An experimentis conductedtoinvestigatetheeffects of four metal oxides on several
ID: 3395606 • Letter: A
Question
An experimentis conductedtoinvestigatetheeffects of four metal oxides on severalcementproperties. The four factors are all run at two levels and one response of interest is the mean bulk density(g/cm3). The four factors and their levels are
Factor
Low Level (-1)
High Level (+1)
A: %Fe2O3
0
30
B: %ZnO
0
15
C: %PbO
0
2.5
D: %Cr2O3
0
2.5
Typical results from this type of experiment aregiven in thefollowingtable:
Run
A
B
C
D
Density
1
-1
-1
-1
1
2.001
2
1
-1
-1
-1
2.062
3
-1
1
-1
-1
2.019
4
1
1
-1
1
2.059
5
-1
-1
1
-1
1.990
6
1
-1
1
1
2.076
7
-1
1
1
1
2.038
8
1
1
1
-1
2.118
Test ifthe main factoreffectsaresignificantor not. Test alsothesignificanceof 2-way interactioneffects. (Use a significancelevel of =0.10)
Factor
Low Level (-1)
High Level (+1)
A: %Fe2O3
0
30
B: %ZnO
0
15
C: %PbO
0
2.5
D: %Cr2O3
0
2.5
Explanation / Answer
Analysis of Variance for C1 (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0.0111375 0.00568076 0.00142019 * *
A 1 0.0089111 0.00000560 0.00000560 * *
B 1 0.0013781 0.00004978 0.00004978 * *
C 1 0.0008201 0.00061678 0.00061678 * *
D 1 0.0000281 0.00071881 0.00071881 * *
2-Way Interactions 3 0.0013224 0.00132237 0.00044079 * *
A*B 1 0.0000911 0.00009113 0.00009113 * *
A*C 1 0.0005281 0.00052813 0.00052813 * *
A*D 1 0.0007031 0.00070312 0.00070312 * *
Residual Error 0 * * *
Total 7 0.0124599
Estimated Coefficients for C1 using data in uncoded units
Term Coef
Constant 2.04537
A 0.0333750
B 0.0131250
C 0.0101250
D -0.00187500
A*B -0.00337500
A*C 0.00812500
A*D -0.00937500
here the the experiment done in one replicate hence the MSE will not defined. only sum of square can be obtained. The sum of square are given above.
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