Hypotheses Testing for two groups given a specific independent value

[JUMMY]

How do I test that xx scores are the same for the UGA and USC students with a xxx of 3.00 given the data below?

data have;
input university $ xxx xx@@;
datalines;

UGA 2.1 440 UGA 2.2 330 UGA 2.2 460 UGA 2.3 460 UGA 2.4 480 
UGA 2.6 510 UGA 3.3 560 UGA 3.4 670 UGA 3.5 630 UGA 3.6 680 
UNC 2.4 470 UNC 2.7 650 UNC 2.8 550 UNC 2.9 600 UNC 3.1 660 
UNC 3.2 670 UNC 3.4 690 UNC 3.5 690 UNC 3.5 730 UNC 3.5 760 
USC 2.2 430 USC 2.3 440 USC 2.4 480 USC 2.5 480 USC 2.9 570 
USC 3.0 510 USC 3.2 580 USC 3.5 630 USC 3.6 770 USC 3.9 760 
;

proc print;
run;

[Reeza]

Use an ESTIMATE statement within the PROC GLM.

[PGStats]

Use the AT option in the LSMEANS statement (available in many procs):

proc glm data=have;
class university;
model xx = xxx | university;
lsmeans university / at xxx=3 pdiff;
run;

                                 The GLM Procedure
                            Least Squares Means at xxx=3

                                                       LSMEAN
                       university       xx LSMEAN      Number

                       UGA             562.411348           1
                       UNC             627.000000           2
                       USC             574.772370           3


                     Least Squares Means for effect university
                        Pr > |t| for H0: LSMean(i)=LSMean(j)

                               Dependent Variable: xx

                   i/j              1             2             3

                      1                      0.0040        0.5421
                      2        0.0040                      0.0133
                      3        0.5421        0.0133


NOTE: To ensure overall protection level, only probabilities associated with
      pre-planned comparisons should be used.

[JUMMY]

@PGStats, is there anyway I can use PROC REG to do this?

[PGStats]

Nothing simple. Proc reg is not meant for that.

[Reeza]

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@JUMMY wrote:
@PGStats, is there anyway I can use PROC REG to do this?

---

Why the fixation on PROC REG?

[JUMMY]

@Reeza, because that is what I am comfortable with at this point.

[PaigeMiller]

@JUMMY 

If you are going to do modeling in SAS, and you have categorical variables, then PROC GLM is a fundamental tool that you need to learn. It will make your life easier, and enable you to fit a very wide selection of models. And in this case @PGStats has provided the solution.

As you can see, no one wants you to create dummy variables for PROC REG.

[JUMMY]

@PGStats, based on the output above, how do we draw conclusions? I am not sure how PROC GLM works?

[PGStats]

The model fitted in the above analysis is an ANCOVA (analysis of covariance). It is covered in every textbook about analysis of variance. The analysis tests for a difference between groups (universities) after correction for a covariate (xxx). The results displayed in the lsmeans table indicate that there is no significant difference between UGA and USC xx scores when xxx=3. This is also evident on the graph.

[JUMMY]

@PGStats,and what would be the hypothesis test statement. That is, null and alternative statement?

[PGStats]

Quoting you @JUMMY , the null hypothesis would be:

"xx scores are the same for the UGA and USC students with a xxx of 3.00"