1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 70         
 71         /* sampvar.sas */
 72         title 'Sample variation method for selecting sample size';
 73         
 74         /* Suppose we are planning a 2x3x4 analysis of covariance,
 75         with two covariates, and factors named A, B and C. We
 76         are setting it up as a regression model, with one dummy
 77         variable for A, 2 dummy variables for B, and 3 for C.
 78         Interactions are represented by product terms, and there
 79         are 2 products for the AxB interaction, 3 for AxC, 6 for
 80         BxC, and 1*2*3 = 6 for AxBxC. The regression coefficients
 81         for these plus two for the covariates and one for the
 82         intercept give us p = 26. The null hypothesis is that of no
 83         BxC interaction, so s = 6. The "other effects in the
 84         model" for which we are "controlling" are represented
 85         by 2 covariates and 17 dummy variables and products of
 86         dummy variables. */
 87         
 88         proc iml;
 NOTE: IML Ready
 89              title2 'Find n given a';
 90              alpha = 0.05;
 90       !                     /* Significance level.                     */
 91              s = 6;
 91       !                     /* Numerator df = # Expl vars tested.      */
 92              p = 26;
 92       !                     /* There are p beta parameters.            */
 93              a = .10  ;
 93       !                     /* Proportion of remaining variation after */
 94                            /* controlling for all other variables.    */
 95            /* Initializing ... */
 95       !                            pval = 1;
 95       !                                      n = p;
 96            do until (pval <= alpha);
 97               n = n+1 ;
 98               F = (n-p)/s * a/(1-a);
 99               df2 = n-p;
 100              pval = 1-probf(F,s,df2);
 101           end;
 102           print "Required sample size is" n;
 103           quit;
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.02 seconds
       user cpu time       0.01 seconds
       system cpu time     0.01 seconds
       memory              2276.84k
       OS Memory           29604.00k
       Timestamp           04/01/2020 08:08:58 AM
       Step Count                        77  Switch Count  1
       Page Faults                       0
       Page Reclaims                     974
       Page Swaps                        0
       Voluntary Context Switches        7
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           8
       
 
 104        
 105        /* In the potato data, there are 3 potatoes per treatment
 106           combination in a temperature (2 levels) by Bacteria type
 107           (3 levels) by oxygen level (3 levels) design. What pro-
 108           portion of remaining variation is required for the
 109           main effect of bacteria type to be significant? */
 110        
 111        proc iml;
 NOTE: IML Ready
 112           title2 'Find a given n';
 113           alpha = 0.05;
 113      !                   /* Significance level.                */
 114           s = 2;
 114      !                   /* Numerator df = # Expl vars tested. */
 115           p = 18;
 115      !                   /* There are p beta parameters.       */
 116           n = 54  ;
 116      !                   /* Sample size                        */
 117        
 118           /* Initializing ... */
 118      !                            a = 0;
 118      !                                   df2 = n-p;
 119           do until (pval <= alpha);
 120              a = a + .001 ;
 121              F = (n-p)/s * a/(1-a);
 122              pval = 1-probf(F,s,df2);
 123             end;
 124             print "Required proportion of remaining variation is" a;
 125             quit;
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.01 seconds
       user cpu time       0.01 seconds
       system cpu time     0.00 seconds
       memory              587.25k
       OS Memory           29860.00k
       Timestamp           04/01/2020 08:08:58 AM
       Step Count                        78  Switch Count  1
       Page Faults                       0
       Page Reclaims                     164
       Page Swaps                        0
       Voluntary Context Switches        8
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           0
       
 
 126        
 127        
 128        
 129        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 140