STA429/1007 F 2004 Handout 6: The Potato Data
Custom tests and contrasts in factorial ANOVA
/* potato.sas */
options linesize=79 noovp formdlim='_';
title 'Rotten potatos: STA429/1007 F 2004';
title2 'Custom tests with proc reg and proc glm';
data spud;
infile 'potato2.dat' firstobs=2; /* Skip the first line that R uses */
input id bact temp rot;
if temp=1 and bact=1 then mu11=1; else mu11=0;
if temp=1 and bact=2 then mu12=1; else mu12=0;
if temp=1 and bact=3 then mu13=1; else mu13=0;
if temp=2 and bact=1 then mu21=1; else mu21=0;
if temp=2 and bact=2 then mu22=1; else mu22=0;
if temp=2 and bact=3 then mu23=1; else mu23=0;
combo = 10*temp+bact;
proc means;
class bact temp;
var rot;
/* Better looking output from proc tabulate */
proc tabulate;
class bact temp;
var rot;
table (temp all),(bact all) * (mean*rot);
proc glm;
title3 'Standard 2-way ANOVA with proc glm';
class bact temp;
model rot=temp|bact;
means temp*bact;
/* Now generate the tests for main effects and interaction, and also 2 tests
for bacteria type, once just for low temp and once just for high. Do this
first with test statements in proc reg, and then with contrasts in proc glm.
BACTERIA TYPE
TEMP 1 2 3
1 mu11 mu12 mu13
2 mu21 mu22 mu23
*/
proc reg;
title3 'Using the proc reg test statement';
model rot = mu11--mu23 / noint;
overall: test mu11=mu12=mu13=mu21=mu22=mu23;
temper: test mu11+mu12+mu13=mu21+mu22+mu23;
bacter: test mu11+mu21=mu12+mu22,
mu12+mu22=mu13+mu23;
B_by_T: test mu11-mu21=mu12-mu22=mu13-mu23;
BjustLO: test mu11=mu12=mu13;
BjustHI: test mu21=mu22=mu23;
/* Definition: A contrast is a linear combination whose coefficients
add to zero. We can test whether collections of contrasts
of cell means are all to equal zero.*/
proc glm;
title3 'Test contrasts with proc glm';
class combo;
model rot=combo;
contrast 'Main Effect for Temerature'
combo 1 1 1 -1 -1 -1;
contrast 'Main Effect for Bacteria'
combo 1 -1 0 1 -1 0,
combo 0 1 -1 0 1 -1;
contrast 'Temperature by Bacteria Interaction'
combo 1 -1 0 -1 1 0,
combo 0 1 -1 0 -1 1;
contrast 'Bacteria Just for Low Temp'
combo 1 -1 0 0 0 0,
combo 0 1 -1 0 0 0;
contrast 'Bacteria Just for High Temp'
combo 0 0 0 1 -1 0,
combo 0 0 0 0 1 -1;
Here is potato.lst
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Rotten potatos: STA429/1007 F 2004 1
Custom tests with proc reg and proc glm
15:11 Saturday, October 16, 2004
The MEANS Procedure
Analysis Variable : rot
N
bact temp Obs N Mean Std Dev Minimum
-----------------------------------------------------------------------------
1 1 9 9 3.5555556 4.2752518 0
2 9 9 7.0000000 3.5355339 0
2 1 9 9 4.7777778 3.1135903 0
2 9 9 13.5555556 6.3267510 3.0000000
3 1 9 9 8.0000000 4.5552168 2.0000000
2 9 9 19.5555556 5.5251948 8.0000000
-----------------------------------------------------------------------------
Analysis Variable : rot
N
bact temp Obs Maximum
---------------------------------------------
1 1 9 9.0000000
2 9 10.0000000
2 1 9 10.0000000
2 9 23.0000000
3 1 9 15.0000000
2 9 26.0000000
---------------------------------------------
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Rotten potatos: STA429/1007 F 2004 2
Custom tests with proc reg and proc glm
15:11 Saturday, October 16, 2004
-----------------------------------------------------------------------
| | bact | |
| |--------------------------------------| |
| | 1 | 2 | 3 | All |
| |------------+------------+------------+------------|
| | Mean | Mean | Mean | Mean |
| |------------+------------+------------+------------|
| | rot | rot | rot | rot |
|-----------------+------------+------------+------------+------------|
|temp | | | | |
|-----------------| | | | |
|1 | 3.56| 4.78| 8.00| 5.44|
|-----------------+------------+------------+------------+------------|
|2 | 7.00| 13.56| 19.56| 13.37|
|-----------------+------------+------------+------------+------------|
|All | 5.28| 9.17| 13.78| 9.41|
-----------------------------------------------------------------------
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Rotten potatos: STA429/1007 F 2004 3
Custom tests with proc reg and proc glm
Standard 2-way ANOVA with proc glm
15:11 Saturday, October 16, 2004
The GLM Procedure
Class Level Information
Class Levels Values
bact 3 1 2 3
temp 2 1 2
Number of observations 54
_______________________________________________________________________________
Rotten potatos: STA429/1007 F 2004 4
Custom tests with proc reg and proc glm
Standard 2-way ANOVA with proc glm
15:11 Saturday, October 16, 2004
The GLM Procedure
Dependent Variable: rot
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 5 1652.814815 330.562963 15.05 <.0001
Error 48 1054.222222 21.962963
Corrected Total 53 2707.037037
R-Square Coeff Var Root MSE rot Mean
0.610562 49.81676 4.686466 9.407407
Source DF Type I SS Mean Square F Value Pr > F
temp 1 848.0740741 848.0740741 38.61 <.0001
bact 2 651.8148148 325.9074074 14.84 <.0001
bact*temp 2 152.9259259 76.4629630 3.48 0.0387
Source DF Type III SS Mean Square F Value Pr > F
temp 1 848.0740741 848.0740741 38.61 <.0001
bact 2 651.8148148 325.9074074 14.84 <.0001
bact*temp 2 152.9259259 76.4629630 3.48 0.0387
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Rotten potatos: STA429/1007 F 2004 5
Custom tests with proc reg and proc glm
Standard 2-way ANOVA with proc glm
15:11 Saturday, October 16, 2004
The GLM Procedure
Level of Level of -------------rot-------------
bact temp N Mean Std Dev
1 1 9 3.5555556 4.27525178
1 2 9 7.0000000 3.53553391
2 1 9 4.7777778 3.11359028
2 2 9 13.5555556 6.32675097
3 1 9 8.0000000 4.55521679
3 2 9 19.5555556 5.52519482
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Rotten potatos: STA429/1007 F 2004 6
Custom tests with proc reg and proc glm
Using the proc reg test statement
15:11 Saturday, October 16, 2004
The REG Procedure
Model: MODEL1
Dependent Variable: rot
NOTE: No intercept in model. R-Square is redefined.
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 6431.77778 1071.96296 48.81 <.0001
Error 48 1054.22222 21.96296
Uncorrected Total 54 7486.00000
Root MSE 4.68647 R-Square 0.8592
Dependent Mean 9.40741 Adj R-Sq 0.8416
Coeff Var 49.81676
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
mu11 1 3.55556 1.56216 2.28 0.0273
mu12 1 4.77778 1.56216 3.06 0.0036
mu13 1 8.00000 1.56216 5.12 <.0001
mu21 1 7.00000 1.56216 4.48 <.0001
mu22 1 13.55556 1.56216 8.68 <.0001
mu23 1 19.55556 1.56216 12.52 <.0001
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Rotten potatos: STA429/1007 F 2004 7
Custom tests with proc reg and proc glm
Using the proc reg test statement
15:11 Saturday, October 16, 2004
The REG Procedure
Model: MODEL1
Test overall Results for Dependent Variable rot
Mean
Source DF Square F Value Pr > F
Numerator 5 330.56296 15.05 <.0001
Denominator 48 21.96296
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Rotten potatos: STA429/1007 F 2004 8
Custom tests with proc reg and proc glm
Using the proc reg test statement
15:11 Saturday, October 16, 2004
The REG Procedure
Model: MODEL1
Test temper Results for Dependent Variable rot
Mean
Source DF Square F Value Pr > F
Numerator 1 848.07407 38.61 <.0001
Denominator 48 21.96296
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Rotten potatos: STA429/1007 F 2004 9
Custom tests with proc reg and proc glm
Using the proc reg test statement
15:11 Saturday, October 16, 2004
The REG Procedure
Model: MODEL1
Test bacter Results for Dependent Variable rot
Mean
Source DF Square F Value Pr > F
Numerator 2 325.90741 14.84 <.0001
Denominator 48 21.96296
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Rotten potatos: STA429/1007 F 2004 10
Custom tests with proc reg and proc glm
Using the proc reg test statement
15:11 Saturday, October 16, 2004
The REG Procedure
Model: MODEL1
Test B_by_T Results for Dependent Variable rot
Mean
Source DF Square F Value Pr > F
Numerator 2 76.46296 3.48 0.0387
Denominator 48 21.96296
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Rotten potatos: STA429/1007 F 2004 11
Custom tests with proc reg and proc glm
Using the proc reg test statement
15:11 Saturday, October 16, 2004
The REG Procedure
Model: MODEL1
Test BjustLO Results for Dependent Variable rot
Mean
Source DF Square F Value Pr > F
Numerator 2 47.44444 2.16 0.1264
Denominator 48 21.96296
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Rotten potatos: STA429/1007 F 2004 12
Custom tests with proc reg and proc glm
Using the proc reg test statement
15:11 Saturday, October 16, 2004
The REG Procedure
Model: MODEL1
Test BjustHI Results for Dependent Variable rot
Mean
Source DF Square F Value Pr > F
Numerator 2 354.92593 16.16 <.0001
Denominator 48 21.96296
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Rotten potatos: STA429/1007 F 2004 13
Custom tests with proc reg and proc glm
Test contrasts with proc glm
15:11 Saturday, October 16, 2004
The GLM Procedure
Class Level Information
Class Levels Values
combo 6 11 12 13 21 22 23
Number of observations 54
_______________________________________________________________________________
Rotten potatos: STA429/1007 F 2004 14
Custom tests with proc reg and proc glm
Test contrasts with proc glm
15:11 Saturday, October 16, 2004
The GLM Procedure
Dependent Variable: rot
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 5 1652.814815 330.562963 15.05 <.0001
Error 48 1054.222222 21.962963
Corrected Total 53 2707.037037
R-Square Coeff Var Root MSE rot Mean
0.610562 49.81676 4.686466 9.407407
Source DF Type I SS Mean Square F Value Pr > F
combo 5 1652.814815 330.562963 15.05 <.0001
Source DF Type III SS Mean Square F Value Pr > F
combo 5 1652.814815 330.562963 15.05 <.0001
Contrast DF Contrast SS Mean Square
Main Effect for Temerature 1 848.0740741 848.0740741
Main Effect for Bacteria 2 651.8148148 325.9074074
Temperature by Bacteria Interaction 2 152.9259259 76.4629630
Bacteria Just for Low Temp 2 94.8888889 47.4444444
Bacteria Just for High Temp 2 709.8518519 354.9259259
Contrast F Value Pr > F
Main Effect for Temerature 38.61 <.0001
Main Effect for Bacteria 14.84 <.0001
Temperature by Bacteria Interaction 3.48 0.0387
Bacteria Just for Low Temp 2.16 0.1264
Bacteria Just for High Temp 16.16 <.0001