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Inputting the Confidence Rating data set, table 27.1, p. 1076.
data confidence; input score block treat; cards; 1 1 1 5 1 2 8 1 3 2 2 1 8 2 2 14 2 3 7 3 1 9 3 2 16 3 3 6 4 1 13 4 2 18 4 3 12 5 1 14 5 2 17 5 3 ; run;
Fig. 27.2, p. 1077.
data plot;
set confidence;
if block=1 then b1=score;
if block=2 then b2=score;
if block=3 then b3=score;
if block=4 then b4=score;
if block=5 then b5=score;
run;
goptions reset=all;
symbol1 c=blue v=dot i=join;
symbol2 c=red v=circle i=join;
symbol3 c=green v=triangle i=join;
symbol4 c=purple v=plus i=join;
symbol5 c=cyan v=: i=join;
axis1 order=(0 to 20 by 5) label=(a=90 'Confidence Rating');
axis2 offset=(5,5);
legend1 label=none value=(height=.75 font=swiss 'Block 1' 'Block 2' 'Block 3' 'Block 4' 'Block 5' )
position=(top left inside) mode=share cborder=black;
proc gplot data=plot;
plot (b1 b2 b3 b4 b5)*treat/ overlay vaxis=axis1 haxis=axis2 legend=legend1;
run;
quit;
goptions reset=all;
Table 27.3, ANOVA table for Confidence Rating data, p. 1080.
proc glm data=confidence; class block treat; model score = treat block; output out=outglm r=resid p=predict; run; quit;
The GLM Procedure
Class Level Information
Class Levels Values
block 5 1 2 3 4 5
treat 3 1 2 3
Number of observations 15
The GLM Procedure
Dependent Variable: score
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 6 374.1333333 62.3555556 20.90 0.0002
Error 8 23.8666667 2.9833333
Corrected Total 14 398.0000000
R-Square Coeff Var Root MSE score Mean
0.940034 17.27233 1.727233 10.00000
Source DF Type I SS Mean Square F Value Pr > F
treat 2 202.8000000 101.4000000 33.99 0.0001
block 4 171.3333333 42.8333333 14.36 0.0010
Source DF Type III SS Mean Square F Value Pr > F
treat 2 202.8000000 101.4000000 33.99 0.0001
block 4 171.3333333 42.8333333 14.36 0.0010
Fig. 27.5, Residual plot, p. 1083.
symbol v=dot c=blue h=.8; proc gplot data=outglm; plot resid*predict; run; quit; proc capability data=outglm noprint; qqplot resid; run;
Testing if there is an interaction between blocks and treatment, p. 1083-1084.
ods listing close;
proc glm data=confidence;
class block treat;
model score = treat block;
ods output overallanova=overall modelanova=model;
run;
quit;
ods listing;
ods output close;
data _null_;
set overall;
if source='Corrected Total' then call symput('overall', ss);
run;
data _null_;
set model ;
if hypothesistype=1 and source='treat' then call symput('sstr', ss);
if hypothesistype=1 and source='block' then call symput('ssbk', ss);
if hypothesistype=1 and source='treat' then call symput('dftr', df);
if hypothesistype=1 and source='block' then call symput('dfbk', df);
run;
%put they here are &overall &sstr &ssbk &dftr &dfbk; /*check numbers in log file*/
proc sql;
create table temp1 as
select score, block, treat , mean(score) as yj
from confidence
group by block;
quit;
proc sql noprint;
create table temp2 as
select *, mean(score) as yi
from temp1
group by treat;
quit;
proc sql noprint;
select mean(score) into :meanp from temp1;
quit;
%put here is the grand mean = &meanp; /*check numbers in log file*/
proc sql noprint;
select sum( (yi - 10)*(yj-10)*score ) into :total
from temp2;
quit;
%put here is &total; /*check numbers in log file*/
data final;
msa = &sstr/(&dftr+1);
msb = &ssbk/(&dfbk+1);
sstr_bk = (&total*&total) / ( msa*msb );
ssrem = &overall - &sstr - &ssbk - sstr_bk;
f = sstr_bk/( ssrem/((&dftr+1)*(&dfbk+1) - (&dftr+1) - (&dfbk+1)) );
p_value = 1- cdf('F',f, 1, (&dftr+1)*(&dfbk+1) - (&dftr+1) - (&dfbk+1) );
run;
proc print data=final;
run;
Obs msa msb sstr_bk ssrem f p_value 1 67.6 34.2667 0.26267 23.6040 0.077896 0.78823
Pairwise comparisons using the Tukey procedure and a 95% family confidence coefficient, p. 1086.
proc glm data=confidence; class block treat; model score=block treat; lsmeans treat/ cl adjust=tukey pdiff; ods output lsmeans=temp; run; quit;
The GLM Procedure
Class Level Information
Class Levels Values
block 5 1 2 3 4 5
treat 3 1 2 3
Number of observations 15
The GLM Procedure
Dependent Variable: score
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 6 374.1333333 62.3555556 20.90 0.0002
Error 8 23.8666667 2.9833333
Corrected Total 14 398.0000000
R-Square Coeff Var Root MSE score Mean
0.940034 17.27233 1.727233 10.00000
Source DF Type I SS Mean Square F Value Pr > F
block 4 171.3333333 42.8333333 14.36 0.0010
treat 2 202.8000000 101.4000000 33.99 0.0001
Source DF Type III SS Mean Square F Value Pr > F
block 4 171.3333333 42.8333333 14.36 0.0010
treat 2 202.8000000 101.4000000 33.99 0.0001
The GLM Procedure
Least Squares Means
Adjustment for Multiple Comparisons: Tukey
LSMEAN
treat score LSMEAN Number
1 5.6000000 1
2 9.8000000 2
3 14.6000000 3
Least Squares Means for effect treat
Pr > |t| for H0: LSMean(i)=LSMean(j)
Dependent Variable: score
i/j 1 2 3
1 0.0121 <.0001
2 0.0121 0.0058
3 <.0001 0.0058
treat score LSMEAN 95% Confidence Limits
1 5.600000 3.818746 7.381254
2 9.800000 8.018746 11.581254
3 14.600000 12.818746 16.381254
Least Squares Means for Effect treat
Difference Simultaneous 95%
Between Confidence Limits for
i j Means LSMean(i)-LSMean(j)
1 2 -4.200000 -7.321443 -1.078557
1 3 -9.000000 -12.121443 -5.878557
2 3 -4.800000 -7.921443 -1.678557
Fig. 17.4, p. 728.
goptions reset=all; symbol v=dot c=blue h=.8; proc capability data=temp noprint; qqplot LSMean; run; quit;
Evaluating the efficiency of blocking by age of executives in the Confidence Rating, p. 1090.
ods listing close;
proc glm data=confidence;
class block treat;
model score = treat block;
ods output overallanova=overall modelanova=model;
run;
quit;
ods listing;
ods output close;
data _null_;
set model ;
if hypothesistype=1 and source='block' then call symput('msbk', ms);
if hypothesistype=1 and source='treat' then call symput('dftr', df);
if hypothesistype=1 and source='block' then call symput('dfbk', df);
run;
%put they here are &msbk &dftr &dfbk; /*check numbers in log file*/
data _null_;
set overall;
if source='Error' then call symput('mse', ms);
if source='Error' then call symput('dfe', df);
run;
%put they here are &mse &dfe; /*check numbers in log file*/
data temp;
Ehat = (&dfbk*&msbk + (&dfbk+1)*&dftr*&mse )/( ((&dfbk+1)*(&dftr+1) - 1)*&mse );
Eprime = (((&dfe+1)*(12+3))/( (&dfe+3)*(12+1)))*Ehat;
run;
proc print data=temp;
run;
Obs Ehat Eprime 1 4.81644 4.54699
Regression approach to randomized block design. Generating the appropriate variables when applying deviation coding to both the block variable and the treatment variable, table 27.5, p. 1092.
Note: For more information on deviation coding please refer to chapter 5 in our webbook at http://www.ats.ucla.edu/stat/sas/webbooks/reg/chapter5/sasreg5.htm .
data reg; set confidence; x1 =0; if block=1 then x1=1; else if block=5 then x1=-1; x2 =0; if block=2 then x2=1; else if block=5 then x2=-1; x3 =0; if block=3 then x3=1; else if block=5 then x3=-1; x4 =0; if block=4 then x4=1; else if block=5 then x4=-1; x5=0; if treat=1 then x5=1; else if treat=3 then x5=-1; x6=0; if treat=2 then x6=1; else if treat=3 then x6=-1; run; proc reg data=reg; model score = x1-x6; block: test x1=x2=x3=x4=0; treatment: test x5=x6=0; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: score
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 374.13333 62.35556 20.90 0.0002
Error 8 23.86667 2.98333
Corrected Total 14 398.00000
Root MSE 1.72723 R-Square 0.9400
Dependent Mean 10.00000 Adj R-Sq 0.8951
Coeff Var 17.27233
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t
Intercept 1 10.00000 0.44597 22.42 <.0001
x1 1 -5.33333 0.89194 -5.98 0.0003
x2 1 -2.00000 0.89194 -2.24 0.0552
x3 1 0.66667 0.89194 0.75 0.4762
x4 1 2.33333 0.89194 2.62 0.0308
x5 1 -4.40000 0.63070 -6.98 0.0001
x6 1 -0.20000 0.63070 -0.32 0.7593
The REG Procedure
Model: MODEL1
Test block Results for Dependent Variable score
Mean
Source DF Square F Value Pr > F
Numerator 4 42.83333 14.36 0.0010
Denominator 8 2.98333
The REG Procedure
Model: MODEL1
Test treatment Results for Dependent Variable score
Mean
Source DF Square F Value Pr > F
Numerator 2 101.40000 33.99 0.0001
Denominator 8 2.98333
Inputting the Produce Layout data, table 27.6a, p. 1095.
data produce; input sales block layout; cards; 75.3 1 1 69.8 1 2 87.7 1 3 64.3 2 1 70.0 2 2 71.1 2 3 59.0 3 1 45.4 3 2 71.8 3 3 44.2 4 1 35.1 4 2 61.0 4 3 21.7 5 1 59.9 5 2 25.3 5 3 ; run;
Creating the rank variable and statistics of the rank variable by layout, table 27.6b, p. 1095.
proc rank data=produce out=results ties=low; by block; var sales; ranks salesrank; run; proc sql; create table temp as select * , sum(salesrank) as Rj, mean(salesrank) as Rjbar from results group by layout; quit; proc print data=temp; run;
Obs sales block layout salesrank Rj Rjbar 1 59.0 3 1 2 8 1.6 2 64.3 2 1 1 8 1.6 3 21.7 5 1 1 8 1.6 4 44.2 4 1 2 8 1.6 5 75.3 1 1 2 8 1.6 6 59.9 5 2 3 8 1.6 7 35.1 4 2 1 8 1.6 8 70.0 2 2 2 8 1.6 9 69.8 1 2 1 8 1.6 10 45.4 3 2 1 8 1.6 11 25.3 5 3 2 14 2.8 12 87.7 1 3 3 14 2.8 13 71.1 2 3 3 14 2.8 14 61.0 4 3 3 14 2.8 15 71.8 3 3 3 14 2.8
Nonparametric F-test for a layout effect in the Produce Layout data, p. 1095.
proc glm data=results; class layout block; model salesrank = layout block; run; quit;
The GLM Procedure
Class Level Information
Class Levels Values
layout 3 1 2 3
block 5 1 2 3 4 5
Number of observations 15
The GLM Procedure
Dependent Variable: salesrank Rank for Variable sales
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 6 4.80000000 0.80000000 1.23 0.3820
Error 8 5.20000000 0.65000000
Corrected Total 14 10.00000000
R-Square Coeff Var Root MSE salesrank Mean
0.480000 40.31129 0.806226 2.000000
Source DF Type I SS Mean Square F Value Pr > F
layout 2 4.80000000 2.40000000 3.69 0.0731
block 4 0.00000000 0.00000000 0.00 1.0000
Source DF Type III SS Mean Square F Value Pr > F
layout 2 4.80000000 2.40000000 3.69 0.0731
block 4 0.00000000 0.00000000 0.00 1.0000
A regression approach to dealing with missing observations. Inputting data, table 27.7a, p. 1098.
data missing; input score block treat; cards; 10 1 2 9 1 3 11 2 1 10 2 2 7 2 3 6 3 1 4 3 2 3 3 3 ; run;
Generating the variables for the deviation coding for the block and treatment variables, p. 1098.
data missing;
set missing;
x1 = 0;
if block=1 then x1=1;
else if block=3 then x1=-1;
x2 = 0;
if block=2 then x2=1;
else if block=3 then x2=-1;
x3 = 0;
if treat=1 then x3=1;
else if treat=3 then x3=-1;
x4 = 0;
if treat=2 then x4=1;
else if treat=3 then x4=-1;
run;
Anova output table 27.8a, p. 1100 and test of treatment 1 vs. treatment 3, p. 1099.
proc glm data=missing; class treat block; model score = treat block; estimate 'treat1 vs. treat3' treat 1 0 -1; run; quit;
The GLM Procedure
Class Level Information
Class Levels Values
treat 3 1 2 3
block 3 1 2 3
Number of observations 8
The GLM Procedure
Dependent Variable: score
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 4 60.66666667 15.16666667 34.12 0.0078
Error 3 1.33333333 0.44444444
Corrected Total 7 62.00000000
R-Square Coeff Var Root MSE score Mean
0.978495 8.888889 0.666667 7.500000
Source DF Type I SS Mean Square F Value Pr > F
treat 2 6.83333333 3.41666667 7.69 0.0660
block 2 53.83333333 26.91666667 60.56 0.0038
Source DF Type III SS Mean Square F Value Pr > F
treat 2 12.50000000 6.25000000 14.06 0.0299
block 2 53.83333333 26.91666667 60.56 0.0038
Standard
Parameter Estimate Error t Value Pr > |t|
treat1 vs. treat3 3.33333333 0.63828474 5.22 0.0137
Regression output, table 27.8b and 27.8c, p. 1100.
proc reg data=missing; model score = x1-x4 / covb; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: score
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 4 60.66667 15.16667 34.12 0.0078
Error 3 1.33333 0.44444
Corrected Total 7 62.00000
Root MSE 0.66667 R-Square 0.9785
Dependent Mean 7.50000 Adj R-Sq 0.9498
Coeff Var 8.88889
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 8.00000 0.24845 32.20 <.0001
x1 1 2.33333 0.38490 6.06 0.0090
x2 1 1.33333 0.33333 4.00 0.0280
x3 1 1.66667 0.38490 4.33 0.0227
x4 1 1.11022E-16 0.33333 0.00 1.0000
Covariance of Estimates
Variable Intercept x1 x2 x3 x4
Intercept 0.0617283951 0.024691358 -0.012345679 0.024691358 -0.012345679
x1 0.024691358 0.1481481481 -0.074074074 0.049382716 -0.024691358
x2 -0.012345679 -0.074074074 0.1111111111 -0.024691358 0.012345679
x3 0.024691358 0.049382716 -0.024691358 0.1481481481 -0.074074074
x4 -0.012345679 -0.024691358 0.012345679 -0.074074074 0.1111111111
Inputting Task Completion data, table 27.10, p. 1107.
data completion; input time gender motivation distraction rep; cards; 12 1 1 1 1 8 1 1 1 2 3 2 1 1 1 9 2 1 1 2 7 1 1 2 1 5 1 1 2 2 5 2 1 2 1 9 2 1 2 2 14 1 2 1 1 16 1 2 1 2 11 2 2 1 1 9 2 2 1 2 15 1 2 2 1 13 1 2 2 2 10 2 2 2 1 14 2 2 2 2 ; run;
ANOVA for the Task Completion data, table 1108.
Note: The bars is a special notation which indicates that all the interactions should be included even the three-way interaction.
proc glm data=completion; class gender motivation distraction; model time = gender|motivation|distraction; random gender; run; quit;
The GLM Procedure
Class Level Information
Class Levels Values
gender 2 1 2
motivation 2 1 2
distraction 2 1 2
Number of observations 16
The GLM Procedure
Dependent Variable: time
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 7 172.0000000 24.5714286 3.93 0.0369
Error 8 50.0000000 6.2500000
Corrected Total 15 222.0000000
R-Square Coeff Var Root MSE time Mean
0.774775 25.00000 2.500000 10.00000
Source DF Type I SS Mean Square F Value Pr > F
gender 1 25.0000000 25.0000000 4.00 0.0805
motivation 1 121.0000000 121.0000000 19.36 0.0023
gender*motivation 1 4.0000000 4.0000000 0.64 0.4468
distraction 1 1.0000000 1.0000000 0.16 0.6996
gender*distraction 1 16.0000000 16.0000000 2.56 0.1483
motivatio*distractio 1 4.0000000 4.0000000 0.64 0.4468
gender*motiva*distra 1 1.0000000 1.0000000 0.16 0.6996
Source DF Type III SS Mean Square F Value Pr > F
gender 1 25.0000000 25.0000000 4.00 0.0805
motivation 1 121.0000000 121.0000000 19.36 0.0023
gender*motivation 1 4.0000000 4.0000000 0.64 0.4468
distraction 1 1.0000000 1.0000000 0.16 0.6996
gender*distraction 1 16.0000000 16.0000000 2.56 0.1483
motivatio*distractio 1 4.0000000 4.0000000 0.64 0.4468
gender*motiva*distra 1 1.0000000 1.0000000 0.16 0.6996
<some output has been omitted>
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