Applied Statistics and Probability for Engineers

The computations are usually arranged in an ANOVA table, such as is shown in Table 13-11.

Generally, a computer software package will be used to perform the analysis of variance for

the randomized complete block design.

EXAMPLE 13-5 An experiment was performed to determine the effect of four different chemicals on the

strength of a fabric. These chemicals are used as part of the permanent press finishing

process. Five fabric samples were selected, and a randomized complete block design

was run by testing each chemical type once in random order on each fabric sample. The

data are shown in Table 13-12. We will test for differences in means using an ANOVA with

0.01.

The sums of squares for the analysis of variance are computed as follows:



1 5.7 22  1 8.8 22  1 6.9 22  1 17.8 22

5



1 39.2 22

20

18.04

SSTreatments a

4

i 1

y^2 i.

b



y..^2

ab

 1 1.3 22  1 1.6 22 p 1 3.4 22 

(^1) 39.2 22
20
25.69
SST a
4
i 1
a
5
j 1
y
2
ij
y^2 ..
ab
13-4 RANDOMIZED COMPLETE BLOCK DESIGN 495
Table 13-11 ANOVA for a Randomized Complete Block Design
Source of Degrees of
Variation Sum of Squares Freedom Mean Square F 0
Treatments SSTreatments a 1
Blocks SSBlocks b 1
Error SSE(by subtraction) (a1)(b1)
Total SST ab 1
SSE
1 a 121 b 12
SSBlocks
b 1
MSTreatments
MSE
SSTreatments
a 1
Table 13-12 Fabric Strength Data—Randomized Complete Block Design
Treatment Treatment
Fabric Sample Totals Averages
Chemical Type 1 2 3 4 5
1 1.3 1.6 0.5 1.2 1.1 5.7 1.14
2 2.2 2.4 0.4 2.0 1.8 8.8 1.76
3 1.8 1.7 0.6 1.5 1.3 6.9 1.38
4 3.9 4.4 2.0 4.1 3.4 17.8 3.56
Block totals 9.2 10.1 3.5 8.8 7.6 39.2(y..)
Block averages y.j 2.30 2.53 0.88 2.20 1.90 1.96(y..)
y.j
yi. yi.
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