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Program
7
OPTIONS LS=80 NODATE PAGENO=1;
TITLE 'Randomized block design--RB and GRB';
DATA rb;
INPUT block treat score;
CARDS;
1 1 144
1 2 129
1 3 135
2 1 132
2 2 124
2 3 128
3 1 120
3 2 112
3 3 115
4 1 115
4 2 108
4 3 110
5 1 102
5 2 99
5 3 101
6 1 83
6 2 82
6 3 83
;
PROC GLM;
CLASS block treat;
MODEL score=block treat;
RANDOM block/TEST;
TITLE2 'RB design';
RUN;
DATA grb;
INPUT block treat score;
CARDS;
1 1 144
1 1 142
1 2 124
1 2 128
1 3 138
1 3 136
2 1 134
2 1 130
2 2 121
2 2 127
2 3 125
2 3 131
3 1 122
3 1 120
3 2 100
3 2 108
3 3 111
3 3 109
;
PROC GLM;
CLASS block treat;
MODEL score=block treat block*treat;
TEST H=treat E=block*treat;
MEANS treat/TUKEY E=block*treat;
TITLE2 'GRB design'; RUN;
Randomized block design--RB and GRB 1
RB design
General Linear Models Procedure
Class Level Information
Class Levels Values
BLOCK 6 1 2 3 4 5 6
TREAT 3 1 2 3
Number of observations in data set = 18
Randomized block design--RB and GRB 2
RB design
General Linear Models Procedure
Dependent Variable: SCORE
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 5652.0000000 807.4285714 130.23 0.0001
Error 10 62.0000000 6.2000000
Corrected Total 17 5714.0000000
R-Square C.V. Root MSE SCORE Mean
0.989149 2.216599 2.4899799 112.33333
Source DF Type I SS Mean Square F Value Pr > F
BLOCK 5 5504.0000000 1100.8000000 177.55 0.0001
TREAT 2 148.0000000 74.0000000 11.94 0.0022
Source DF Type III SS Mean Square F Value Pr > F
BLOCK 5 5504.0000000 1100.8000000 177.55 0.0001
TREAT 2 148.0000000 74.0000000 11.94 0.0022
Randomized block design--RB and GRB 3
RB design
General Linear Models Procedure
Source Type III Expected Mean Square
BLOCK Var(Error) + 3 Var(BLOCK)
TREAT Var(Error) + Q(TREAT)
Randomized block design--RB and GRB 4
RB design
General Linear Models Procedure
Tests of Hypotheses for Mixed Model Analysis of Variance
Dependent Variable: SCORE
Source: BLOCK
Error: MS(Error)
Denominator Denominator
DF Type III MS DF MS F Value Pr > F
5 1100.8 10 6.2 177.5484 0.0001
Source: TREAT
Error: MS(Error)
Denominator Denominator
DF Type III MS DF MS F Value Pr > F
2 74 10 6.2 11.9355 0.0022
Randomized block design--RB and GRB 5
GRB design
General Linear Models Procedure
Class Level Information
Class Levels Values
BLOCK 3 1 2 3
TREAT 3 1 2 3
Number of observations in data set = 18
Randomized block design--RB and GRB 6
GRB design
General Linear Models Procedure
Dependent Variable: SCORE
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 8 2420.0000000 302.5000000 29.59 0.0001
Error 9 92.0000000 10.2222222
Corrected Total 17 2512.0000000
R-Square C.V. Root MSE SCORE Mean
0.963376 2.557777 3.1972210 125.00000
Source DF Type I SS Mean Square F Value Pr > F
BLOCK 2 1761.3333333 880.6666667 86.15 0.0001
TREAT 2 588.0000000 294.0000000 28.76 0.0001
BLOCK*TREAT 4 70.6666667 17.6666667 1.73 0.2274
Source DF Type III SS Mean Square F Value Pr > F
BLOCK 2 1761.3333333 880.6666667 86.15 0.0001
TREAT 2 588.0000000 294.0000000 28.76 0.0001
BLOCK*TREAT 4 70.6666667 17.6666667 1.73 0.2274
Tests of Hypotheses using the Type III MS for BLOCK*TREAT as an error term
Source DF Type III SS Mean Square F Value Pr > F
TREAT 2 588.00000000 294.00000000 16.64 0.0115
Randomized block design--RB and GRB 7
GRB design
General Linear Models Procedure
Tukey's Studentized Range (HSD) Test for variable: SCORE
NOTE: This test controls the type I experimentwise error rate, but
generally has a higher type II error rate than REGWQ.
Alpha= 0.05 df= 4 MSE= 17.66667
Critical Value of Studentized Range= 5.040
Minimum Significant Difference= 8.6488
Means with the same letter are not significantly different.
Tukey Grouping Mean N TREAT
A 132.000 6 1
A
B A 125.000 6 3
B
B 118.000 6 2
Comments: peng@indiana.edu
Dr. Peng's Home Page: Dr.
Chao-Ying Joanne Peng
Copyright
1999, The Trustees of Indiana
University
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