SAS Programs for Selecting Sample Size
/************************** sampvar1.sas **************************/
/* Finds n needed for significance, for a given proportion of */
/* remaining variation */
/*******************************************************************/
options linesize = 79 pagesize = 200;
data explvar; /* Can replace alpha, s, p, and a below. */
alpha = 0.05; /* Significance level. */
s = 6; /* Numerator df = # IVs being tested. */
p = 26; /* There are p beta parameters. */
a = .10 ; /* Proportion of remaining variation after */
/* controlling for all other variables. */
/* Initializing ... */ pval = 1; n = p+1;
do until (pval <= alpha);
F = (n-p)/s * a/(1-a);
df2 = n-p;
pval = 1-probf(F,s,df2);
n = n+1 ;
end;
/* When finished, n is one too many */
n = n-1; F = (n-p)/s * a/(1-a); df2 = n-p;
pval = 1-probf(F,s,df2);
put ' *********************************************************';
put ' ';
put ' For a multiple regression model with ' p 'betas, ';
put ' testing ' s ' variables controlling for the others,';
put ' a sample size of ' n 'is needed for significance at the';
put ' alpha = ' alpha 'level, when the effect explains a = ' a ;
put ' of the remaining variation after allowing for all other ';
put ' variables in the model. ';
put ' F = ' F ',df = (' s ',' df2 '), p = ' pval;
put ' ';
put ' *********************************************************';
/************************** sampvar2.sas ****************************/
/* Finds proportion of remaining variation needed for significance, */
/* given sample size n */
/*********************************************************************/
options linesize = 79 pagesize = 200;
data explvar; /* Replace alpha, s, p, and a below. */
alpha = 0.05; /* Significance level. */
s = 6; /* Numerator df = # IVs being tested. */
p = 26; /* There are p beta parameters. */
n = 120 ; /* Sample size */
/* Initializing ... */ pval = 1; a = 0; df2 = n-p;
do until (pval <= alpha);
F = (n-p)/s * a/(1-a);
pval = 1-probf(F,s,df2);
a = a + .001 ;
end;
/* When finished, a is .001 too much */
a = a-.001; F = (n-p)/s * a/(1-a); pval = 1-probf(F,s,df2);
put ' ******************************************************';
put ' ';
put ' For a multiple regression model with ' p 'betas, ';
put ' testing ' s ' variables at significance level ';
put ' alpha = ' alpha ' controlling for the other variables,';
put ' and a sample size of ' n', the variables need to explain';
put ' a = ' a ' of the remaining variation to be significant.';
put ' F = ' F ', df = (' s ',' df2 '), p = ' pval;
put ' ';
put ' *******************************************************';
/*********************** popvar.sas *****************************/
options linesize = 79 pagesize = 200;
data fpower; /* Replace alpha, s, p, and wantpow below */
alpha = 0.05; /* Significance level */
s = 6; /* Numerator df = # IVs being tested */
p = 26; /* There are p beta parameters */
a = .10 ; /* Effect size */
wantpow = .80; /* Find n to yield this power. */
power = 0; n = p+1; oneminus = 1-alpha; /* Initializing ... */
do until (power >= wantpow);
ncp = (n-p)*a/(1-a);
df2 = n-p;
power = 1-probf(finv(oneminus,s,df2),s,df2,ncp);
n = n+1 ;
end;
n = n-1;
put ' *********************************************************';
put ' ';
put ' For a multiple regression model with ' p 'betas, ';
put ' testing ' s 'independent variables using alpha = ' alpha ',';
put ' a sample size of ' n 'is needed';
put ' in order to have probability ' wantpow 'of rejecting H0';
put ' for an effect of size a = ' a ;
put ' ';
put ' *********************************************************';