{{alias}}( x, y, sigmax, sigmay[, options] ) Computes a two-sample z-test. By default, the function performs a two-sample z-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 and known standard deviations `sigmax` and `sigmay`. The returned object comes with a `.print()` method which when invoked will print a formatted output of the results of the hypothesis test. Parameters ---------- x: Array First data array. y: Array Second data array. sigmax: number Known standard deviation of first group. sigmay: number Known standard deviation of second group. options: Object (optional) Options. options.alpha: number (optional) Number in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`. options.alternative: string (optional) 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'`. options.difference: number (optional) Number denoting the difference in means under the null hypothesis. Default: `0`. Returns ------- out: Object Test result object. out.alpha: number Used significance level. out.rejected: boolean Test decision. out.pValue: number p-value of the test. out.statistic: number Value of test statistic. out.ci: Array 1-alpha confidence interval for the mean. out.nullValue: number Assumed difference in means under H0. out.xmean: number Sample mean of `x`. out.ymean: number Sample mean of `y`. out.alternative: string Alternative hypothesis (`two-sided`, `less` or `greater`). out.method: string Name of test. out.print: Function Function to print formatted output. Examples -------- // Drawn from Normal(0,2): > var x = [ -0.21, 0.14, 1.65, 2.11, -1.86, -0.29, 1.48, 0.81, 0.86, 1.04 ]; // Drawn from Normal(1,2): > var y = [ -1.53, -2.93, 2.34, -1.15, 2.7, -0.12, 4.22, 1.66, 3.43, 4.66 ]; > var out = {{alias}}( x, y, 2.0, 2.0 ) { alpha: 0.05, rejected: false, pValue: ~0.398, statistic: ~-0.844 ci: [ ~-2.508, ~0.988 ], alternative: 'two-sided', method: 'Two-sample z-test', nullValue: 0, xmean: ~0.573, ymean: ~1.328 } // Print table output: > var table = out.print() Two-sample z-test Alternative hypothesis: True difference in means is not equal to 0 pValue: 0.3986 statistic: -0.8441 95% confidence interval: [-2.508,0.998] Test Decision: Fail to reject null in favor of alternative at 5% significance level // Choose a different significance level than `0.05`: > out = {{alias}}( x, y, 2.0, 2.0, { 'alpha': 0.4 }); > table = out.print() Two-sample z-test Alternative hypothesis: True difference in means is not equal to 0 pValue: 0.3986 statistic: -0.8441 60% confidence interval: [-1.5078,-0.0022] Test Decision: Reject null in favor of alternative at 40% significance level // Perform one-sided tests: > out = {{alias}}( x, y, 2.0, 2.0, { 'alternative': 'less' }); > table = out.print() Two-sample z-test Alternative hypothesis: True difference in means is less than 0 pValue: 0.1993 statistic: -0.8441 95% confidence interval: [-Infinity,0.7162] Test Decision: Fail to reject null in favor of alternative at 5% significance level > out = {{alias}}( x, y, 2.0, 2.0, { 'alternative': 'greater' }); > table = out.print() Two-sample z-test Alternative hypothesis: True difference in means is greater than 0 pValue: 0.8007 statistic: -0.8441 95% confidence interval: [-2.2262,Infinity] Test Decision: Fail to reject null in favor of alternative at 5% significance level // Test for a difference in means besides zero: > var rnorm = {{alias:@stdlib/random/base/normal}}.factory({ 'seed': 372 }); > x = new Array( 100 ); > for ( i = 0; i < x.length; i++ ) { ... x[ i ] = rnorm( 2.0, 1.0 ); ... } > y = new Array( 100 ); ... for ( i = 0; i < x.length; i++ ) { ... y[ i ] = rnorm( 0.0, 2.0 ); ... } > out = {{alias}}( x, y, 1.0, 2.0, { 'difference': 2.0 }) { rejected: false, pValue: ~0.35, statistic: ~-0.935 ci: [ ~1.353, ~2.229 ], // ... } See Also --------