Student's tTest
Twosample Student's tTest.
Installation
npm install @stdlib/statsttest2
Usage
var ttest2 = require( '@stdlib/statsttest2' );
ttest2( x, y[, opts] )
By default, the function performs a twosample ttest for the null hypothesis that the data in arrays or typed arrays x
and y
is independently drawn from normal distributions with equal means.
// Student's sleep data:
var x = [ 0.7, 1.6, 0.2, 1.2, 0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
var y = [ 1.9, 0.8, 1.1, 0.1, 0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
var out = ttest2( x, y );
/* e.g., returns
{
'rejected': false,
'pValue': ~0.079,
'statistic': ~1.861,
'ci': [ ~3.365, ~0.205 ],
// ...
}
*/
The returned object comes with a .print()
method which when invoked will print a formatted output of the results of the hypothesis test. print
accepts a digits
option that controls the number of decimal digits displayed for the outputs and a decision
option, which when set to false
will hide the test decision.
console.log( out.print() );
/* e.g., =>
Welch twosample ttest
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.0794
statistic: 1.8608
95% confidence interval: [3.3655,0.2055]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
The function accepts the following options
:

alpha:
number
in the interval[0,1]
giving the significance level of the hypothesis test. Default:0.05
. 
alternative: Either
twosided
,less
orgreater
. Indicates whether the alternative hypothesis is thatx
has a larger mean thany
(greater
),x
has a smaller mean thany
(less
) or the means are the same (twosided
). Default:twosided
. 
difference:
number
denoting the difference in means under the null hypothesis. Default:0
. 
variance:
string
indicating if the test should be conducted under the assumption that the unknown variances of the normal distributions areequal
orunequal
. Default:unequal
.
By default, the hypothesis test is carried out at a significance level of 0.05
. To choose a different significance level, set the alpha
option.
var x = [ 0.7, 1.6, 0.2, 1.2, 0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
var y = [ 1.9, 0.8, 1.1, 0.1, 0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
var out = ttest2( x, y, {
'alpha': 0.1
});
var table = out.print();
/* e.g., returns
Welch twosample ttest
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.0794
statistic: 1.8608
90% confidence interval: [3.0534,0.1066]
Test Decision: Reject null in favor of alternative at 10% significance level
*/
By default, a twosided test is performed. To perform either of the onesided tests, set the alternative
option to less
or greater
.
// Student's sleep data:
var x = [ 0.7, 1.6, 0.2, 1.2, 0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
var y = [ 1.9, 0.8, 1.1, 0.1, 0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
var out = ttest2( x, y, {
'alternative': 'less'
});
var table = out.print();
/* e.g., returns
Welch twosample ttest
Alternative hypothesis: True difference in means is less than 0
pValue: 0.0397
statistic: 1.8608
df: 17.7765
95% confidence interval: [Infinity,0.1066]
Test Decision: Reject null in favor of alternative at 5% significance level
*/
out = ttest2( x, y, {
'alternative': 'greater'
});
table = out.print();
/* e.g., returns
Welch twosample ttest
Alternative hypothesis: True difference in means is greater than 0
pValue: 0.9603
statistic: 1.8608
df: 17.7765
95% confidence interval: [3.0534,Infinity]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
As a default choice, the ttest2
function carries out the Welch test (using the Satterthwaite approximation for the degrees of freedom), which does not have the requirement that the variances of the underlying distributions are equal. If the equal variances assumption seems warranted, set the variance
option to equal
.
var x = [ 2, 3, 1, 4 ];
var y = [ 1, 2, 3, 1, 2, 5, 3, 4 ];
var out = ttest2( x, y, {
'variance': 'equal'
});
var table = out.print();
/* e.g., returns
Twosample ttest
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.8848
statistic: 0.1486
df: 10
95% confidence interval: [1.9996,1.7496]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
To test whether the difference in the population means is equal to some other value than 0
, set the difference
option.
var normal = require( '@stdlib/randombasenormal' ).factory;
var rnorm = normal({
'seed': 372
});
var x = [];
var i;
for ( i = 0; i < x.length; i++ ) {
x.push( rnorm( 2.0, 3.0 ) );
}
var y = [];
for ( i = 0; i < x.length; i++ ) {
y.push( rnorm( 1.0, 3.0 ) );
}
var out = ttest2( x, y, {
'difference': 1.0,
'variance': 'equal'
});
/* e.g., returns
{
'rejected': false,
'pValue': ~0.642,
'statistic': ~0.466,
'ci': [ ~0.0455, ~1.646 ],
// ...
}
*/
var table = out.print();
/* e.g., returns
Twosample ttest
Alternative hypothesis: True difference in means is not equal to 1
pValue: 0.6419
statistic: 0.4657
df: 198
95% confidence interval: [0.0455,1.646]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
Examples
var incrspace = require( '@stdlib/arraybaseincrspace' );
var ttest2 = require( '@stdlib/statsttest2' );
var a = incrspace( 1, 11, 1 );
var b = incrspace( 7, 21, 1 );
var out = ttest2( a, b );
var table = out.print();
/* e.g., returns
Welch twosample ttest
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0
statistic: 5.4349
95% confidence interval: [11.0528,4.9472]
Test Decision: Reject null in favor of alternative at 5% significance level
*/
See Also

@stdlib/stats/ttest
: onesample and paired Student's tTest.
Notice
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