# 2.13.2.2 Hypothesis Testing

Origin/OriginPro supports the following set of X-Functions for hypothesis testing:

Name Brief Description
rowttest2 (Pro Only) Perform a two-sample t-test on rows.
ttest1 Compare the sample mean to the hypothesized population mean.
ttest2 Compare the sample means of two samples.
ttestpair Determine whether two sample means are equal in the case that they are matched.
vartest1
(Pro Only)
Determine whether the sample variance is equal to a specified value.
vartest2
(Pro Only)
Determine whether two sample variances are equal.

For a full description of these X-functions, including input and output arguments, please see the Hypothesis Testing.

## One-Sample T-Test

If you need to know whether the mean value of a sample is consistent with a hypothetical value for a given confidence level, consider using the one-sample T-test. Note that this test assumes that the sample is a normally distributed population. Before we apply the one-sample T-test, we should verify this assumption.

//Import a sample data
newbook;
fname$= system.path.program$ + "Samples\Statistics\diameter.dat";
impasc;

//Normality test
swtest irng:=col(a) prob:=p1;
if (p1 < 0.05)
{
type "The sample is not likely to follow a normal distribution."
}
else
{
// Test whether the mean is 21
ttest1 irng:=col(1) mean:=21 tail:=two prob:=p2;
if (p2 < 0.05) {
type "At the 0.05 level, the population mean is";
type "significantly different from 21."; }
else {
type "At the 0.05 level, the population mean is NOT";
type "significantly different from 21."; }
}

## Two-Sample T-Test

The ttest2 X-Function is provided for performing two-sample t-test. The example below shows how to use it and print the results.

// Import sample data
newbook;
string fpath$= "Samples\Statistics\time_raw.dat"; string fname$ = system.path.program$+ fpath$;
impAsc;

// Perform two-sample t-test on two columns
// Sample variance is not assumed to be equal
ttest2 irng:=(col(1), col(2)) equal:=0;

// Type some results
type "Value of t-test statistic is $(ttest2.stat)"; type "Degree of freedom is$(ttest2.df)";
type "P-value is $(ttest2.prob)"; type "Conf. levels in 95% is ($(ttest2.lcl), $(ttest2.ucl))"; The rowttest2 X-Function can be used to perform a two-sample T-test on rows. The following example demonstrates how to compute the corresponding probability value for each row: // Import sample data newbook; string fpath$ = "Samples\Statistics\ANOVA\Two-Way_ANOVA_raw.dat";
fname$= system.path.program$ + fpath$; impasc; // Two-sample T-test on a row rowttest2 irng1:=(col(a):col(c)) irng2:=(col(d):col(f)) tail:=two prob:=<new>; ## Pair-Sample T-Test Origin provides the ttestpair X-Function for pair-sample t-test analysis, so to determine whether the means of two same-sized and dependent samples from a normal distribution are equal or not, and calculates the confidence interval for the difference between the means. The example below first imports a data file, and then perform pair-sample t-test, and then output the related results. // Import sample data newbook; string fpath$ = "Samples\Statistics\abrasion_raw.dat";
string fname$= system.path.program$ + fpath$; impasc; // Perform pair-sample t-test one two columns // Hypothetical means difference is 0.5 // And Tail is upper tailed ttestpair irng:=(col(1), col(2)) mdiff:=0.5 tail:=upper; // Type the results type "Value of paired-sample t-test statistic is$(ttestpair.stat)";
type "Degree of freedom for the paired-sample t-test is $(ttestpair.df)"; type "P-value is$(ttestpair.prob)";
type "Conf. levels in 95% is ($(ttestpair.lcl),$(ttestpair.ucl))";

## One-Sample Test for Variance

X-Function vartest1 is used to perform a chi-squared variance test, so to determine whether the sample from a normal distribution could have a given hypothetical vaiance value. The following example will perform one-sample test for variance, and output the P-value.

// Import sample data
newbook;
string fpath$= "Samples\Statistics\vartest1.dat"; string fname$ = system.path.program$+ fpath$;
impasc;

// Perform F-test
// Tail is two tailed
// Test variance is 2.0
// P-value stored in variable p
vartest1 irng:=col(1) var:=2.0 tail:=two prob:=p;

// Ouput P-value
p = ;

## Two-Sample Test for Variance (F-Test)

F-test, also called two-sample test for variance, is performed by using vartest2 X-Function.

// Import sample data
newbook;
string fpath$= "Samples\Statistics\time_raw.dat"; string fname$ = system.path.program$+ fpath$;
impasc;

// Perform F-test
// And Tail is upper tailed
vartest2 irng:=(col(1), col(2)) tail:=upper;

// Output the result tree
vartest2.=;