| 1 | /*************************************************************************
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| 2 | Copyright (c) 2007, Sergey Bochkanov (ALGLIB project).
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| 3 |
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| 4 | >>> SOURCE LICENSE >>>
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| 5 | This program is free software; you can redistribute it and/or modify
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| 6 | it under the terms of the GNU General Public License as published by
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| 7 | the Free Software Foundation (www.fsf.org); either version 2 of the
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| 8 | License, or (at your option) any later version.
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| 9 |
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| 10 | This program is distributed in the hope that it will be useful,
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| 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 13 | GNU General Public License for more details.
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| 14 |
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| 15 | A copy of the GNU General Public License is available at
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| 16 | http://www.fsf.org/licensing/licenses
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| 17 |
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| 18 | >>> END OF LICENSE >>>
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| 19 | *************************************************************************/
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| 20 |
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| 21 | using System;
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| 22 |
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| 23 | namespace alglib
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| 24 | {
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| 25 | public class stest
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| 26 | {
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| 27 | /*************************************************************************
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| 28 | Sign test
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| 29 |
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| 30 | This test checks three hypotheses about the median of the given sample.
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| 31 | The following tests are performed:
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| 32 | * two-tailed test (null hypothesis - the median is equal to the given
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| 33 | value)
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| 34 | * left-tailed test (null hypothesis - the median is greater than or
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| 35 | equal to the given value)
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| 36 | * right-tailed test (null hypothesis - the median is less than or
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| 37 | equal to the given value)
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| 38 |
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| 39 | Requirements:
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| 40 | * the scale of measurement should be ordinal, interval or ratio (i.e.
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| 41 | the test could not be applied to nominal variables).
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| 42 |
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| 43 | The test is non-parametric and doesn't require distribution X to be normal
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| 44 |
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| 45 | Input parameters:
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| 46 | X - sample. Array whose index goes from 0 to N-1.
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| 47 | N - size of the sample.
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| 48 | Median - assumed median value.
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| 49 |
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| 50 | Output parameters:
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| 51 | BothTails - p-value for two-tailed test.
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| 52 | If BothTails is less than the given significance level
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| 53 | the null hypothesis is rejected.
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| 54 | LeftTail - p-value for left-tailed test.
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| 55 | If LeftTail is less than the given significance level,
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| 56 | the null hypothesis is rejected.
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| 57 | RightTail - p-value for right-tailed test.
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| 58 | If RightTail is less than the given significance level
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| 59 | the null hypothesis is rejected.
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| 60 |
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| 61 | While calculating p-values high-precision binomial distribution
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| 62 | approximation is used, so significance levels have about 15 exact digits.
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| 63 |
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| 64 | -- ALGLIB --
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| 65 | Copyright 08.09.2006 by Bochkanov Sergey
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| 66 | *************************************************************************/
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| 67 | public static void onesamplesigntest(ref double[] x,
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| 68 | int n,
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| 69 | double median,
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| 70 | ref double bothtails,
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| 71 | ref double lefttail,
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| 72 | ref double righttail)
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| 73 | {
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| 74 | int i = 0;
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| 75 | int gtcnt = 0;
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| 76 | int necnt = 0;
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| 77 |
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| 78 | if( n<=1 )
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| 79 | {
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| 80 | bothtails = 1.0;
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| 81 | lefttail = 1.0;
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| 82 | righttail = 1.0;
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| 83 | return;
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| 84 | }
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| 85 |
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| 86 | //
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| 87 | // Calculate:
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| 88 | // GTCnt - count of x[i]>Median
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| 89 | // NECnt - count of x[i]<>Median
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| 90 | //
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| 91 | gtcnt = 0;
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| 92 | necnt = 0;
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| 93 | for(i=0; i<=n-1; i++)
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| 94 | {
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| 95 | if( (double)(x[i])>(double)(median) )
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| 96 | {
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| 97 | gtcnt = gtcnt+1;
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| 98 | }
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| 99 | if( (double)(x[i])!=(double)(median) )
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| 100 | {
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| 101 | necnt = necnt+1;
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| 102 | }
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| 103 | }
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| 104 | if( necnt==0 )
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| 105 | {
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| 106 |
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| 107 | //
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| 108 | // all x[i] are equal to Median.
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| 109 | // So we can conclude that Median is a true median :)
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| 110 | //
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| 111 | bothtails = 0.0;
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| 112 | lefttail = 0.0;
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| 113 | righttail = 0.0;
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| 114 | return;
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| 115 | }
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| 116 | bothtails = 2*binomialdistr.binomialdistribution(Math.Min(gtcnt, necnt-gtcnt), necnt, 0.5);
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| 117 | lefttail = binomialdistr.binomialdistribution(gtcnt, necnt, 0.5);
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| 118 | righttail = binomialdistr.binomialcdistribution(gtcnt-1, necnt, 0.5);
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| 119 | }
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| 120 | }
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| 121 | }
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