OPTIONS LS=75 NODATe;

/* Though we've seen this example several times, we'll now consider 
using simple linear regression techniques to test for a difference
in mean length by sex */

DATA spiders;
   DO sex = 'm','f';
      male=(sex='m');   /* indicator variable: 1 for males, 0 for females */
      INPUT sp_length @;
      OUTPUT;
   END;
   CARDS;
5.2  8.25
4.7  9.8
5.7  6.1
5.65  9
5.75  9.5
4.7  9.95
4.8  10.8
6.2  9.3
5.5  6.3
5.95  8.3
5.75  5.9
5.95  6.6
5.4  8.75
5.65  8.35
5.9  7.05
7.5  7.05
5.2  7.55
6.2  7
5.85  8.7
7  8.3
6.45  8.45
6.35  8.1
5.85  7.8
5.75  8
6.1  7.95
6.55  7.55
6.95  9.1
6.8  8
6.35  7.5
5.8  9.6
;
RUN;

/*
Consider a t-test.  Compute the pooled variance, sp^2, by 
hand from the PROC MEANS output. 
*/
  
*PROC TTEST;   /* it is a good habit to specify the dataset */
PROC TTEST DATA=spiders;
   CLASS sex;
   VAR sp_length;
RUN;

/* 
Using the PROC TTEST output,
Find the estimated difference of population mean lengths
(females-males).  Find a confidence interval for this
difference and a pvalue that it is zero.
*/


/* 
Uncomment the PROC REG code to carry out statistical
inference that is equivalent to the t-test using PROC REG.  
The regression model has one predictor variable "male"
which is just an 0-1 indicator for males.
*/

/*
PROC REG DATA=spiders;
   MODEL sp_length=male;
   PLOT RESIDUAL.*PREDICTED.;
RUN;
*/
/*
Using the PROC REG output,
Find the estimated difference of population mean lengths
(females-males).  Find a confidence interval for this
difference and a pvalue that it is zero.
*/

/* 
Note evidence of inhomogeneity of variance from both
the PROC REG plot and the F-TEST from PROC TTEST
*/

DATA spiders;
   SET spiders;
   ly=LOG(sp_length);
   * Try the log transformation; 
run;

/*
PROC TTEST DATA=spiders;
   TITLE "log-transformed spiderlengths";
   CLASS sex;
   VAR ly;
RUN;

PROC REG DATA=spiders;
   TITLE "log-transformed spiderlengths";
   MODEL ly=male;
   PLOT RESIDUAL.*PREDICTED.;
RUN;
*/