Civil Engineering Reference
In-Depth Information
Table 8.16
Factors and dependent variable analyzed in the ANOVA analysis of Brite Series 1
Factors (independent variables)
f
r3
(MPa): 0, 1.49, 3.05, 4.85
Transverse reinforcement, A
sw
/s (cm
2
/m): 0, 1.4, 2.8
Codes: EHE08, MC2010, RILEM
Dependent variable
Shear safety margin (SM)
Table 8.17
Analysis of variance (ANOVA) for SM on shear
—
type III sums of squares (Series 1)
Source of variation
Sum of Squares
d.f
Mean square
F-ratio
p-value
Main effects
A: f
R3
(MPa)
0.0750528
3
0.0250176
22.99
0.0000
B: A
sw
/s (cm
2
/m)
0.631839
2
0.315919
290.25
0.0000
C: Code
0.0546722
2
0.0273361
25.12
0.0001
Interactions
AB
0.132739
6
0.0221231
20.33
0.0000
AC
0.0419722
6
0.00699537
6.43
0.0032
BC
0.0184944
4
0.00462361
4.25
0.0227
Residual
0.0130611
12
0.00108843
Total (corrected) 0.967831 35
All F-ratios are based on the residual mean square error
In this case, Series 1, have been possible to study double interactions, because
there are enough residual degrees of freedom (d.f.), this is:
d.f. (effect A) = 3; d.f. (effect B) = 2; d.f. (effect C) = 2
d.f. (interaction AB) = 6; d.f. (interaction AC) = 6; d.f. (interaction BC) = 4
d.f. (residual) = d.f. (total)
d.f. (simple effects)
−
d.f. (interactions) = 35
−
3
−
2
−
-
2
4=12
As d.f. (residual) = 12 then double interactions can be studied.
−
6
−
6
−
So in this case there are enough degrees of freedom to study interactions. Higher
order interactions could be considered but, in general, not occur almost in practice,
and is also dif
cult to interpret [
14
]. Henceforth, only double interactions will be
studied. There is a double interaction between two factors, whether the effect of one
of them is different according to the variant of the other factor considered. By
means of ANOVA table, one knows what simple effects and what interactions are
statistically signi
cant value of
p-value only would indicate that at least one of the levels of this factor differs from
the others, but does not specify which ones differ. A simple way to clarify this issue
cant, being those with p-value < 0.005. But a signi
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