SAS(Statistical Analysis System)
EXAMPLE SAS FILES for
Exercise 3, page 359
Case 1: Data within SAS FILE
DATA one;
INPUT temp sugar;
CARDS;
1.0 8.1
1.1 7.8
.
.
.
2.0 10.5
;
PROC REG DATA=one;
Model sugar=temp;
Title 'Example 3, page 359';
RUN;
Brief Discussion of Components of the SAS File:
DATA Step
DATA STATEMENT - the first DATA statement names the data set
whose variables are defined in the INPUT statement
-- in the above, we create data set 'one'
INPUT STATEMENT - 2 forms
1. Freefield - can be used when data values are separated by 1
or more blanks
INPUT NAME $ AGE SEX $ SCORE;
($ indicates character variable)
2. Formatted - data occur in fixed columns
INPUT NAME $ 1-20 AGE 22-24 SEX $ 26 SCORE 28-30;
PROGRAM STATEMENTS (optional and not used in the above example
- could have been used to modify data
1. calculate new variables
2. modify existing variables
3. select a subset of data set upon which the statistical
analysis will be performed.
CARDS STATEMENT
- used to indicate that the next records in the file
contain the actual data and the semicolon after the data
indicates the end of the data itself
SPECIFYING THE ANALYSIS -- PROC STATEMENTS
GENERAL FORM
PROC xxxxx; - implies procedure is to be run on most recently
created data set
PROC xxxxx DATA = data set name;
Note: I did not have to specify DATA=one in the above example
Examples PROCs:
PROC REG - regression analysis
PROC ANOVA - analysis of variance
PROC GLM - general linear model
PROC MEANS - basic statistics, t-test for H0: m=0
PROC PLOT - plotting
PROC TTEST - t-tests
PROC UNIVARIATE - descriptive stats, box-plots, stem & leaf
General Cautions and comments:
1. Each statement should be concluded with a semicolon
2. SAS names can be from 1 to 8 characters in length and must
begin with a letter or an underscore
Case 2: Data in an External File
FILENAME f1 'ex3p359.data';
DATA one;
INFILE f1;
INPUT temp sugar;
PROC REG DATA=one;
MODEL sugar=temp;
Title 'Example 3, page 359';
RUN;
Discussion:
The data resides in external file "ex3p359.data" and is given the name f1 for this SAS run. However, in the DATA step, we give the data set to be analyzed the name "one". Additional data sets can be created within the SAS file.
Running the SAS job on TITAN
Files such as "internal.sas", "external.sas", and "ex3p359.data" are files that are usually created on your UNIX machine using an editor such as VI or PICO. For this particular example, a UNIX editor was used to create the file "internal.sas". To then run this SAS job on a UNIX machine that has access to SAS, type the command
sas internal
Two files will be created:
(1) internal.log -- which gives information on the run (time,
etc. along with any error messages.
(2) internal.lst -- the output from the SAS run. (errors may
cause this file to not be created.)
EXAMPLE FILES ON INTERNET
The SAS files and the data for Example 3, p.359 are avaiable for downloading. These files are as follows:
1. internal.sas - the SAS file in (1) above with data
contained within the SAS file
2. external.sas - the SAS file in (2) above for the case
in which data are in an external file
3. ex3p359.data - the external data file containing the
data for Example3, p.359
EXAMPLE 3, page 359 SAS Output
Example 3, page 359
The REG Procedure
Model: MODEL1
Dependent Variable: sugar
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 3.60009 3.60009 9.00 0.0150
Error 9 3.60173 0.40019
Corrected Total 10 7.20182
Root MSE 0.63261 R-Square 0.4999
Dependent Mean 9.12727 Adj R-Sq 0.4443
Coeff Var 6.93096
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 6.41364 0.92464 6.94 <.0001
temp 1 1.80909 0.60317 3.00 0.0150
EXERCISE 3 - page 408
filename cook 'ex3p408.data';
Data one;
infile cook;
input y x1 x2;
proc REG;
model y=x1 x2;
title 'Exercise 3, page 408';
run;
Exercise 3, page 408
Model: MODEL1
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 10953.20257 5476.60129 12688.741 0.0001
Error 7 3.02128 0.43161
C Total 9 10956.22385
Root MSE 0.65697 R-square 0.9997
Dep Mean 48.91500 Adj R-sq 0.9996
C.V. 1.34309
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 0.579988 0.60685346 0.956 0.3710
X1 1 2.712238 0.20208644 13.421 0.0001
X2 1 2.049707 0.04808181 42.630 0.0001
DATA IN TABLE 12.4 - page 433
STEPWISE RESULTS FROM SAS
Stepwise Procedure for Dependent Variable Y
Step 1 Variable X1 Entered R-square = 0.89698302 C(p) = 39.63635101
DF Sum of Squares Mean Square F Prob>F
Regression 1 288.14682495 288.14682495 60.95 0.0001
Error 7 33.09317505 4.72759644
Total 8 321.24000000
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 19.01108007 5.42271930 58.10583282 12.29 0.0099
X1 0.51797020 0.06634651 288.14682495 60.95 0.0001
Note: These F values
are the squares of the
usual t-values in SAS
See 3rd page.
Bounds on condition number: 1, 1
------
Step 2 Variable X3 Entered R-square = 0.98821914 C(p) = 2.10454082
DF Sum of Squares Mean Square F Prob>F
Regression 2 317.45551809 158.72775905 251.65 0.0001
Error 6 3.78448191 0.63074698
Total 8 321.24000000
Parameter Standard Type II
Variable Estimate Error Sum of Squares F Prob>F
INTERCEP 20.10845029 1.98725776 64.58088391 102.39 0.0001
X1 0.41362967 0.02866328 131.34899803 208.24 0.0001
X3 2.02533400 0.29711598 29.30869314 46.47 0.0005
Bounds on condition number: 1.398946, 5.595783
------
All variables left in the model are significant at the 0.1500 level.
No other variable met the 0.1500 significance level for entry into the model.
Summary of Stepwise Procedure for Dependent Variable Y
Variable Number Partial Model
Step Entered Removed In R**2 R**2 C(p) F Prob>F
1 X1 1 0.8970 0.8970 39.6364 60.9500 0.0001
2 X3 2 0.0912 0.9882 2.1045 46.4666 0.0005
This is the end of the SAS STEPWISE output.
NOTICE: SAS picked 2 independent variables and then stopped. The next pages show SAS output from standard PROC REG. Each set of output on the following pages is from a separate running of PROC REG.
SAS file that produced the Stepwise output shown above.
filename infant 'tablep433.data';
Data one;
infile infant;
input y x1 x2 x3 x4;
proc reg;
model y=x1 x2 x3 x4/selection=stepwise;
run;
Standard SAS PROC REG Printout for 3 Features
- to show why STEPWISE Procedure stopped with 2 features
X1, X3, and X4
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 3 317.64101 105.88034 147.097 0.0001
Error 5 3.59899 0.71980
C Total 8 321.24000
Root MSE 0.84841 R-square 0.9888
Dep Mean 60.96667 Adj R-sq 0.9821
C.V. 1.39160
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 21.873528 4.07388552 5.369 0.0030
X1 1 0.412771 0.03066663 13.460 0.0001
X3 1 2.202668 0.47198905 4.667 0.0055
X4 1 -0.078945 0.15551477 -0.508 0.6333
Note: p-value for X4
is too large.
X1, X3, and X2
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 3 318.25027 106.08342 177.413 0.0001
Error 5 2.98973 0.59795
C Total 8 321.24000
Root MSE 0.77327 R-square 0.9907
Dep Mean 60.96667 Adj R-sq 0.9851
C.V. 1.26835
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 5.629827 12.70680159 0.443 0.6762
X1 1 0.080984 0.28988008 0.279 0.7911
X3 1 3.069358 0.95066097 3.229 0.0232
X2 1 0.771498 0.66918975 1.153 0.3011
Note:X2 really “messes up”
the p-values, and the p-value
for X2 is too large
Showing Standard SAS PROC Reg Output for X1 and for X1 & X3
- for comparison with the the STEPWISE Output
X1
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 288.14682 288.14682 60.950 0.0001
Error 7 33.09318 4.72760
C Total 8 321.24000
Root MSE 2.17430 R-square 0.8970
Dep Mean 60.96667 Adj R-sq 0.8823
C.V. 3.56638
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 19.011080 5.42271930 3.506 0.0099
X1 1 0.517970 0.06634651 7.807 0.0001
X1 and X3
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 317.45552 158.72776 251.650 0.0001
Error 6 3.78448 0.63075
C Total 8 321.24000
Root MSE 0.79420 R-square 0.9882
Dep Mean 60.96667 Adj R-sq 0.9843
C.V. 1.30267
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 20.108450 1.98725776 10.119 0.0001
X1 1 0.413630 0.02866328 14.431 0.0001
X3 1 2.025334 0.29711598 6.817 0.0005
Standard SAS PROC REG Output for all 4 Independent Variables
X1, X2, X3, and X4
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 4 318.27442 79.56860 107.323 0.0003
Error 4 2.96558 0.74140
C Total 8 321.24000
Root MSE 0.86104 R-square 0.9908
Dep Mean 60.96667 Adj R-sq 0.9815
C.V. 1.41232
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 7.147532 16.45961128 0.434 0.6865
X1 1 0.100094 0.33970898 0.295 0.7829
X2 1 0.726417 0.78590156 0.924 0.4076
X3 1 3.075837 1.05917874 2.904 0.0439
X4 1 -0.030042 0.16646232 -0.180 0.8656
Note: Even though the overall
p-value is small (.0003),
there is much confusion
concerning the contribution of
the individual X variables
- this is probably due to
multicollinearity
SAS file to run the multiple regression based on X1 and X3 and print 3 residual plots
filename infant 'tablep433.data';
Data one;
infile infant;
input y x1 x2 x3 x4;
proc reg lp;
model y=x1 x3;
plot residual.*x1;
plot residual.*x3;
plot residual.*obs.;
title 'Residual Plots';
run;
SAS Output – Notice that the output on this page is the same as the output previously shown for using X1 and X3.
Residual
Model: MODEL1
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 317.45552 158.72776 251.650 0.0001
Error 6 3.78448 0.63075
C Total 8 321.24000
Root MSE 0.79420 R-square 0.9882
Dep Mean 60.96667 Adj R-sq 0.9843
C.V. 1.30267
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 20.108450 1.98725776 10.119 0.0001
X1 1 0.413630 0.02866328 14.431 0.0001
X3 1 2.025334 0.29711598 6.817 0.0005
Residual Plots
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------+------+------+------+------+------+------+------+------+------
65 70 75 80 85 90 95 100 105
X1
Residual Plots
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2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
X3
Residual Plots
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------+------+------+------+------+------+------+------+------+------
1 2 3 4 5 6 7 8 9
Observation Number OBS NUM
CAR DATA EXAMPLE
For this analysis, 5 gasoline types (A - E) were to be tested. Twenty cars
were selected for testing and were assigned randomly to the groups (i.e. the
gasoline types). Thus, in the analysis, each gasoline type was tested on
4 cars. A performance-based octane reading was obtained for each car,
and the question is whether the gasolines differ with respect to this octane
reading.
The data set follows:
A 91.7
A 91.2
A 90.9
A 90.6
B 91.7
B 91.9
B 90.9
B 90.9
C 92.4
C 91.2
C 91.6
C 91.0
D 91.8
D 92.2
D 92.0
D 91.4
E 93.1
E 92.9
E 92.4
E 92.4
The SAS file used:
FILENAME f1 'car.data';
Options ls=80;
DATA one;
INFILE f1;
INPUT gas$ octane;
PROC GLM;
CLASS gas;
MODEL octane=gas;
TITLE 'Gasoline Example - Completely Randomized Design';
MEANS gas/duncans;
RUN;
PROC MEANS mean var;
RUN;
PROC MEANS mean var;
class gas;
run;
The SAS Output follows:
Gasoline Example - Completely Randomized Design
General Linear Models Procedure
Dependent Variable: OCTANE
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 4 6.10800000 1.52700000 6.80 0.0025
Error 15 3.37000000 0.22466667
Corrected Total 19 9.47800000
R-Square C.V. Root MSE OCTANE Mean
0.644440 0.516836 0.4739902 91.710000
Source DF Type I SS Mean Square F Value Pr > F
GAS 4 6.10800000 1.52700000 6.80 0.0025
Source DF Type III SS Mean Square F Value Pr > F
GAS 4 6.10800000 1.52700000 6.80 0.0025
Gasoline Example - Completely Randomized Design
General Linear Models Procedure
Duncan's Multiple Range Test for variable: OCTANE
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha= 0.05 df= 15 MSE= 0.224667
Number of Means 2 3 4 5
Critical Range .7144 .7489 .7703 .7849
Means with the same letter are not significantly different.
Duncan Grouping Mean N GAS
A 92.7000 4 E
B 91.8500 4 D
B
B 91.5500 4 C
B
B 91.3500 4 B
B
B 91.1000 4 A
Output from PROC MEANS:
Gasoline Example - Completely Randomized
Analysis Variable : OCTANE
Mean Variance
------
91.7100000 0.4988421
------
Gasoline Example - Completely Randomized Design
Analysis Variable : OCTANE
GAS N Obs Mean Variance
------
A 4 91.1000000 0.2200000
B 4 91.3500000 0.2766667
C 4 91.5500000 0.3833333
D 4 91.8500000 0.1166667
E 4 92.7000000 0.1266667
------
BALLOON DATA
Col. 1-2 - observation number
Col. 3 - color (1=pink, 2=yellow, 3=orange, 4=blue)
Col. 4-7 - inflation time in seconds
1122.4
2324.6
3120.3
4419.8
5324.3
6222.2
7228.5
8225.7
9320.2
10119.6
11228.8
12424.0
13417.1
14419.3
15324.2
16115.8
17218.3
18117.5
19418.7
20322.9
21116.3
22414.0
23416.6
24218.1
25218.9
26416.0
27220.1
28322.5
29316.0
30119.3
31115.9
32320.3
SAS file for running "Balloon Data"
data balloon;
infile 'balloon.data';
input
runcov 1-2
color 3-3
time 4-7
;
proc glm;
classes color;
model time=color;
title 'ANOVA --- Balloon Data';
means color/duncans;
run;
SAS OUTPUT
ANOVA --- Balloon Data
General Linear Models Procedure
Dependent Variable: TIME
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 126.15125000 42.05041667 3.85 0.0200
Error 28 305.64750000 10.91598214
Corrected Total 31 431.79875000
R-Square C.V. Root MSE TIME Mean
0.292153 16.31069 3.3039343 20.256250
General Linear Models Procedure
Duncan's Multiple Range Test for variable: TIME
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha= 0.05 df= 28 MSE= 10.91598
Number of Means 2 3 4
Critical Range 3.384 3.556 3.667
Means with the same letter are not significantly different.
Duncan Grouping Mean N COLOR
A 22.575 8 2
A
A 21.875 8 3
B 18.388 8 1
B
B 18.188 8 4
RANDOMIZED COMPLETE BLOCK DESIGN FOR GASOLINE DATA
The first variable (A - E) indicates gas as it did with the Completely
Randomized Design. The second variable (B1 - B4) indicates car. In this
design, there are only 4 cars, and the 5 gas types are tested on each car
as mentioned in lecture.
A B1 91.7
A B2 91.2
A B3 90.9
A B4 90.6
B B1 91.7
B B2 91.9
B B3 90.9
B B4 90.9
C B1 92.4
C B2 91.2
C B3 91.6
C B4 91.0
D B1 91.8
D B2 92.2
D B3 92.0
D B4 91.4
E B1 93.1
E B2 92.9
E B3 92.4
E B4 92.4
SAS file for Randomized Complete Block Design for gas data.
FILENAME f1 'carblk.data';
Options ls=80;
DATA one;
INFILE f1;
INPUT gas$ block$ octane;
PROC ANOVA;
CLASS gas block;
MODEL octane=gas block;
TITLE 'Gasoline Example -Randomized Complete Block Design';
MEANS gas/duncans;
RUN;
PROC MEANS mean var;
class block;
RUN;
PROC MEANS mean var;
class gas;
run;
Gasoline Example -Randomized Complete Block Design
Analysis of Variance Procedure
Class Level Information
Class Levels Values
GAS 5 A B C D E
BLOCK 4 B1 B2 B3 B4
Number of observations in data set = 20
Dependent Variable: OCTANE
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 8.30200000 1.18600000 12.10 0.0001
Error 12 1.17600000 0.09800000
Corrected Total 19 9.47800000
R-Square C.V. Root MSE OCTANE Mean
0.875923 0.341347 0.3130495 91.710000
Source DF Anova SS Mean Square F Value Pr > F
GAS 4 6.10800000 1.52700000 15.58 0.0001
BLOCK 3 2.19400000 0.73133333 7.46 0.0044
Duncan's Multiple Range Test for variable: OCTANE
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha= 0.05 df= 12 MSE= 0.098
Number of Means 2 3 4 5
Critical Range .4823 .5048 .5185 .5275
Means with the same letter are not significantly different.
Duncan Grouping Mean N GAS
A 92.7000 4 E
B 91.8500 4 D
B
C B 91.5500 4 C
C B
C B 91.3500 4 B
C
C 91.1000 4 A
Gasoline Example -Randomized Complete Block Design
Analysis Variable : OCTANE
BLOCK N Obs Mean Variance
------
B1 5 92.1400000 0.3730000
B2 5 91.8800000 0.5170000
B3 5 91.5600000 0.4430000
B4 5 91.2600000 0.4880000
------
Gasoline Example -Randomized Complete Block Design
Analysis Variable : OCTANE
GAS N Obs Mean Variance
------
A 4 91.1000000 0.2200000
B 4 91.3500000 0.2766667
C 4 91.5500000 0.3833333
D 4 91.8500000 0.1166667
E 4 92.7000000 0.1266667
------
STIMULUS EXAMPLE: 2-Factor ANOVA
Personal computer presents stimulus, and person responds:
Study of how RESPONSE TIME is effected by a WARNING:
WARNING given prior to stimulus:
- auditory or visual
- 5 sec, 10 sec, or 15 sec before stimulus
TABLE OF RESPONSE TIMES
WARNING TYPE
Auditory / Visual.204 / .257
5 sec / .170 / .279
.181 / .269
WARNING / .167 / .283
TIME / 10 sec / .182 / .235
.187 / .260
.202 / .256
15 sec / .198 / .281
.236 / .258
STMULUS EXAMPLE (2-Factor ANOVA):
Data:
Factor A: A=auditory warning, V=visual warning
Factor B: Time between warning and stimulus
Variable: Reaction time (I called it "response" in SAS)
A 5 .204
A 5 .170
A 5 .181
A 10 .167
A 10 .182
A 10 .187
A 15 .202
A 15 .198
A 15 .236
V 5 .257
V 5 .279
V 5 .269
V 10 .283
V 10 .235
V 10 .260
V 15 .256
V 15 .281
V 15 .258
SAS File:
FILENAME f1 'stimulus.data';
Options ls=80;
DATA one;
INFILE f1;
INPUT type$ time response;
PROC GLM;
class type time;
MODEL response=type time type*time;
Title 'Stimulus Example -- 2-way ANOVA';
MEANS type time/Duncan;
RUN;
PROC MEANS mean var;
class type time;
var response;
run;
Stimulus Example -- 2-way ANOVA
General Linear Models Procedure
Class Level Information
Class Levels Values
TYPE 2 A V
TIME 3 5 10 15
Number of observations in data set = 18
Dependent Variable: RESPONSE
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 0.02554894 0.00510979 17.66 0.0001
Error 12 0.00347200 0.00028933
Corrected Total 17 0.02902094
R-Square C.V. Root MSE RESPONSE Mean
0.880362 7.458622 0.0170098 0.2280556
Source DF Type I SS Mean Square F Value Pr > F
TYPE 1 0.02354450 0.02354450 81.38 0.0001
TIME 2 0.00115811 0.00057906 2.00 0.1778
TYPE*TIME 2 0.00084633 0.00042317 1.46 0.2701
Source DF Type III SS Mean Square F Value Pr > F
TYPE 1 0.02354450 0.02354450 81.38 0.0001
TIME 2 0.00115811 0.00057906 2.00 0.1778
TYPE*TIME 2 0.00084633 0.00042317 1.46 0.2701
Stimulus Example -- 2-way ANOVA
General Linear Models Procedure
Duncan's Multiple Range Test for variable: RESPONSE
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha= 0.05 df= 12 MSE= 0.000289
Number of Means 2
Critical Range .01747
Means with the same letter are not significantly different.
Duncan Grouping Mean N TYPE
A 0.264222 9 V
B 0.191889 9 A
Duncan's Multiple Range Test for variable: RESPONSE
Alpha= 0.05 df= 12 MSE= 0.000289
Number of Means 2 3
Critical Range .02140 .02240
Means with the same letter are not significantly different.
Duncan Grouping Mean N TIME
A 0.238500 6 15
A
A 0.226667 6 5
A
A 0.219000 6 10
Stimulus Example -- 2-way ANOVA
Analysis Variable : RESPONSE
The MEANS Procedure
Analysis Variable : response
N
type time Obs Mean Variance
------
A 5 3 0.1850000 0.000301000
10 3 0.1786667 0.000108333
15 3 0.2120000 0.000436000
V 5 3 0.2683333 0.000121333
10 3 0.2593333 0.000576333
15 3 0.2650000 0.000193000
------
PILOT PLANT DATA
Variable = Chemical Yield
Factors:A – Temperature (160, 180)
B – Catalyst (C1 , C2)
160 C1 59
160 C1 61
160 C1 50
160 C1 58
180 C1 74
180 C1 70
180 C1 69
180 C1 67
160 C2 50
160 C2 54
160 C2 46
160 C2 44
180 C2 81
180 C2 85
180 C2 79
180 C2 81
SAS File for 2-Factor Factorial Analysis of
Pilot-Plant Data
FILENAME f1 'pilot.data';
Options ls=80;
DATA one;
INFILE f1;
INPUT temp catalyst$ yield;
PROC GLM;
class temp catalyst;
MODEL yield=temp catalyst temp*catalyst;
Title 'Pilot Plant Example -- 2-way ANOVA';
MEANS temp catalyst/Duncan;
RUN;
PROC MEANS;
class temp catalyst;
var yield;
run;
SAS Output
Pilot Plant Example -- 2-way ANOVA
General Linear Models Procedure
Dependent Variable: YIELD
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 2525.0000000 841.6666667 58.05 0.0001
Error 12 174.0000000 14.5000000
Corrected Total 15 2699.0000000
R-Square C.V. Root MSE YIELD Mean
0.935532 5.926672 3.8078866 64.250000
Source DF Type I SS Mean Square F Value Pr > F
TEMP 1 2116.0000000 2116.0000000 145.93 0.0001
CATALYST 1 9.0000000 9.0000000 0.62 0.4461
TEMP*CATALYST 1 400.0000000 400.0000000 27.59 0.0002
Duncan's Multiple Range Test for variable: YIELD
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha= 0.05 df= 12 MSE= 14.5
Number of Means 2
Critical Range 4.148
Means with the same letter are not significantly different.
Duncan Grouping Mean N TEMP
A 75.750 8 180
B 52.750 8 160
Duncan's Multiple Range Test for variable: YIELD
NOTE: This test controls the type I comparisonwise error rate, not
the experimentwise error rate
Alpha= 0.05 df= 12 MSE= 14.5
Number of Means 2
Critical Range 4.148
Means with the same letter are not significantly different.
Duncan Grouping Mean N CATALYST
A 65.000 8 C2
A
A 63.500 8 C1
PROC PRINT Output:
Pilot Plant Example -- 2-way
Analysis Variable : YIELD
TEMP CATALYST N Obs N Mean Std Dev Minimum
------
160 C1 4 4 57.0000000 4.8304589 50.0000000
C2 4 4 48.5000000 4.4347116 44.0000000
180 C1 4 4 70.0000000 2.9439203 67.0000000
C2 4 4 81.5000000 2.5166115 79.0000000
------
TEMP CATALYST N Obs Maximum
------
160 C1 4 61.0000000
C2 4 54.0000000
180 C1 4 74.0000000
C2 4 85.0000000
------
POPCORN EXAMPLE – 3-FACTOR FACTORIAL MODEL
1 500 5 73.8
1 500 5 65.5
1 500 4.5 70.3
1 500 4.5 91.0
1 500 4 72.7
1 500 4 81.9
1 600 5 70.8
1 600 5 75.3
1 600 4.5 78.7
1 600 4.5 88.7
1 600 4 74.1
1 600 4 72.1
2 500 5 73.7
2 500 5 65.8
2 500 4.5 93.4
2 500 4.5 76.3
2 500 4 45.3
2 500 4 47.6
2 600 5 79.3
2 600 5 86.5
2 600 4.5 92.2
2 600 4.5 84.7
2 600 4 66.3
2 600 4 45.7
3 500 5 62.5
3 500 5 65.0
3 500 4.5 50.1
3 500 4.5 81.5
3 500 4 51.4
3 500 4 67.7
3 600 5 82.1
3 600 5 74.5
3 600 4.5 71.5
3 600 4.5 80.0
3 600 4 64.0
3 600 4 77.0
FILENAME f1 'popcorn.data';
Options ls=80;
DATA one;
INFILE f1;
INPUT brand power time percent;
PROC GLM;
class brand power time;
MODEL percent=brand power time brand*power brand*time power*time brand*power*time;
Title 'Popcorn Example -- 3-Factor ANOVA';
MEANS brand power time/Duncan;
RUN;
PROC MEANS;
class brand power time;
var percent;
run;
Popcorn Example -- 3-Factor ANOVA
General Linear Models Procedure
Class Level Information
Class Levels Values
BRAND 3 1 2 3
POWER 2 500 600
TIME 3 4 5 4.5
Number of observations in data set = 36
Popcorn Example -- 3-Factor ANOVA
General Linear Models Procedure
Dependent Variable: PERCENT
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 17 4065.7288889 239.1605229 2.73 0.0206
Error 18 1577.8700000 87.6594444
Corrected Total 35 5643.5988889
R-Square C.V. Root MSE PERCENT Mean
0.720414 12.96867 9.3626623 72.194444
Source DF Type I SS Mean Square F Value Pr > F
BRAND 2 331.1005556 165.5502778 1.89 0.1801
POWER 1 455.1111111 455.1111111 5.19 0.0351
TIME 2 1554.5755556 777.2877778 8.87 0.0021
BRAND*POWER 2 196.0405556 98.0202778 1.12 0.3485
BRAND*TIME 4 1433.8577778 358.4644444 4.09 0.0157
POWER*TIME 2 47.7088889 23.8544444 0.27 0.7648
BRAND*POWER*TIME 4 47.3344444 11.8336111 0.13 0.9673
Popcorn Example -- 3-Factor ANOVA
General Linear Models Procedure
Duncan's Multiple Range Test for variable: PERCENT