Environmental Engineering Reference
In-Depth Information
Table 14. Sequential model sum of squares for response Lead
Squares
Prob > F
Sum of
Source
DF
Mean
Square
Value
Mean
268.34
1
268.34
Linear
248.60
2
124.30
11.43
0.0021
Quadratic
92.98
3
30.99
9.32
0.0055
Suggested
Special
Cubic
4.45
1
4.45
1.41
0.2742
Cubic
22.14
3
7.38
1560.94
< 0.0001
Suggested
Residual
0.019
4
4.728E-003
Total
636.53
14
45.47
A lack of fit test can also be performed using ANOVA. A lack of fit test
means that the selected model should have insignificant lack-of-fit. ie, we
want the model to fit the data. To do so, the residual sum of squares is
partitioned into lack-of-fit and pure error (from replicates) components. The
mean squares and F statistic are calculated, and the ―Prob > F‖ is determined.
The desired result is an insignificant lack-of-fit, indicated by a ―Prob > F‖
greater than 0.05. For compressive strength, the lack-of-fit test (Table 15) for
the special cubic model gives ―Prob > F‖ equal to 0.7706, which is not
significant. Table 15 shows that the special cubic model provided a lack of fit
test value of 0.77 for response compressive strength, indicating that the model
fits the data. Lack of fit tests values for other responses such as water
absorption, shrinkage, density, leaching of lead are given in Tables 16 to Table
19.
Table 15. Lack of fit test for response compressive strength
Source
Sum of
Squares
DF
Mean
Square
F Value
Proc>F
Linear
2477.35
7
353.91
127.48
0.0002
Quadratic
344.74
4
86.19
31.05
0.0029
Special Cubic
3.21
3
1.07
0.38
0.7706
Cubic
0.0
0
Pure error
11.10
4
2.78
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