Usage

1var ttest2 = require( '@stdlib/stats-ttest2' );

ttest2( x, y[, opts] )

By default, the function performs a two-sample t-test for the null hypothesis that the data in arrays or typed arrays x and y is independently drawn from normal distributions with equal means.

1// Student's sleep data:
2var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
3var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
4
5var out = ttest2( x, y );
6/* e.g., returns
7    {
8        'rejected': false,
9        'pValue': ~0.079,
10        'statistic': ~-1.861,
11        'ci': [ ~-3.365, ~0.205 ],
12        // ...
13    }
14*/

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.

1console.log( out.print() );
2/* e.g., =>
3    Welch two-sample t-test
4
5    Alternative hypothesis: True difference in means is not equal to 0
6
7        pValue: 0.0794
8        statistic: -1.8608
9        95% confidence interval: [-3.3655,0.2055]
10
11    Test Decision: Fail to reject null in favor of alternative at 5% significance level
12*/

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 two-sided, less or greater. Indicates whether the alternative hypothesis is that x has a larger mean than y (greater), x has a smaller mean than y (less) or the means are the same (two-sided). Default: two-sided.
• 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 are equal or unequal. 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.

1var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
2var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
3
4var out = ttest2( x, y, {
5    'alpha': 0.1
6});
7var table = out.print();
8/* e.g., returns
9    Welch two-sample t-test
10
11    Alternative hypothesis: True difference in means is not equal to 0
12
13        pValue: 0.0794
14        statistic: -1.8608
15        90% confidence interval: [-3.0534,-0.1066]
16
17    Test Decision: Reject null in favor of alternative at 10% significance level
18*/

By default, a two-sided test is performed. To perform either of the one-sided tests, set the alternative option to less or greater.

1// Student's sleep data:
2var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
3var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
4
5var out = ttest2( x, y, {
6    'alternative': 'less'
7});
8var table = out.print();
9/* e.g., returns
10    Welch two-sample t-test
11
12    Alternative hypothesis: True difference in means is less than 0
13
14        pValue: 0.0397
15        statistic: -1.8608
16        df: 17.7765
17        95% confidence interval: [-Infinity,-0.1066]
18
19    Test Decision: Reject null in favor of alternative at 5% significance level
20*/
21
22out = ttest2( x, y, {
23    'alternative': 'greater'
24});
25table = out.print();
26/* e.g., returns
27    Welch two-sample t-test
28
29    Alternative hypothesis: True difference in means is greater than 0
30
31        pValue: 0.9603
32        statistic: -1.8608
33        df: 17.7765
34        95% confidence interval: [-3.0534,Infinity]
35
36    Test Decision: Fail to reject null in favor of alternative at 5% significance level
37*/

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.

1var x = [ 2, 3, 1, 4 ];
2var y = [ 1, 2, 3, 1, 2, 5, 3, 4 ];
3
4var out = ttest2( x, y, {
5    'variance': 'equal'
6});
7var table = out.print();
8/* e.g., returns
9    Two-sample t-test
10
11    Alternative hypothesis: True difference in means is not equal to 0
12
13        pValue: 0.8848
14        statistic: -0.1486
15        df: 10
16        95% confidence interval: [-1.9996,1.7496]
17
18    Test Decision: Fail to reject null in favor of alternative at 5% significance level
19*/

To test whether the difference in the population means is equal to some other value than 0, set the difference option.

1var normal = require( '@stdlib/random-base-normal' ).factory;
2
3var rnorm = normal({
4    'seed': 372
5});
6
7var x = [];
8var i;
9for ( i = 0; i < x.length; i++ ) {
10    x.push( rnorm( 2.0, 3.0 ) );
11}
12
13var y = [];
14for ( i = 0; i < x.length; i++ ) {
15    y.push( rnorm( 1.0, 3.0 ) );
16}
17
18var out = ttest2( x, y, {
19    'difference': 1.0,
20    'variance': 'equal'
21});
22/* e.g., returns
23    {
24        'rejected': false,
25        'pValue': ~0.642,
26        'statistic': ~-0.466,
27        'ci': [ ~-0.0455, ~1.646 ],
28        // ...
29    }
30*/
31
32var table = out.print();
33/* e.g., returns
34    Two-sample t-test
35
36    Alternative hypothesis: True difference in means is not equal to 1
37
38        pValue: 0.6419
39        statistic: -0.4657
40        df: 198
41        95% confidence interval: [-0.0455,1.646]
42
43    Test Decision: Fail to reject null in favor of alternative at 5% significance level
44*/