinted with permission from reference 18. 

The main effects plot represents the response (vertical axis) versus the levels of the factor under consideration (horizontal axis, see Figure 2.2). Each point represents the mean response obtained at each level. For our example (see Figure 2.2), the mean responses (yield) for factor A at the low and high levels are 82.5% and 86.75%, respectively. That is to say, the increase in yield (effect of A, pH) is 4.25% when we change the pH from 3 to 5. 

Any input variable that has a large ANOVA contribution from an estimated (corrected) main effect but does not appear in any large ANOVA contributions from interaction effects has its estimated (uncorrected) main effect plotted. Approximate pointwise confidence intervals based on the standard error can also be shown. 

Figure 10. Main effect plots of applied voltage (b) on average fiber diameter [55].

Main Effects Plot (fitted means) for void content... 

Figure 8. Main effects plot for horizontal sections.

Main Effects Plot is used to plot data when there are multiple faetors. The points in the plot are the means of the response variable at the various levels of eaeh factor, with a reference line drawn at the grand mean of the response data. 

Factors A and B are, by far, the most important in affecting the proportion of parts that end up with cracks. The lower values for these factors result in less cracks in the parts. The main effects plots for all factors are given in Figure 5. The Main Effects plots for only the statistically significant factors... 

Main Effects Plot (data means) for ArcSine... 

Figure 6 Main effect plots for statistically significant effects (A, B, and H).

The result summaries can be examined by main effects plots which show the mean value of each output at each level of each factor. When there are replications, as here, it is also possible to investigate the effect of the parameters on the variability of the responses. The standard deviation of the responses for the three replications represents the variability of the output. The log transformation of the standard deviations is taken to make sure that the assumptions of approximate normality and constant variability are obeyed. Although these assumptions are not necessary for main effects plots, they are necessary for the statistical analysis described below. 

For brevity, only the main effects plots for mean time to spall (tj), mean diff (Am) and sd diff (sd(Am)) are shown in Figs 18.3-18.5. 

Main effects plot for mean time to spall, t. ... 

The main effects plot for the log (standard deviation) of Am is given in Fig. 18.5. It can be seen in Fig. 18.5 that higher temperature increases the variation in Am. Thus there is more scatter between the quantities of spall from Alloy 800 as the temperature increases. There is little or no apparent effect from the other factors. 

The main effects plots show how the parameters affect the response variables. They do not, however, confirm which effects are statistically significant. In any plot, one factor will always have the greatest effect, but if it is not statistically significant then the apparent effect may not be real and therefore may not be repeatable. 

Note that the orthogonal contrast for Qdwell assumes that the levels are equally spaced whereas the factor levels are actually 4,8 and 20 h which are not equally spaced. This will tend to bias the contrast value so that Qdwell is larger than it should be. The half normal plot should be looked at in conjunction with the main effects plot. The main effects plot for time to spall shows that the effect of upper dwell time is approximately linear which supports the lack of significance in the half normal plot in Fig. 18.6. 

Main Effects Plot - Data Means for Fibre diameter... 

Figure 8.2. Main effects plots for fiber diameter [Source Reference 3].

Statistical analysis results are shown in the format of the Pareto analysis (see table 2, 3 and 4) and of the main effects plot for the three mentioned outputs (see figure 7, 8, 9). 

The major findings from the density analysis are that all factors have a significant effect on part density, there are multiple interactions, the nitrogen vent pressure is the most critical to control density, the interaction and main effects plots show that there is an optimal setting at the center points for all factors except nitrogen vent pressure, and higher nitrogen vent pressures result in reduced effects from the other factors. 

Graph 3 Pareto Chart of the Standardized Effects on tensile modulus Main Effects Plot (data means) for Peak Stress... 

Graph 3 Main Effects Plot for tensile modulus... 

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