NAME

Statistics::TTest - Perl module to perform T-test on 2 independent samples

SYNOPSIS

use Statistics::PointEstimation;
use Statistics::TTest;
my @r1=();
my @r2=();
my $rand;
       
 for($i=1;$i<=32;$i++) #generate a uniformly distributed sample with mean=5   
 {

         $rand=rand(10);
         push @r1,$rand;
         $rand=rand(10)-2;
         push @r2,$rand;
 }


my $ttest = new Statistics::TTest;  
$ttest->set_significance(90);
$ttest->load_data(\@r1,\@r2);  
$ttest->output_t_test();   
$ttest->set_significance(99);
$ttest->print_t_test();  #list out t-test related data
 
#the following thes same as calling output_t_test()
       my $s1=$ttest->{s1};  #sample 1  a Statistics::PointEstimation object
       my $s2=$ttest->{s2};  #sample 2  a Statistics::PointEstimation object
       print "*****************************************************\n\n";
       $s1->output_confidence_interval('1');
       print "*****************************************************\n\n";
       $s2->output_confidence_interval('2');
       print "*****************************************************\n\n";

       print "Comparison of these 2 independent samples.\n";
       print "\t F-statistic=",$ttest->f_statistic()," , cutoff F-statistic=",$ttest->f_cutoff(),
               " with alpha level=",$ttest->alpha*2," and  df =(",$ttest->df1,",",$ttest->df2,")\n"; 
       if($ttest->{equal_variance})
       { print "\tequal variance assumption is accepted(not rejected) since F-statistic < cutoff F-statistic\n";}
       else
       { print "\tequal variance assumption is  rejected since F-statistic > cutoff F-statistic\n";}

       print "\tdegree of freedom=",$ttest->df," , t-statistic=T=",$ttest->t_statistic," Prob >|T|=",$ttest->{t_prob},"\n";
       print "\tthe null hypothesis (the 2 samples have the same mean) is ",$ttest->null_hypothesis(),
                " since the alpha level is ",$ttest->alpha()*2,"\n";
       print "\tdifference of the mean=",$ttest->mean_difference(),", standard error=",$ttest->standard_error(),"\n";
       print "\t the estimate of the difference of the mean is ", $ttest->mean_difference()," +/- ",$ttest->delta(),"\n\t",
               " or (",$ttest->lower_clm()," to ",$ttest->upper_clm," ) with ",$ttest->significance," % of confidence\n"; 
 

DESCRIPTION

This is the Statistical T-Test module to compare 2 independent samples. It takes 2 array of point measures, compute the confidence intervals using the PointEstimation module (which is also included in this package) and use the T-statistic to test the null hypothesis. If the null hypothesis is rejected, the difference will be given as the lower_clm and upper_clm of the TTest object.

AUTHOR

Yun-Fang Juan , Yahoo! Inc. (yunfang@yahoo-inc.com)

SEE ALSO

Statistics::Descriptive Statistics::Distributions Statistics::PointEstimation