repl.txt (3624B)
1 2 {{alias}}( x, sigma[, options] ) 3 Computes a one-sample z-test. 4 5 The function performs a one-sample z-test for the null hypothesis that the 6 data in array or typed array `x` is drawn from a normal distribution with 7 mean zero and standard deviation `sigma`. 8 9 The returned object comes with a `.print()` method which when invoked will 10 print a formatted output of the results of the hypothesis test. 11 12 Parameters 13 ---------- 14 x: Array<number> 15 Data array. 16 17 sigma: number 18 Known standard deviation. 19 20 options: Object (optional) 21 Options. 22 23 options.alpha: number (optional) 24 Number in the interval `[0,1]` giving the significance level of the 25 hypothesis test. Default: `0.05`. 26 27 options.alternative: string (optional) 28 Indicates whether the alternative hypothesis is that the mean of `x` is 29 larger than `mu` (`greater`), smaller than `mu` (`less`) or equal to 30 `mu` (`two-sided`). Default: `'two-sided'`. 31 32 options.mu: number (optional) 33 Hypothesized true mean under the null hypothesis. Set this option to 34 test whether the data comes from a distribution with the specified `mu`. 35 Default: `0`. 36 37 Returns 38 ------- 39 out: Object 40 Test result object. 41 42 out.alpha: number 43 Used significance level. 44 45 out.rejected: boolean 46 Test decision. 47 48 out.pValue: number 49 p-value of the test. 50 51 out.statistic: number 52 Value of test statistic. 53 54 out.ci: Array<number> 55 1-alpha confidence interval for mean. 56 57 out.nullValue: number 58 Assumed mean value under H0. 59 60 out.sd: number 61 Standard error. 62 63 out.alternative: string 64 Alternative hypothesis (`two-sided`, `less` or `greater`). 65 66 out.method: string 67 Name of test (`One-Sample z-test`). 68 69 out.print: Function 70 Function to print formatted output. 71 72 Examples 73 -------- 74 // One-sample z-test: 75 > var rnorm = {{alias:@stdlib/random/base/normal}}.factory( 0.0, 2.0, { 'seed': 212 }); 76 > var x = new Array( 100 ); 77 > for ( var i = 0; i < x.length; i++ ) { 78 ... x[ i ] = rnorm(); 79 ... } 80 > var out = {{alias}}( x, 2.0 ) 81 { 82 alpha: 0.05, 83 rejected: false, 84 pValue: ~0.180, 85 statistic: ~-1.34, 86 ci: [ ~-0.66, ~0.124 ], 87 ... 88 } 89 90 // Choose custom significance level and print output: 91 > arr = [ 2, 4, 3, 1, 0 ]; 92 > out = {{alias}}( arr, 2.0, { 'alpha': 0.01 }); 93 > table = out.print() 94 One-sample z-test 95 96 Alternative hypothesis: True mean is not equal to 0 97 98 pValue: 0.0253 99 statistic: 2.2361 100 99% confidence interval: [-0.3039,4.3039] 101 102 Test Decision: Fail to reject null in favor of alternative at 1% 103 significance level 104 105 106 // Test for a mean equal to five: 107 > var arr = [ 4, 4, 6, 6, 5 ]; 108 > out = {{alias}}( arr, 1.0, { 'mu': 5 }) 109 { 110 rejected: false, 111 pValue: 1, 112 statistic: 0, 113 ci: [ ~4.123, ~5.877 ], 114 // ... 115 } 116 117 // Perform one-sided tests: 118 > arr = [ 4, 4, 6, 6, 5 ]; 119 > out = {{alias}}( arr, 1.0, { 'alternative': 'less' }) 120 { 121 alpha: 0.05, 122 rejected: false, 123 pValue: 1, 124 statistic: 11.180339887498949, 125 ci: [ -Infinity, 5.735600904580115 ], 126 // ... 127 } 128 > out = {{alias}}( arr, 1.0, { 'alternative': 'greater' }) 129 { 130 alpha: 0.05, 131 rejected: true, 132 pValue: 0, 133 statistic: 11.180339887498949, 134 ci: [ 4.264399095419885, Infinity ], 135 //... 136 } 137 138 See Also 139 -------- 140