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TTest(3)	      User Contributed Perl Documentation	      TTest(3)

	Statistics::TTest - Perl module	to perform T-test on 2 independent samples
	Statistics::TTest::Sufficient -	Perl module to perfrom T-Test on 2 indepdent samples using sufficient statistics

	#example for Statistics::TTest
	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

		 push @r1,$rand;
		 push @r2,$rand;

	my $ttest = new	Statistics::TTest;
	$ttest->print_t_test();	 #list out t-test related data

	#the following thes same as calling output_t_test() (you can check if $ttest->{valid}==1 to check if the data is valid.)
	my $s1=$ttest->{s1};  #sample 1	 a Statistics::PointEstimation object
	my $s2=$ttest->{s2};  #sample 2	 a Statistics::PointEstimation object
	print "*****************************************************\n\n";
	print "*****************************************************\n\n";
	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";
	{ print	"\tequal variance assumption is	accepted(not rejected) since F-statistic < cutoff F-statistic\n";}
	{ 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";

	#example for Statistics::TTest::Sufficient
	use Statistics::PointEstimation;
	use Statistics::TTest;

	my %sample1=(
	       'count' =>30,
	       'mean' =>3.98,
	       'variance' =>2.63

	my %sample2=(

	my $ttest = new	Statistics::TTest::Sufficient;

	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.

	This module is a subclass of Statistics::TTest.	Instead	of taking the real data	points as the input,
	it will	compute	the confidence intervals based on the sufficient statistics and	the sample size	inputted.
	To use this module, you	need to	pass the sample	size, the sample mean ,	and the	sample variance	into the load_data()
	function. The output will be exactly the same as the Statistics::TTest Module.

       Yun-Fang	Juan , Yahoo! Inc.  (

       Statistics::Descriptive Statistics::Distributions

perl v5.24.1			  2003-07-24			      TTest(3)


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