ssrs 2012 barcode font Analysis of Variance in Software

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CHAPTER 9 Analysis of Variance
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Table 9-32 Variation Rows (Machines), vr 51.0 Columns (Shifts), vc 8.1 Replications (Days of Week), vrep 11.4 Interaction, vi 6.5 Random or Residual, vr 73.4 e v Total, 150.4 Degrees of Freedom 3 1 Mean Square 17.0 8.1 17.0 2.621 8.1 2.621 2.85 2.621 2.167 2.621 F 6.49 3.05
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9.22. Describe how analysis of variance techniques can be used for three-way classification or three-factor experiments (with single entries). Display the analysis of variance table to be used in such case.
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We assume that classification is made into A groups, denoted by A1, . . . , Aa; B groups, denoted by B1, . . . , Bb; and C groups, denoted by C1, . . . , Cc. The value which is in Aj, Bk, and Cl is denoted by xjkl. The value xjk., for # example, denotes the mean of values in the C class when Aj and Bk are kept fixed. Similar meanings are given to xj.l and x.kl. The value xj.. is the mean of values for the B and C classes when Aj is fixed. Finally x denotes the # # # # grand mean. There will be a total variation given by (1) v a (xjkl
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which can be broken into seven variations, as indicated in Table 9-33. These variations are between classes of the same type and between classes of different types (interactions). The interaction between all classes is as before called the residual, or random, variation. The seven variations into which (1) can be broken are given by v where vA bc a (xj.. #
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CHAPTER 9 Analysis of Variance
Table 9-33 Variation Degrees of Freedom Mean Square vA a 1 (a
^ s A >s 2 ABC a 1, 1)(b 1)(c ^ s B >s 2 ABC b 1, 1)(b 1)(c ^2 ^ s C >s 2 ABC c 1, 1)(b 1)(c ^2
vA (Between A Groups)
1) df
vB (Between B Groups)
vB b 1 (a
1) df
vc (Between C Groups)
vC c 1 vAB 1)(b (a
1) df
vAB (Between A and B Groups)
1)(b
s AB
^ s AB >s 2 ABC (a 1)(b 1), 1)(b 1)(c 1) df ^2 ^ s BC >s 2 ABC (b 1)(c 1), 1)(b 1)(c 1) df ^2 ^ s CA >s 2 ABC (c 1)(a 1), 1)(b 1)(c 1) df ^2
vBC (Between B and C Groups)
1)(c
s BC
vBC 1)(c
vCA (Between C and A Groups)
1)(a
s CA
vCA 1)(a
vABC (Between A, B, and C Groups) v (Total)
1)(b
1)(c
s ABC
vABC 1)(b 1)(c
SUPPLEMENTARY PROBLEMS
One-way classification or one-factor experiments
9.23. An experiment is performed to determine the yields of 5 different varieties of wheat, A, B, C, D, E. Four plots of land are assigned to each variety, and the yields (in bushels per acre) are as shown in Table 9-34. Assuming the plots to be of similar fertility and that varieties are assigned at random to plots, determine if there is a significant difference in yields at levels of significance (a) 0.05, (b) 0.01. Table 9-34 Table 9-35 A B C D E 20 17 23 15 21 12 14 16 17 14 15 12 18 20 17 19 A 15 B 14 C 12 D 18 29 34 32 30 33 31 31 37 35 33 34 30 32 40 42 38 30 34 33 38 36 40 31 35
CHAPTER 9 Analysis of Variance
9.24. A company wishes to test 4 different types of tires, A, B, C, D. The lifetimes of the tires, as determined from their treads, are given (in thousands of miles) in Table 9-35, where each type has been tried on 6 similar automobiles assigned at random to tires. Test at the (a) 0.05, (b) 0.01 levels whether there is a difference in tires. 9.25. A teacher wishes to test three different teaching methods, I, II, III. To do this, three groups of 5 students each are chosen at random, and each group is taught by a different method. The same examination is then given to all the students, and the grades in Table 9-36 are obtained. Determine at (a) the 0.05, (b) the 0.01 level whether there is a significant difference in the teaching methods.
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