/* SAS example to analyze Nested Design */

/* these are the training-school data from class and Chapter 26 */

DATA trschool;
INPUT SCORE SCHOOL INSTRUCTOR OBS;
cards;
  25  1  1  1
  29  1  1  2
  14  1  2  1
  11  1  2  2
  11  2  1  1
   6  2  1  2
  22  2  2  1
  18  2  2  2
  17  3  1  1
  20  3  1  2
   5  3  2  1
   2  3  2  2
;
run;

/* We run PROC GLM with SCHOOL and INSTRUCTOR as the two factors listed */
/* in the CLASS statement. In the MODEL statement, we indicate that the */
/* levels of INSTRUCTOR are nested within the levels of SCHOOL with the */
/* INSTRUCTOR(SCHOOL) syntax for the second factor.                     */

PROC GLM data = trschool;
  CLASS SCHOOL INSTRUCTOR;
  MODEL SCORE = SCHOOL INSTRUCTOR(SCHOOL);
  OUTPUT OUT = pred  p=ybar r=resid;
run;

/* We see that the 3 schools differ in mean score (F* = 11.18, P-value = .0095) */
/* and that instructors within at least one school have different mean scores   */
/* (F* = 27.02, P-value = .0007).                                               */

/* ************************************************************************* */

/* To determine in WHICH schools the instructor effects are significant, we    */
/* further decompose the SSB(A) into SSB(A_1), SSB(A_2), and SSB(A_3).         */

PROC GLM data = trschool;
  BY SCHOOL;
  CLASS INSTRUCTOR;
  MODEL SCORE = INSTRUCTOR;
run;

/* Note SAS gives (over 3 pages) the following results:                              */
/* Atlanta school: MSB(A_1)=210.25 => F* = 210.25/7 = 30.0  (we divide this by hand) */
/* Chicago school: MSB(A_2)=132.25 => F* = 132.25/7 = 18.9  (we divide this by hand) */
/* San Fran school: MSB(A_3)=225.0 => F* = 225/7 = 32.14    (we divide this by hand) */
/* Note that each of these is divided by the original MSE of 7.                      */

/* Since F(0.95,1,6) = 5.99, then: At the 0.05 level, instructors within the     */
/* Atlanta school have different mean scores; at the 0.05 level, instructors     */
/* within the Chicago school have different mean scores; and at the 0.05         */
/* level, instructors within the San Francisco school have different mean        */
/* scores.  The FAMILY significance level for this SET of tests is at most 0.15. */

/* ************************************************************************** */

/* Some Residual Plots to Check the Standard Model Assumptions: */

/* Residual Plots and Q-Q plots: */

goptions reset=all;

symbol1 v=circle l=32  c = black;
PROC GPLOT data=pred;
 PLOT resid*ybar/vref=0;    /* Residuals Plotted vs. Fitted Values */
 PLOT resid*SCHOOL/vref=0;   /* Residuals Plotted for each SCHOOL Level */
run;
PROC UNIVARIATE noprint data=pred;
  QQPLOT resid / normal;    /* Normal Q-Q Plot of Residuals */
run;