Statistics for Environmental Engineers

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0.757


1.352

о


о


со


ш


р


1 Water content


123


13


2 Compaction effort


23


12


A


3 Time

-5


0


5


1 0


Effect on density


■10


FIGURE 27.4 Normal probability plot of the estimated main effects and interactions.


1.    The average density over the eight experimental design conditions is 114.7.


2.    Increasing water content from 4 to 10% increases the density by an average of 12.45 lb/ft3.


3.    Increasing compaction effort from 60 to 260 psi increases density by an average of 6.40 lb/ft .


4.    Increasing reaction time from 5 to 20 min decreases density by an average of 7.50 lb/ft3.


5.    These main effects are additive because the interactions are zero. Therefore, increasing both water content and compaction effort from their low to high values increases density by 12.45 + 6.40 = 18.85 lb/ft3.

Comments


Two-level factorial experiments are a way of investigating a large number of variables with a minimum number of experiments. In general, a k variable two-level factorial experiment will require 2k experimental runs. A 22 experiment evaluates two variables in four runs, a 23 experiment evaluates three variables in eight runs, a 24 design evaluates four variables in sixteen runs, etc. The designs are said to be full or saturated. From this small number of runs it is possible to estimate the average level of the response, к main effects, all two-factor interactions, and all higher-order interactions. Furthermore, these main effects and interactions are estimated independently of each other. Each main effect independently estimates the change associated with one experimental factor, and only one.

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