Statistics for Environmental Engineers

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Figure 27.4 is a plot of the estimated effects estimated against the normal order scores. Random effects will fall along a straight line on this plot. These are not statistically significant. We consider them to have values of zero. Nonrandom effects will fall off the line; these effects will be the largest (in absolute value). The nonrandom effects are considered to be statistically significant.


In this case a straight line covers the two~ and three.factor interactions on the normal plot. None of the interactions are significant. The significant effects are the main effects of water content, compaction effort, and reaction time. Notice that it is possible to draw a straight line that covers the main effects and leaves the interactions off the line. Such an interpretation — significant interactions and insignificant main effects — is not physically plausible. Furthermore, effects of near~zero magnitude cannot be significant when effects with larger absolute values are not.


TABLE 27.4


Effects, Plotting Positions, and Normal Order Scores for Figure 27.4


Order number i


1


2


3


4


5


6


7


Identity of effect


3


12


23


123


13


2


1


Effect


-7.5


-2.85


-1.80


-0.35


2.05


6.40


12.45


P = 100(i 0.5)/7


0.07


0.21


0.36


0.50


0.64


0.79


0.93


Normal order scores


-1.352


-0.757


-0.353


0


0.353

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