Example 43.2: FreemanTukey and tTests with Bootstrap Resampling
The data for the following example are the same as for
Example 43.1, except that a continuous variable T has been
added.
data a;
input S1 S2 T Dose;
datalines;
0 1 104 1
1 0 80 1
0 1 104 1
0 1 104 1
0 1 100 1
1 0 104 1
1 0 85 2
1 0 60 2
0 1 89 2
1 0 96 2
0 1 96 2
1 0 99 2
1 0 60 3
1 0 50 3
1 0 80 3
0 1 98 3
0 1 99 3
1 0 50 3
;
proc multtest data=a bootstrap nsample=10000
pvals seed=37081 outsamp=res;
test ft(S1 S2 / lowertailed) mean(T / lowertailed);
class Dose;
contrast 'Linear Trend' 0 1 2;
run;
proc print data=res(obs=36);
run;
The BOOTSTRAP option in the PROC MULTTEST statement requests
bootstrap resampling, and NSAMPLE=10000 requests 10,000 bootstrap
samples. The seed for the random number generation is 37081. The
OUTSAMP=RES option requests an output SAS data set containing the
10,000 bootstrap samples.
The TEST statement specifies the FreemanTukey test for S1 and
S2 and specifies the ttest for T. Both tests are
lowertailed. The grouping variable in the CLASS statement is
Dose, and the coefficients across the levels of Dose are 0,
1, and 2, as specified in the CONTRAST statement. PROC PRINT displays
the first 36 observations of the Res data set containing the
bootstrap samples.
The results from this analysis are listed in Output 43.2.1.
Output 43.2.1: FT and ttests with Bootstrap Resampling
Model Information 
Test for discrete variables: 
FreemanTukey 
Test for continuous variables: 
Mean ttest 
Tails for discrete tests: 
Lowertailed 
Tails for continuous tests: 
Lowertailed 
Strata adjustment? 
No 
Pvalue adjustment: 
Bootstrap 
Center continuous variables? 
Yes 
Number of resamples: 
10000 
Seed: 
37081 

The information in the preceding table corresponds to the
specifications in the invocation of PROC MULTTEST.
Contrast Coefficients 
Contrast 
Dose 
1 
2 
3 
Linear Trend 
0 
1 
2 

The preceding table shows the coefficients from the CONTRAST
statement, and they model a linear trend.
Discrete Variable Tabulations 
Variable 
Dose 
Count 
NumObs 
Percent 
S1 
1 
2 
6 
33.33 
S1 
2 
4 
6 
66.67 
S1 
3 
4 
6 
66.67 
S2 
1 
4 
6 
66.67 
S2 
2 
2 
6 
33.33 
S2 
3 
2 
6 
33.33 
Continuous Variable Tabulations 
Variable 
Dose 
NumObs 
Mean 
Standard Deviation 
T 
1 
6 
99.3333 
9.6056 
T 
2 
6 
87.5000 
14.4326 
T 
3 
6 
72.8333 
22.7017 

The summary statistics in the preceding table for S1 and
S2 are the same as those from Example 43.1. The variables
S1 and S2 are discrete, and T is a continuous
variable. The mean, standard deviation, and sample size for each
level of Dose is listed in the table for T. The
pvalues for S1 and S2 are from the FreemanTukey
test, and the pvalues for T are from the ttest.
pValues 
Variable 
Contrast 
Raw 
Bootstrap 
S1 
Linear Trend 
0.8547 
1.0000 
S2 
Linear Trend 
0.1453 
0.4471 
T 
Linear Trend 
0.0070 
0.0253 

The pvalues are listed in the preceding table. The Raw column
contains the results from the tests on the original data, and the
Bootstrap column contains the bootstrap resampled adjustment to
raw_p. Note that the adjusted pvalues are larger than the raw
pvalues for all three variables. The adjusted pvalues more
accurately reflect the correlation of the raw pvalues, the small
size of the data, and the multiple testing.
Obs 
_sample_ 
_class_ 
_obs_ 
S1 
S2 
T 
1 
1 
1 
11 
0 
1 
8.5000 
2 
1 
1 
16 
0 
1 
25.1667 
3 
1 
1 
16 
0 
1 
25.1667 
4 
1 
1 
14 
1 
0 
22.8333 
5 
1 
1 
18 
1 
0 
22.8333 
6 
1 
1 
14 
1 
0 
22.8333 
7 
1 
2 
4 
0 
1 
4.6667 
8 
1 
2 
12 
1 
0 
11.5000 
9 
1 
2 
8 
1 
0 
27.5000 
10 
1 
2 
7 
1 
0 
2.5000 
11 
1 
2 
3 
0 
1 
4.6667 
12 
1 
2 
12 
1 
0 
11.5000 
13 
1 
3 
13 
1 
0 
12.8333 
14 
1 
3 
5 
0 
1 
0.6667 
15 
1 
3 
8 
1 
0 
27.5000 
16 
1 
3 
5 
0 
1 
0.6667 
17 
1 
3 
13 
1 
0 
12.8333 
18 
1 
3 
6 
1 
0 
4.6667 
19 
2 
1 
8 
1 
0 
27.5000 
20 
2 
1 
3 
0 
1 
4.6667 
21 
2 
1 
9 
0 
1 
1.5000 
22 
2 
1 
13 
1 
0 
12.8333 
23 
2 
1 
14 
1 
0 
22.8333 
24 
2 
1 
12 
1 
0 
11.5000 
25 
2 
2 
14 
1 
0 
22.8333 
26 
2 
2 
18 
1 
0 
22.8333 
27 
2 
2 
15 
1 
0 
7.1667 
28 
2 
2 
6 
1 
0 
4.6667 
29 
2 
2 
13 
1 
0 
12.8333 
30 
2 
2 
1 
0 
1 
4.6667 
31 
2 
3 
7 
1 
0 
2.5000 
32 
2 
3 
7 
1 
0 
2.5000 
33 
2 
3 
6 
1 
0 
4.6667 
34 
2 
3 
13 
1 
0 
12.8333 
35 
2 
3 
4 
0 
1 
4.6667 
36 
2 
3 
6 
1 
0 
4.6667 

The preceding table lists the first 36 observations of the SAS data
set resulting from the OUTSAMP=RES option in the PROC MULTTEST
statement. The entire data set has 180,000
observations. The _sample_ variable
is the sample indicator and _class_ indicates the resampling
group, that is, the level of the CLASS variable assigned to the new
observation. The number of the observation in the
original data set is represented by _obs_. Also listed are
the values of the original test variables, S1 and S2,
and the meancentered values of T.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.