/* Monte Carlo study of the one-way ANOVA 
   check the violations of the assumptions
	1. two independent samples 
	2. normal distributions
	3. equal variance?
*/

/* Macro Variables used to initialize the simulation */

* Group 1;
%let mean1 = 73;
%let stdev1 = 2.5;
%let n1 = 30;
%let dist1 = 'normal';

* Group 2;
%let mean2 = 72;
%let stdev2 = 2.5;
%let n2 = 30;
%let dist2 = 'normal';

* Group 3;
%let mean3 = 64;
%let stdev3 = 2;
%let n3 = 30;
%let dist3 = 'normal';

data normal1;
	do i=1 to &n1; drop i;
	x = rand(&dist1, &mean1, &stdev1);
	samp = 'A';
	output normal1;
end;

*proc print data=normal1;
*run;

data normal2;
	do i=1 to &n2; drop i;
	x = rand(&dist2, &mean2, &stdev2);
	samp = 'B';
	output normal2;
end;

*proc print data=normal2;
*run;

data normal3;
	do i=1 to &n3; drop i;
	x = rand(&dist3, &mean3, &stdev3);
	samp = 'C';
	output normal3;
end;

*proc print data=normal3;
*run;

* merge the data into one dataset with the same variables;
data normal;
	set normal1 normal2 normal3;
run;

*proc print data=normal;
*run;

proc univariate;
	by samp;
run;

proc boxplot data=normal;
	plot x*samp / boxstyle=schematic boxwidth=15;
run;

proc anova data=normal;
	class samp;
	model x = samp;
	means samp / SNK SCHEFFE ALPHA=0.1;
run;