2
*****************************************************************;
3
*** Example of unbalanced CRD with
experimental error ***;
4
*** From Snedecor & Cochran, 1967
(pg
278)
***;
5
*****************************************************************;
6
OPTIONS PS=256 LS=132 NOCENTER NODATE
PAGENO=1 NONUMBER;
7
dm 'log;clear;output;clear';
8
DATA MICE onebyone; INFILE CARDS
MISSOVER;
9
INPUT STRAIN $ 1-4 DAYS NUMBER;
10
TITLE1 'EXST7015: DAYS TO DEATH FOR MICE INOCULATED WITH 3 TYPHOID
STRAINS';
11
TITLE2 'UNEQUAL NUMBER OF MICE IN
EACH TREATMENT';
12
do i = 1 to number by 1; output onebyone; end;
13
output mice;
14
CARDS;
NOTE:
The data set WORK.MICE has 31 observations and 4 variables.
NOTE:
The data set WORK.ONEBYONE has 224 observations and 4 variables.
NOTE:
DATA statement used:
real time
0.08 seconds
cpu
time
0.08 seconds
14
!
RUN;
46
;
47
PROC MIXED DATA=OnebyOne cl covtest;
CLASSES STRAIN;
48
TITLE3 'ANALYSIS OF VARIANCE with
PROC MIXED';
49
MODEL DAYS = STRAIN / htype=3
DDFM=Satterthwaite;
50
repeated / group=strain;
51
LSMEANS STRAIN / ADJUST=TUKEY
pdiff;
52
LSMEANS STRAIN / ADJUST=SCHEFFE
pdiff;
53
LSMEANS STRAIN / ADJUST=BON
pdiff;
54
*NOTE that normally only one
post-ANOVA examination would be
55
done.
We have done several here for comparison. ;
56
RUN;
NOTE:
Convergence criteria met.
NOTE:
The PROCEDURE MIXED printed page 1.
NOTE:
PROCEDURE MIXED used:
real time
0.11 seconds
cpu
time
0.11 seconds
EXST7015:
DAYS TO DEATH FOR MICE INOCULATED WITH 3 TYPHOID STRAINS
UNEQUAL
NUMBER OF MICE IN EACH TREATMENT
ANALYSIS
OF VARIANCE with PROC MIXED
The
Mixed Procedure
Model Information
Data
Set
WORK.ONEBYONE
Dependent
Variable
DAYS
Covariance
Structure Variance
Components
Group
Effect
STRAIN
Estimation
Method
REML
Residual
Variance Method None
Fixed
Effects SE Method Model-Based
Degrees
of Freedom Method Satterthwaite
Class Level Information
Class
Levels
Values
STRAIN
3
11C 9D DSC1
Dimensions
Covariance
Parameters
3
Columns
in
X
4
Columns
in
Z
0
Subjects
224
Max
Obs Per
Subject
1
Observations
Used
224
Observations
Not
Used
0
Total
Observations
224
Iteration History
Iteration
Evaluations -2 Res Log
Like Criterion
0
1 1027.49256195
1
1
1012.92789611 0.00000000
Convergence criteria met.
Covariance
Parameter Estimates
Standard Z
Cov
Parm Group
Estimate
Error Value Pr Z
Alpha Lower Upper
Residual
STRAIN 11C 5.8633
1.0795 5.43
<.0001
0.05 4.2127 8.7221
Residual
STRAIN 9D 1.8989
0.4903 3.87
<.0001
0.05 1.2126 3.3928
Residual
STRAIN DSC1
6.6327 0.8164
8.12
<.0001 0.05
5.2839
8.5761
Fit Statistics
-2
Res Log
Likelihood 1012.9
AIC
(smaller is better) 1018.9
AICC
(smaller is better) 1019.0
BIC
(smaller is better) 1029.2
Null
Model Likelihood Ratio Test
DF
Chi-Square Pr > ChiSq
2
14.56 0.0007
Type 3 Tests of Fixed Effects
Num Den
Effect
DF
DF F Value Pr > F
STRAIN
2
114 70.10 <.0001
Least Squares Means
Standard
Effect
STRAIN
Estimate
Error DF
t Value Pr > |t|
STRAIN
11C
7.3667
0.3126 59
23.57 <.0001
STRAIN
9D
4.0323
0.2475 30
16.29 <.0001
STRAIN
DSC1
7.7970 0.2233
132
34.91 <.0001
STRAIN
11C
7.3667
0.3126 59
23.57 <.0001
STRAIN
9D
4.0323
0.2475 30
16.29 <.0001
STRAIN
DSC1
7.7970 0.2233
132
34.91 <.0001
STRAIN
11C
7.3667
0.3126 59
23.57 <.0001
STRAIN
9D
4.0323
0.2475 30
16.29 <.0001
STRAIN
DSC1
7.7970
0.2233
132 34.91
<.0001
Differences of Least Squares Means
Standard
Effect
STRAIN _STRAIN
Estimate
Error DF
t Value Pr > |t|
Adjustment Adj P
STRAIN
11C
9D
3.3344 0.3987
88.1
8.36 <.0001
Tukey-Kramer <.0001
STRAIN
11C
DSC1
-0.4303 0.3842
121 -1.12
0.2649
Tukey-Kramer 0.5037
STRAIN
9D
DSC1
-3.7647 0.3334
85.8 -11.29
<.0001 Tukey-Kramer <.0001
STRAIN
11C
9D
3.3344 0.3987
88.1
8.36 <.0001
Scheffe <.0001
STRAIN
11C
DSC1 -0.4303
0.3842
121
-1.12 0.2649
Scheffe 0.5358
STRAIN
9D
DSC1
-3.7647 0.3334
85.8 -11.29
<.0001
Scheffe <.0001
STRAIN
11C
9D
3.3344 0.3987
88.1
8.36 <.0001
Bonferroni <.0001
STRAIN
11C
DSC1
-0.4303 0.3842
121 -1.12
0.2649
Bonferroni 0.7950
STRAIN
9D
DSC1
-3.7647 0.3334
85.8 -11.29
<.0001 Bonferroni
<.0001
57
PROC GLM DATA=MICE; CLASSES STRAIN;
FREQ
NUMBER;
58
TITLE3 'ANALYSIS OF VARIANCE with
PROC GLM';
59
MODEL DAYS = STRAIN;
60
MEANS STRAIN / LSD TUKEY
SCHEFFE BON;
61
run;
NOTE:
PROCEDURE GLM used:
real time
0.09 seconds
cpu
time
0.09 seconds
EXST7015:
DAYS TO DEATH FOR MICE INOCULATED WITH 3 TYPHOID STRAINS
UNEQUAL
NUMBER OF MICE IN EACH TREATMENT
ANALYSIS
OF VARIANCE with PROC GLM
The
GLM Procedure
Class Level Information
Class
Levels Values
STRAIN
3 11C 9D DSC1
Number
of observations 224
Dependent
Variable: DAYS
Frequency:
NUMBER
Sum of
Source
DF
Squares Mean Square F
Value
Pr > F
Model
2
359.794413
179.897207 31.10
<.0001
Error
221
1278.419872 5.784705
Corrected
Total
223 1638.214286
R-Square
Coeff Var Root MSE
DAYS
Mean
0.219626
33.58801
2.405141 7.160714
Source
DF Type I
SS Mean Square F
Value
Pr > F
STRAIN
2 359.7944135
179.8972067 31.10
<.0001
Source
DF
Type III SS Mean Square F
Value
Pr > F
STRAIN
2 359.7944135
179.8972067 31.10
<.0001
t
Tests (LSD) for DAYS
NOTE:
This test controls the Type I comparisonwise error rate, not the
experimentwise
error rate.
Alpha
0.05
Error
Degrees of Freedom 221
Error
Mean Square 5.784705
Critical
Value of t 1.97076
Comparisons
significant at the 0.05 level are indicated by ***.
Difference
STRAIN
Between 95% Confidence
Comparison
Means Limits
DSC1
- 11C
0.4303 -0.3068
1.1675
DSC1
- 9D
3.7647 2.8194
4.7101 ***
11C -
DSC1
-0.4303 -1.1675 0.3068
11C -
9D
3.3344 2.2860 4.3828
***
9D
- DSC1
-3.7647 -4.7101 -2.8194
***
9D
- 11C
-3.3344 -4.3828 -2.2860
***
EXST7015:
DAYS TO DEATH FOR MICE INOCULATED WITH 3 TYPHOID STRAINS
UNEQUAL
NUMBER OF MICE IN EACH TREATMENT
ANALYSIS
OF VARIANCE with PROC GLM
The
GLM Procedure
Tukey's
Studentized Range (HSD) Test for DAYS
NOTE:
This test controls the Type I experimentwise error rate.
Alpha
0.05
Error
Degrees of
Freedom
221
Error
Mean
Square
5.784705
Critical
Value of Studentized Range 3.33708
Comparisons
significant at the 0.05 level are indicated by ***.
Difference
STRAIN
Between Simultaneous 95%
Comparison
Means Confidence Limits
DSC1
- 11C
0.4303
-0.4523 1.3129
DSC1
- 9D
3.7647 2.6328
4.8966 ***
11C -
DSC1
-0.4303 -1.3129 0.4523
11C -
9D
3.3344 2.0791 4.5897
***
9D
- DSC1
-3.7647 -4.8966 -2.6328
***
9D
- 11C
-3.3344 -4.5897 -2.0791
***
Bonferroni
(Dunn) t Tests for DAYS
NOTE:
This test controls the Type I experimentwise error rate, but it
generally has a
higher Type II error rate than Tukey's for
all
pairwise comparisons.
Alpha
0.05
Error
Degrees of Freedom 221
Error
Mean Square 5.784705
Critical
Value of t 2.41234
Comparisons
significant at the 0.05 level are indicated by ***.
Difference
STRAIN
Between Simultaneous 95%
Comparison
Means
Confidence Limits
DSC1
- 11C
0.4303 -0.4720
1.3326
DSC1
- 9D
3.7647 2.6076
4.9219 ***
11C -
DSC1
-0.4303 -1.3326 0.4720
11C -
9D
3.3344 2.0511 4.6178
***
9D
- DSC1
-3.7647 -4.9219 -2.6076
***
9D
- 11C
-3.3344 -4.6178 -2.0511
***
Scheffe's
Test for DAYS
NOTE:
This test controls the Type I experimentwise error rate, but it
generally has a
higher Type II error rate than Tukey's for
all
pairwise comparisons.
Alpha
0.05
Error
Degrees of Freedom 221
Error
Mean Square 5.784705
Critical
Value of F 3.03671
Comparisons
significant at the 0.05 level are indicated by ***.
Difference
STRAIN
Between Simultaneous 95%
Comparison
Means Confidence Limits
DSC1
- 11C
0.4303 -0.4915
1.3521
DSC1
- 9D
3.7647 2.5826
4.9469 ***
11C -
DSC1
-0.4303 -1.3521 0.4915
11C -
9D
3.3344 2.0234 4.6455
***
9D
- DSC1
-3.7647 -4.9469 -2.5826
***
9D
- 11C
-3.3344 -4.6455 -2.0234
***
Modified: August 16, 2004
James P. Geaghan