This script performs a randomization test (permutation test) to evaluate the age difference between fired and non-fired employees. It first calculates the observed difference via PROC TTEST. Then, it uses PROC IML to generate 1000 random permutations of the data. These permuted datasets are mass-analyzed by PROC TTEST to construct the null distribution of the mean difference. Finally, an empirical p-value is estimated by comparing the observed statistic to the generated distribution.
Data Analysis
Type : CREATION_INTERNE
Data is created directly within the script via a DATA step using the DATALINES statement (Status and Age variables).
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DATA STEP Data
Explanation : Creation of the initial 'discriminate' dataset containing individual status and age via internal data (datalines).
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data discriminate;
input Status Age;
/* Status = 0 = Fired
Status = 1 = Not Fired */
datalines;
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;
run;
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DATA discriminate;
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INPUTSTATUS Age;
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/* Status = 0 = Fired
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Status = 1 = Not Fired */
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DATALINES;
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...
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;
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RUN;
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PROC TTEST
Explanation : Execution of Student's T-test on real data to obtain the observed mean difference (reference).
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proc ttest data=discriminate;
class Status;
*may need to convert School to numeric;
var Age;
run;
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PROC TTESTDATA=discriminate;
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class STATUS;
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*may need to convert School to numeric;
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var Age;
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RUN;
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PROC IML Data
Explanation : Use of the IML matrix language to generate 1000 random permutations of the 'Age' variable. Creation of a wide table 'newds' where the first column is the status and the following ones are the permutations.
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ods output off;
ods exclude all;
proc iml ;
use discriminate;
read all var{Status Age} into x;
p=t(ranperm(x[, 2], 1000));
paf=x[, 1]||p;
create newds from paf;
append from paf;
quit;
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ods OUTPUT off;
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ods exclude all;
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PROC IML ;
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use discriminate;
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read all var{STATUS Age} into x;
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p=t(ranperm(x[, 2], 1000));
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paf=x[, 1]||p;
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create newds from paf;
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append from paf;
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QUIT;
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PROC TTEST Data
Explanation : Massive execution of T-tests on the 1000 permuted columns (col2 to col1001) against the status (col1). ODS outputs are suppressed for performance, except for the 'conflimits' table which is saved in 'diff'.
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ods output conflimits=diff;
proc ttest data=newds plots=none;
class col1;
var col2 - col1001;
run;
ods output on;
ods exclude none;
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ods OUTPUT conflimits=diff;
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PROC TTESTDATA=newds plots=none;
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class col1;
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var col2 - col1001;
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RUN;
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ods OUTPUT on;
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ods exclude none;
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PROC UNIVARIATE
Explanation : Analysis of the distribution of randomly generated mean differences (Pooled method) and display of a histogram.
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proc univariate data=diff;
where method="Pooled";
var mean;
histogram mean;
run;
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PROC UNIVARIATEDATA=diff;
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where method="Pooled";
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var mean;
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histogram mean;
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RUN;
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DATA STEP Data
Explanation : Filtering results to count how many permutations produced an absolute difference greater than or equal to the observed value (here hardcoded to 1.9238, which should correspond to the result of the first PROC TTEST).
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data numdiffs;
set diff;
where method="Pooled";
if abs(mean) >=1.9238;
run;
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DATA numdiffs;
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SET diff;
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where method="Pooled";
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IF abs(mean) >=1.9238;
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RUN;
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PROC PRINT
Explanation : Display of extreme permutations to allow manual calculation of the p-value (number of extreme observations / 1000).
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proc print data=numdiffs;
where method="Pooled";
run;
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PROC PRINT
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DATA=numdiffs;
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where method="Pooled";
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RUN;
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