test.md (6833B)
1 ## Statistical Tests 2 3 The test module includes methods that enact popular statistical tests. 4 The tests that are implemented are Z tests, T tests, and F tests. 5 Also included are methods for developing confidence intervals. Currently 6 regression is not included but it should be included soon (once matrix 7 inversion is fixed). 8 9 ## Statistics Instance Functionality 10 11 ### zscore( value[, flag] ) 12 13 Returns the z-score of `value` taking the jStat object as the observed 14 values. `flag===true` denotes use of sample standard deviation. 15 16 ### ztest( value, sides[, flag] ) 17 18 Returns the p-value of `value` taking the jStat object as the observed 19 values. `sides` is an integer value 1 or 2 denoting a 1 or 2 sided z-test. 20 The test defaults to a 2 sided z-test if `sides` is not specified. `flag===true` 21 denotes use of sample standard deviation. 22 23 ### tscore( value ) 24 25 Returns the t-score of `value` taking the jStat object as the observed 26 values. 27 28 ### ttest( value, sides ) 29 30 Returns the p-value of `value` taking the jStat object as the observed 31 values. `sides` is an integer value 1 or 2 denoting a 1 or 2 sided t-test. 32 The test defaults to a 2 sided t-test if `sides` is not specified. 33 34 ### anovafscore() 35 36 Returns the f-score of the ANOVA test on the arrays of the jStat object. 37 38 ### anovaftest() 39 40 Returns the p-value of an ANOVA test on the arrays of the jStat object. 41 42 ## Static Methods 43 44 ## Z Statistics 45 46 ### jStat.zscore( value, mean, sd ) 47 48 Returns the z-score of `value` given the `mean` mean and the `sd` standard deviation 49 of the test. 50 51 ### jStat.zscore( value, array[, flag] ) 52 53 Returns the z-score of `value` given the data from `array`. `flag===true` denotes 54 use of the sample standard deviation. 55 56 ### jStat.ztest( value, mean, sd, sides ) 57 58 Returns the p-value of a the z-test of `value` given the `mean` mean and `sd` standard 59 deviation of the test. `sides` is an integer value 1 or 2 denoting a 60 one or two sided z-test. If `sides` is not specified the test defaults 61 to a two sided z-test. 62 63 ### jStat.ztest( zscore, sides ) 64 65 Returns the p-value of the `zscore` z-score. `sides` is an integer value 1 or 2 66 denoting a one or two sided z-test. If `sides` is not specified the test 67 defaults to a two sided z-test 68 69 ### jStat.ztest( value, array, sides[, flag] ) 70 71 Returns the p-value of `value` given the data from `array`. `sides` is 72 an integer value 1 or 2 denoting a one or two sided z-test. If `sides` 73 is not specified the test defaults to a two sided z-test. `flag===true` 74 denotes the use of the sample standard deviation. 75 76 ## T Statistics 77 78 ### jStat.tscore( value, mean, sd, n ) 79 80 Returns the t-score of `value` given the `mean` mean, `sd` standard deviation, 81 and the sample size `n`. 82 83 ### jStat.tscore( value, array ) 84 85 Returns the t-score of `value` given the data from `array`. 86 87 ### jStat.ttest( value, mean, sd, n, sides ) 88 89 Returns the p-value of `value` given the `mean` mean, `sd` standard deviation, 90 and the sample size `n`. `sides` is an integer value 1 or 2 denoting 91 a one or two sided t-test. If `sides` is not specified the test 92 defaults to a two sided t-test. 93 94 ### jStat.ttest( tscore, n, sides ) 95 96 Returns the p-value of the `tscore` t-score given the sample size `n`. `sides` 97 is an integer value 1 or 2 denoting a one or two sided t-test. 98 If `sides` is not specified the test defaults to a two sided t-test. 99 100 ### jStat.ttest( value, array, sides ) 101 102 Returns the p-value of `value` given the data in `array`. 103 `sides` is an integer value 1 or 2 denoting a one or two sided 104 t-test. If `sides` is not specified the test defaults to a two 105 sided t-test. 106 107 ## F Statistics 108 109 ### jStat.anovafscore( array1, array2, ..., arrayn ) 110 111 Returns the f-score of an ANOVA on the arrays. 112 113 ### jStat.anovafscore( [array1,array2, ...,arrayn] ) 114 115 Returns the f-score of an ANOVA on the arrays. 116 117 ### jStat.anovaftest( array1, array2, ...., arrayn ) 118 119 Returns the p-value of the f-statistic from the ANOVA 120 test on the arrays. 121 122 ### jStat.ftest( fscore, df1, df2) 123 124 Returns the p-value for the `fscore` f-score with a `df1` numerator degrees 125 of freedom and a `df2` denominator degrees of freedom. 126 127 ## Tukey's Range Test 128 129 ### jStat.qscore( mean1, mean2, n1, n2, sd ) 130 131 Returns the q-score of a single pairwise comparison between arrays 132 of mean `mean1` and `mean2`, size `n1` and `n2`, and standard deviation (of 133 all vectors) `sd`. 134 135 ### jStat.qscore( array1, array2, sd ) 136 137 Same as above, but the means and sizes are calculated automatically 138 from the arrays. 139 140 ### jStat.qtest( qscore, n, k ) 141 142 Returns the p-value of the q-score given the total sample size `n` 143 and `k` number of populations. 144 145 ### jStat.qtest( mean1, mean2, n1, n2, sd, n, k ) 146 147 Returns the p-value of a single pairwise comparison between arrays 148 of mean `mean1` and `mean2`, size `n1` and `n2`, and standard deviation (of 149 all vectors) `sd`, where the total sample size is `n` and the number of 150 populations is `k`. 151 152 ### jStat.qtest( array1, array2, sd, n, k ) 153 154 Same as above, but the means and sizes are calculated automatically 155 from the arrays. 156 157 ### jStat.tukeyhsd( arrays ) 158 159 Performs the full Tukey's range test returning p-values for every 160 pairwise combination of the arrays in the format of 161 `[[[index1, index2], pvalue], ...]` 162 163 For example: 164 165 > jStat.tukeyhsd([[1, 2], [3, 4, 5], [6], [7, 8]]) 166 [ [ [ 0, 1 ], 0.10745283896120883 ], 167 [ [ 0, 2 ], 0.04374051946838586 ], 168 [ [ 0, 3 ], 0.007850804224287633 ], 169 [ [ 1, 2 ], 0.32191548545694226 ], 170 [ [ 1, 3 ], 0.03802747415485819 ], 171 [ [ 2, 3 ], 0.5528665999257486 ] ] 172 173 ## Confidence Intervals 174 175 ### jStat.normalci( value, alpha, sd, n ) 176 177 Returns a 1-alpha confidence interval for `value` given 178 a normal distribution with a standard deviation `sd` and a 179 sample size `n` 180 181 ### jStat.normalci( value, alpha, array ) 182 183 Returns a 1-alpha confidence interval for `value` given 184 a normal distribution in the data from `array`. 185 186 ### jStat.tci( value, alpha, sd, n ) 187 188 Returns a 1-alpha confidence interval for `value` given 189 the standard deviation `sd` and the sample size `n`. 190 191 ### jStat.tci( value, alpha, array ) 192 193 Returns a 1-alpha confidence interval for `value` given 194 the data from `array`. 195 196 ### jStat.fn.oneSidedDifferenceOfProportions( p1, n1, p2, n2 ) 197 198 Returns the p-value for a 1-sided test for the difference 199 between two proportions. `p1` is the sample proportion for 200 the first sample, whereas `p2` is the sample proportion for 201 the second sample. Similiarly, `n1` is the sample size of the 202 first sample and `n2` is the sample size for the second sample. 203 204 ### jStat.fn.twoSidedDifferenceOfProportions( p1, n1, p2, n2 ) 205 206 Returns the p-value for a 2-sided test for the difference 207 between two proportions. `p1` is the sample proportion for 208 the first sample, whereas `p2` is the sample proportion for 209 the second sample. Similiarly, `n1` is the sample size of the 210 first sample and `n2` is the sample size for the second sample.