*
chapter_14_table_5

For the hypothetical data contained in Table 14.4, Table 14.5 gives an 
appropriate and substantively interesting set of D variables. The D 
variables (rather than the raw data itself) is used because of the benefits 
and flexibility gained from analyzing the D variables directly (rather than
indirectly as we did with the Table 14.4 data). 

The results of the analysis when the D variables themselves are analyzed
can be obtained by making use of PROC GLM and PROC TTEST. Using PROC GLM 
with D variables for omnibus effects of the main effects and interaction 
requires separate PROC GLM statements with the extra specification
'MANOVA H =_ALL_'. The 'MANOVA H =_ALL_' tells SAS that we want to 
perform a MANOVA on the selected variables (here the D variables we 
defined) considering 'all' dependent variables simultaneously. If we
would have included all of the D variables in a single PROC GLM 
statement, we would have lost information about each of the main effects
and the interaction. Note that the reason we have not previously had
to specify 'MANOVA H =_ALL_' is because we specified that the variables
were repeated (as in the results from Table 14.1 and 14.4) and it was
thus unnecessary. 

Regarding the parameter estimates and confidence intervals for the 
D variables, because each D is analyzed with respect to only itself,
PROC TTEST can be used to obtain parameter estimates and 
confidence intervals. Note that the null hypothesis of interest here 
is that the population mean of the D variables is zero. 

Although we do not illustrate it here, forming other D variables and 
following the procedures outlined will lead to answers of other (potentially) 
interesting questions. For example, the 11th D variable of the chapter tests 
the difference between the eighth degree and the zeroth degree conditions when 
noise is present. Although we do not form and test such a D variable here, with 
the methods we have illustrated, such a D variable could easily be formed and 
analyzed. 
;

LIBNAME md 'd:\data files by type\sas data files\tables';
     Data c14t5;
       SET md.chapter_14_table_5;
Title 'Angle Main Effect';
PROC GLM;
MODEL d1 d2 = / NOUNI;
MANOVA H =_ALL_;
RUN;
Title 'Noise Main Effect';
PROC GLM;
MODEL d3 = / NOUNI;
MANOVA H =_ALL_;
RUN;
Title 'Interaction Main Effect';
PROC GLM;
MODEL d4 d5 = / NOUNI;
MANOVA H =_ALL_;
RUN;
Title 'Parameter Estimates and Confidence Intervals for D Variables';
PROC TTEST H0=0;
RUN;