Stats 3520
                   Random Effects Example: Single Factor 
 
 A university admissions office wishes to study the results of the interview
ratings of prospective students by its staff members. Five staff members are
selected at random and four prospective students are assigned randomly to
each. The results are below:


                             Staff Members

                           A   B   C   D  E
                     
		          86  67  57  83  85
		          75  86  74  80  84
		          94  90  71  96  92
		          86  76  55  99  91

 Is there evidence of a difference among the average rating given by staff
members?

 Since the staff members are selected randomly from all staff members, a
random effects model is appropriate (we want to draw conclusions about all
staff members, not just the 5 used in the design).


##############################################

title 'Random Effect, Single Factor: Interview Ratings';

options linesize=79;

data interview;
   infile 'random.dat';

input Member Rating;

PROC PRINT;

PROC GLM;
    CLASS Member;
    MODEL Rating = Member;
    RANDOM Member/test;

RUN;

                Random Effect, Single Factor: Interview Ratings               

                            Obs    Member    Rating

                              1       1        86  
                              2       2        67  
                              3       3        57  
                              4       4        83  
                              5       5        85  
                              6       1        75  
                              7       2        86  
                              8       3        74  
                              9       4        80  
                             10       5        84  
                             11       1        94  
                             12       2        90  
                             13       3        71  
                             14       4        96  
                             15       5        92  
                             16       1        86  
                             17       2        76  
                             18       3        55  
                             19       4        99  
                             20       5        91  

                Random Effect, Single Factor: Interview Ratings               

                               The GLM Procedure

                           Class Level Information
 
                      Class         Levels    Values

                      Member             5    1 2 3 4 5 


                         Number of observations    20
                Random Effect, Single Factor: Interview Ratings               

                               The GLM Procedure
 
Dependent Variable: Rating   

                                      Sum of
Source                     DF        Squares    Mean Square   F Value   Pr > F

Model                       4    1683.300000     420.825000      5.75   0.0052

Error                      15    1097.250000      73.150000                   

Corrected Total            19    2780.550000                                  


              R-Square     Coeff Var      Root MSE    Rating Mean

              0.605384      10.51356      8.552777       81.35000


Source                     DF      Type I SS    Mean Square   F Value   Pr > F

Member                      4    1683.300000     420.825000      5.75   0.0052


Source                     DF    Type III SS    Mean Square   F Value   Pr > F

Member                      4    1683.300000     420.825000      5.75   0.0052

                Random Effect, Single Factor: Interview Ratings               

                               The GLM Procedure

  Source                  Type III Expected Mean Square

  Member                  Var(Error) + 4 Var(Member)                        

                Random Effect, Single Factor: Interview Ratings               

                               The GLM Procedure
           Tests of Hypotheses for Random Model Analysis of Variance
 
Dependent Variable: Rating   

Source                     DF    Type III SS    Mean Square   F Value   Pr > F

Member                      4    1683.300000     420.825000      5.75   0.0052

Error: MS(Error)           15    1097.250000      73.150000