Simulations in SAS

Significant Effects when there are none

/* Significant effects where there are none */
%let ErrorVariance=1000;
%let nrep=10;
%let nsim=100;
DATA CRD;
 call streaminit(123);
 do isim = 1 to ≁
    do rep=1 to &nrep;
        do trt=1 to 5;
        if trt=1 then y=791.5 + rand('Normal', 0, sqrt(&ErrorVariance)); 
        if trt=2 then y=791.5 + rand('Normal', 0, sqrt(&ErrorVariance));
        if trt=3 then y=791.5 + rand('Normal', 0, sqrt(&ErrorVariance));
        if trt=4 then y=791.5 + rand('Normal', 0, sqrt(&ErrorVariance));
        if trt=5 then y=791.5 + rand('Normal', 0, sqrt(&ErrorVariance));
output;
end;
end;
end;
/* Show how due to randomness, treatment differences may seem to be present if though they are not */
proc sgpanel data=CRD noautolegend;
where isim<11;
panelby isim / columns=5 novarname skipemptycells;
vbox y  / category=trt group=trt;
refline 791.5 / axis=y lineattrs=(color=black pattern=2); 
title 'Boxplot of BW by Treatment';
title2 italic ' No treatment differences in population';
run;
/* show how many differences are significant --> should be around 5% */
proc mixed data=CRD;
by isim;
class trt;
model y = trt / s cl ddfm=kenwardroger ;
lsmeans trt / pdiff=all adjdfe=row adjust=tukey cl;
ods output diffs=differences lsmeans=mixmeans;
run;
data differences;
set differences;
Comparison=catx(' vs ',trt,_trt);
if probt<0.05 then Sign='Yes'; else Sign='No';
run;
ods graphics / height=10in width=10in;
proc sgpanel data=differences noautolegend;
styleattrs datacontrastcolors=(red green);
panelby comparison / rows=2 columns=5 novarname skipemptycells;
scatter x=estimate y=isim / xerrorlower=lower xerrorupper=upper group=Sign groupdisplay=cluster;
refline 0 / axis=x lineattrs=(color=black) label='No Difference' labelpos=min;
rowaxis label='Simulation';
colaxis label='Estimate of treatment difference';
title 'We live in a random world';
title2 italic 'Significant effects where there are none';
run;