/* Using PROC POWER to calculate power or sample size in the one-way ANOVA */

/* Suppose r=4, alpha = 0.05, and the required power for the F-test is 0.80. */

/* Suppose we wish to detect when the four treatment means differ by at least 10 (max - min = 10). */
/* And we believe the standard deviation is 5. */

PROC POWER ;
  onewayanova
  groupmeans = 10 | 15 | 15 | 20 
  stddev = 5
  alpha = 0.05
  npergroup = .
  power = .80;
run; 

/* How does the power/sample size change if the treatment population means are more evenly spead out? */

PROC POWER ;
  onewayanova
  groupmeans = 10 | 13.3 | 16.7 | 20 
  stddev = 5
  alpha = 0.05
  npergroup = .
  power = .80;
run; 

/* We can also specify the sample size we have and determine the power of the F-test we will get. */

PROC POWER ;
  onewayanova
  groupmeans = 10 | 15 | 15 | 20 
  stddev = 5
  alpha = 0.05
  npergroup = 10
  power = . ;
run; 

PROC POWER ;
  onewayanova
  groupmeans = 10 | 13.3 | 16.7 | 20 
  stddev = 5
  alpha = 0.05
  npergroup = 10
  power = . ;
run; 

/* We can see the relationship between power and sample size by plotting the power for a variety of sample sizes: */

PROC POWER ;
  onewayanova
  groupmeans = 10 | 15 | 15 | 20 
  stddev = 5
  alpha = 0.05
  npergroup = 2 to 20 by 1
  power = .;
  plot  x=n min=2 max=20;
run;