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. ([email protected])

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