194 lines
5.5 KiB
Plaintext
194 lines
5.5 KiB
Plaintext
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{{alias}}( x, y[, options] )
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Computes a two-sample Student's t test.
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By default, the function performs a two-sample t-test for the null
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hypothesis that the data in arrays or typed arrays `x` and `y` is
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independently drawn from normal distributions with equal means.
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The returned object comes with a `.print()` method which when invoked will
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print a formatted output of the results of the hypothesis test.
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Parameters
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----------
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x: Array<number>
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First data array.
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y: Array<number>
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Second data array.
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options: Object (optional)
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Options.
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options.alpha: number (optional)
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Number in the interval `[0,1]` giving the significance level of the
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hypothesis test. Default: `0.05`.
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options.alternative: string (optional)
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Either `two-sided`, `less` or `greater`. Indicates whether the
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alternative hypothesis is that `x` has a larger mean than `y`
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(`greater`), `x` has a smaller mean than `y` (`less`) or the means are
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the same (`two-sided`). Default: `'two-sided'`.
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options.difference: number (optional)
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Number denoting the difference in means under the null hypothesis.
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Default: `0`.
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options.variance: string (optional)
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String indicating if the test should be conducted under the assumption
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that the unknown variances of the normal distributions are `equal` or
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`unequal`. As a default choice, the function carries out the Welch test
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(using the Satterthwaite approximation for the degrees of freedom),
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which does not have the requirement that the variances of the underlying
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distributions are equal. If the equal variances assumption seems
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warranted, set the option to `equal`. Default: `unequal`.
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Returns
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-------
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out: Object
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Test result object.
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out.alpha: number
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Used significance level.
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out.rejected: boolean
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Test decision.
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out.pValue: number
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p-value of the test.
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out.statistic: number
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Value of test statistic.
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out.ci: Array<number>
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1-alpha confidence interval for the mean.
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out.nullValue: number
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Assumed difference in means under H0.
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out.xmean: number
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Sample mean of `x`.
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out.ymean: number
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Sample mean of `y`.
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out.alternative: string
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Alternative hypothesis (`two-sided`, `less` or `greater`).
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out.df: number
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Degrees of freedom.
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out.method: string
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Name of test.
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out.print: Function
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Function to print formatted output.
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Examples
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--------
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// Student's sleep data:
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> var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
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> var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
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> var out = {{alias}}( x, y )
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{
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rejected: false,
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pValue: ~0.079,
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statistic: ~-1.861,
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ci: [ ~-3.365, ~0.205 ],
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// ...
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}
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// Print table output:
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> var table = out.print()
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Welch two-sample t-test
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Alternative hypothesis: True difference in means is not equal to 0
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pValue: 0.0794
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statistic: -1.8608
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95% confidence interval: [-3.3655,0.2055]
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Test Decision: Fail to reject null in favor of alternative at 5%
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significance level
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// Choose a different significance level than `0.05`:
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> out = {{alias}}( x, y, { 'alpha': 0.1 });
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> table = out.print()
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Welch two-sample t-test
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Alternative hypothesis: True difference in means is not equal to 0
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pValue: 0.0794
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statistic: -1.8608
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90% confidence interval: [-3.0534,-0.1066]
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Test Decision: Reject null in favor of alternative at 10% significance level
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// Perform one-sided tests:
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> out = {{alias}}( x, y, { 'alternative': 'less' });
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> table = out.print()
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Welch two-sample t-test
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Alternative hypothesis: True difference in means is less than 0
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pValue: 0.0397
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statistic: -1.8608
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df: 17.7765
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95% confidence interval: [-Infinity,-0.1066]
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Test Decision: Reject null in favor of alternative at 5% significance level
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> out = {{alias}}( x, y, { 'alternative': 'greater' });
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> table = out.print()
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Welch two-sample t-test
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Alternative hypothesis: True difference in means is greater than 0
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pValue: 0.9603
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statistic: -1.8608
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df: 17.7765
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95% confidence interval: [-3.0534,Infinity]
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Test Decision: Fail to reject null in favor of alternative at 5%
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significance level
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// Run tests with equal variances assumption:
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> x = [ 2, 3, 1, 4 ];
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> y = [ 1, 2, 3, 1, 2, 5, 3, 4 ];
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> out = {{alias}}( x, y, { 'variance': 'equal' });
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> table = out.print()
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Two-sample t-test
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Alternative hypothesis: True difference in means is not equal to 0
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pValue: 0.8848
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statistic: -0.1486
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df: 10
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95% confidence interval: [-1.9996,1.7496]
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Test Decision: Fail to reject null in favor of alternative at 5%
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significance level
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// Test for a difference in means besides zero:
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> var rnorm = {{alias:@stdlib/random/base/normal}}.factory({ 'seed': 372 });
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> x = new Array( 100 );
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> for ( i = 0; i < x.length; i++ ) {
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... x[ i ] = rnorm( 2.0, 3.0 );
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... }
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> y = new Array( 100 );
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> for ( i = 0; i < x.length; i++ ) {
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... y[ i ] = rnorm( 1.0, 3.0 );
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... }
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> out = {{alias}}( x, y, { 'difference': 1.0, 'variance': 'equal' })
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{
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rejected: false,
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pValue: ~0.642,
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statistic: ~-0.466,
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ci: [ ~-0.0455, ~1.646 ],
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// ...
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}
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See Also
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--------
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