211 lines
6.7 KiB
Markdown
211 lines
6.7 KiB
Markdown
## Statistical Tests
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The test module includes methods that enact popular statistical tests.
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The tests that are implemented are Z tests, T tests, and F tests.
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Also included are methods for developing confidence intervals. Currently
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regression is not included but it should be included soon (once matrix
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inversion is fixed).
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## Statistics Instance Functionality
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### zscore( value[, flag] )
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Returns the z-score of `value` taking the jStat object as the observed
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values. `flag===true` denotes use of sample standard deviation.
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### ztest( value, sides[, flag] )
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Returns the p-value of `value` taking the jStat object as the observed
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values. `sides` is an integer value 1 or 2 denoting a 1 or 2 sided z-test.
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The test defaults to a 2 sided z-test if `sides` is not specified. `flag===true`
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denotes use of sample standard deviation.
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### tscore( value )
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Returns the t-score of `value` taking the jStat object as the observed
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values.
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### ttest( value, sides )
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Returns the p-value of `value` taking the jStat object as the observed
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values. `sides` is an integer value 1 or 2 denoting a 1 or 2 sided t-test.
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The test defaults to a 2 sided t-test if `sides` is not specified.
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### anovafscore()
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Returns the f-score of the ANOVA test on the arrays of the jStat object.
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### anovaftest()
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Returns the p-value of an ANOVA test on the arrays of the jStat object.
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## Static Methods
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## Z Statistics
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### jStat.zscore( value, mean, sd )
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Returns the z-score of `value` given the `mean` mean and the `sd` standard deviation
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of the test.
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### jStat.zscore( value, array[, flag] )
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Returns the z-score of `value` given the data from `array`. `flag===true` denotes
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use of the sample standard deviation.
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### jStat.ztest( value, mean, sd, sides )
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Returns the p-value of a the z-test of `value` given the `mean` mean and `sd` standard
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deviation of the test. `sides` is an integer value 1 or 2 denoting a
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one or two sided z-test. If `sides` is not specified the test defaults
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to a two sided z-test.
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### jStat.ztest( zscore, sides )
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Returns the p-value of the `zscore` z-score. `sides` is an integer value 1 or 2
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denoting a one or two sided z-test. If `sides` is not specified the test
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defaults to a two sided z-test
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### jStat.ztest( value, array, sides[, flag] )
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Returns the p-value of `value` given the data from `array`. `sides` is
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an integer value 1 or 2 denoting a one or two sided z-test. If `sides`
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is not specified the test defaults to a two sided z-test. `flag===true`
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denotes the use of the sample standard deviation.
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## T Statistics
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### jStat.tscore( value, mean, sd, n )
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Returns the t-score of `value` given the `mean` mean, `sd` standard deviation,
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and the sample size `n`.
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### jStat.tscore( value, array )
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Returns the t-score of `value` given the data from `array`.
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### jStat.ttest( value, mean, sd, n, sides )
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Returns the p-value of `value` given the `mean` mean, `sd` standard deviation,
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and the sample size `n`. `sides` is an integer value 1 or 2 denoting
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a one or two sided t-test. If `sides` is not specified the test
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defaults to a two sided t-test.
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### jStat.ttest( tscore, n, sides )
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Returns the p-value of the `tscore` t-score given the sample size `n`. `sides`
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is an integer value 1 or 2 denoting a one or two sided t-test.
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If `sides` is not specified the test defaults to a two sided t-test.
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### jStat.ttest( value, array, sides )
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Returns the p-value of `value` given the data in `array`.
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`sides` is an integer value 1 or 2 denoting a one or two sided
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t-test. If `sides` is not specified the test defaults to a two
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sided t-test.
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## F Statistics
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### jStat.anovafscore( array1, array2, ..., arrayn )
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Returns the f-score of an ANOVA on the arrays.
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### jStat.anovafscore( [array1,array2, ...,arrayn] )
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Returns the f-score of an ANOVA on the arrays.
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### jStat.anovaftest( array1, array2, ...., arrayn )
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Returns the p-value of the f-statistic from the ANOVA
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test on the arrays.
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### jStat.ftest( fscore, df1, df2)
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Returns the p-value for the `fscore` f-score with a `df1` numerator degrees
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of freedom and a `df2` denominator degrees of freedom.
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## Tukey's Range Test
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### jStat.qscore( mean1, mean2, n1, n2, sd )
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Returns the q-score of a single pairwise comparison between arrays
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of mean `mean1` and `mean2`, size `n1` and `n2`, and standard deviation (of
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all vectors) `sd`.
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### jStat.qscore( array1, array2, sd )
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Same as above, but the means and sizes are calculated automatically
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from the arrays.
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### jStat.qtest( qscore, n, k )
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Returns the p-value of the q-score given the total sample size `n`
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and `k` number of populations.
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### jStat.qtest( mean1, mean2, n1, n2, sd, n, k )
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Returns the p-value of a single pairwise comparison between arrays
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of mean `mean1` and `mean2`, size `n1` and `n2`, and standard deviation (of
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all vectors) `sd`, where the total sample size is `n` and the number of
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populations is `k`.
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### jStat.qtest( array1, array2, sd, n, k )
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Same as above, but the means and sizes are calculated automatically
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from the arrays.
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### jStat.tukeyhsd( arrays )
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Performs the full Tukey's range test returning p-values for every
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pairwise combination of the arrays in the format of
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`[[[index1, index2], pvalue], ...]`
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For example:
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> jStat.tukeyhsd([[1, 2], [3, 4, 5], [6], [7, 8]])
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[ [ [ 0, 1 ], 0.10745283896120883 ],
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[ [ 0, 2 ], 0.04374051946838586 ],
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[ [ 0, 3 ], 0.007850804224287633 ],
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[ [ 1, 2 ], 0.32191548545694226 ],
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[ [ 1, 3 ], 0.03802747415485819 ],
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[ [ 2, 3 ], 0.5528665999257486 ] ]
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## Confidence Intervals
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### jStat.normalci( value, alpha, sd, n )
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Returns a 1-alpha confidence interval for `value` given
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a normal distribution with a standard deviation `sd` and a
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sample size `n`
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### jStat.normalci( value, alpha, array )
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Returns a 1-alpha confidence interval for `value` given
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a normal distribution in the data from `array`.
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### jStat.tci( value, alpha, sd, n )
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Returns a 1-alpha confidence interval for `value` given
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the standard deviation `sd` and the sample size `n`.
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### jStat.tci( value, alpha, array )
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Returns a 1-alpha confidence interval for `value` given
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the data from `array`.
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### jStat.fn.oneSidedDifferenceOfProportions( p1, n1, p2, n2 )
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Returns the p-value for a 1-sided test for the difference
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between two proportions. `p1` is the sample proportion for
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the first sample, whereas `p2` is the sample proportion for
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the second sample. Similiarly, `n1` is the sample size of the
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first sample and `n2` is the sample size for the second sample.
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### jStat.fn.twoSidedDifferenceOfProportions( p1, n1, p2, n2 )
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Returns the p-value for a 2-sided test for the difference
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between two proportions. `p1` is the sample proportion for
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the first sample, whereas `p2` is the sample proportion for
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the second sample. Similiarly, `n1` is the sample size of the
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first sample and `n2` is the sample size for the second sample.
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