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comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.html @ 13:cbf34dd4d7e6

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author dwinter
date Tue, 04 Jan 2011 10:02:07 +0100
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4 <FONT color="green">001</FONT> /*<a name="line.1"></a>
5 <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
6 <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a>
7 <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
8 <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
9 <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
10 <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a>
11 <FONT color="green">008</FONT> *<a name="line.8"></a>
12 <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
13 <FONT color="green">010</FONT> *<a name="line.10"></a>
14 <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
15 <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
16 <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
17 <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a>
18 <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a>
19 <FONT color="green">016</FONT> */<a name="line.16"></a>
20 <FONT color="green">017</FONT> package org.apache.commons.math.stat.inference;<a name="line.17"></a>
21 <FONT color="green">018</FONT> <a name="line.18"></a>
22 <FONT color="green">019</FONT> import org.apache.commons.math.MathException;<a name="line.19"></a>
23 <FONT color="green">020</FONT> <a name="line.20"></a>
24 <FONT color="green">021</FONT> /**<a name="line.21"></a>
25 <FONT color="green">022</FONT> * An interface for Chi-Square tests for unknown distributions.<a name="line.22"></a>
26 <FONT color="green">023</FONT> * &lt;p&gt;Two samples tests are used when the distribution is unknown &lt;i&gt;a priori&lt;/i&gt;<a name="line.23"></a>
27 <FONT color="green">024</FONT> * but provided by one sample. We compare the second sample against the first.&lt;/p&gt;<a name="line.24"></a>
28 <FONT color="green">025</FONT> *<a name="line.25"></a>
29 <FONT color="green">026</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.26"></a>
30 <FONT color="green">027</FONT> * @since 1.2<a name="line.27"></a>
31 <FONT color="green">028</FONT> */<a name="line.28"></a>
32 <FONT color="green">029</FONT> public interface UnknownDistributionChiSquareTest extends ChiSquareTest {<a name="line.29"></a>
33 <FONT color="green">030</FONT> <a name="line.30"></a>
34 <FONT color="green">031</FONT> /**<a name="line.31"></a>
35 <FONT color="green">032</FONT> * &lt;p&gt;Computes a<a name="line.32"></a>
36 <FONT color="green">033</FONT> * &lt;a href="http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/chi2samp.htm"&gt;<a name="line.33"></a>
37 <FONT color="green">034</FONT> * Chi-Square two sample test statistic&lt;/a&gt; comparing bin frequency counts<a name="line.34"></a>
38 <FONT color="green">035</FONT> * in &lt;code&gt;observed1&lt;/code&gt; and &lt;code&gt;observed2&lt;/code&gt;. The<a name="line.35"></a>
39 <FONT color="green">036</FONT> * sums of frequency counts in the two samples are not required to be the<a name="line.36"></a>
40 <FONT color="green">037</FONT> * same. The formula used to compute the test statistic is&lt;/p&gt;<a name="line.37"></a>
41 <FONT color="green">038</FONT> * &lt;code&gt;<a name="line.38"></a>
42 <FONT color="green">039</FONT> * &amp;sum;[(K * observed1[i] - observed2[i]/K)&lt;sup&gt;2&lt;/sup&gt; / (observed1[i] + observed2[i])]<a name="line.39"></a>
43 <FONT color="green">040</FONT> * &lt;/code&gt; where<a name="line.40"></a>
44 <FONT color="green">041</FONT> * &lt;br/&gt;&lt;code&gt;K = &amp;sqrt;[&amp;sum(observed2 / &amp;sum;(observed1)]&lt;/code&gt;<a name="line.41"></a>
45 <FONT color="green">042</FONT> * &lt;/p&gt;<a name="line.42"></a>
46 <FONT color="green">043</FONT> * &lt;p&gt;This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that<a name="line.43"></a>
47 <FONT color="green">044</FONT> * both observed counts follow the same distribution.&lt;/p&gt;<a name="line.44"></a>
48 <FONT color="green">045</FONT> * &lt;p&gt;<a name="line.45"></a>
49 <FONT color="green">046</FONT> * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.46"></a>
50 <FONT color="green">047</FONT> * &lt;li&gt;Observed counts must be non-negative.<a name="line.47"></a>
51 <FONT color="green">048</FONT> * &lt;/li&gt;<a name="line.48"></a>
52 <FONT color="green">049</FONT> * &lt;li&gt;Observed counts for a specific bin must not both be zero.<a name="line.49"></a>
53 <FONT color="green">050</FONT> * &lt;/li&gt;<a name="line.50"></a>
54 <FONT color="green">051</FONT> * &lt;li&gt;Observed counts for a specific sample must not all be 0.<a name="line.51"></a>
55 <FONT color="green">052</FONT> * &lt;/li&gt;<a name="line.52"></a>
56 <FONT color="green">053</FONT> * &lt;li&gt;The arrays &lt;code&gt;observed1&lt;/code&gt; and &lt;code&gt;observed2&lt;/code&gt; must have the same length and<a name="line.53"></a>
57 <FONT color="green">054</FONT> * their common length must be at least 2.<a name="line.54"></a>
58 <FONT color="green">055</FONT> * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.55"></a>
59 <FONT color="green">056</FONT> * If any of the preconditions are not met, an<a name="line.56"></a>
60 <FONT color="green">057</FONT> * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.57"></a>
61 <FONT color="green">058</FONT> *<a name="line.58"></a>
62 <FONT color="green">059</FONT> * @param observed1 array of observed frequency counts of the first data set<a name="line.59"></a>
63 <FONT color="green">060</FONT> * @param observed2 array of observed frequency counts of the second data set<a name="line.60"></a>
64 <FONT color="green">061</FONT> * @return chiSquare statistic<a name="line.61"></a>
65 <FONT color="green">062</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.62"></a>
66 <FONT color="green">063</FONT> */<a name="line.63"></a>
67 <FONT color="green">064</FONT> double chiSquareDataSetsComparison(long[] observed1, long[] observed2)<a name="line.64"></a>
68 <FONT color="green">065</FONT> throws IllegalArgumentException;<a name="line.65"></a>
69 <FONT color="green">066</FONT> <a name="line.66"></a>
70 <FONT color="green">067</FONT> /**<a name="line.67"></a>
71 <FONT color="green">068</FONT> * &lt;p&gt;Returns the &lt;i&gt;observed significance level&lt;/i&gt;, or &lt;a href=<a name="line.68"></a>
72 <FONT color="green">069</FONT> * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"&gt;<a name="line.69"></a>
73 <FONT color="green">070</FONT> * p-value&lt;/a&gt;, associated with a Chi-Square two sample test comparing<a name="line.70"></a>
74 <FONT color="green">071</FONT> * bin frequency counts in &lt;code&gt;observed1&lt;/code&gt; and<a name="line.71"></a>
75 <FONT color="green">072</FONT> * &lt;code&gt;observed2&lt;/code&gt;.<a name="line.72"></a>
76 <FONT color="green">073</FONT> * &lt;/p&gt;<a name="line.73"></a>
77 <FONT color="green">074</FONT> * &lt;p&gt;The number returned is the smallest significance level at which one<a name="line.74"></a>
78 <FONT color="green">075</FONT> * can reject the null hypothesis that the observed counts conform to the<a name="line.75"></a>
79 <FONT color="green">076</FONT> * same distribution.<a name="line.76"></a>
80 <FONT color="green">077</FONT> * &lt;/p&gt;<a name="line.77"></a>
81 <FONT color="green">078</FONT> * &lt;p&gt;See {@link #chiSquareDataSetsComparison(long[], long[])} for details<a name="line.78"></a>
82 <FONT color="green">079</FONT> * on the formula used to compute the test statistic. The degrees of<a name="line.79"></a>
83 <FONT color="green">080</FONT> * of freedom used to perform the test is one less than the common length<a name="line.80"></a>
84 <FONT color="green">081</FONT> * of the input observed count arrays.<a name="line.81"></a>
85 <FONT color="green">082</FONT> * &lt;/p&gt;<a name="line.82"></a>
86 <FONT color="green">083</FONT> * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.83"></a>
87 <FONT color="green">084</FONT> * &lt;li&gt;Observed counts must be non-negative.<a name="line.84"></a>
88 <FONT color="green">085</FONT> * &lt;/li&gt;<a name="line.85"></a>
89 <FONT color="green">086</FONT> * &lt;li&gt;Observed counts for a specific bin must not both be zero.<a name="line.86"></a>
90 <FONT color="green">087</FONT> * &lt;/li&gt;<a name="line.87"></a>
91 <FONT color="green">088</FONT> * &lt;li&gt;Observed counts for a specific sample must not all be 0.<a name="line.88"></a>
92 <FONT color="green">089</FONT> * &lt;/li&gt;<a name="line.89"></a>
93 <FONT color="green">090</FONT> * &lt;li&gt;The arrays &lt;code&gt;observed1&lt;/code&gt; and &lt;code&gt;observed2&lt;/code&gt; must<a name="line.90"></a>
94 <FONT color="green">091</FONT> * have the same length and<a name="line.91"></a>
95 <FONT color="green">092</FONT> * their common length must be at least 2.<a name="line.92"></a>
96 <FONT color="green">093</FONT> * &lt;/li&gt;&lt;/ul&gt;&lt;p&gt;<a name="line.93"></a>
97 <FONT color="green">094</FONT> * If any of the preconditions are not met, an<a name="line.94"></a>
98 <FONT color="green">095</FONT> * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.95"></a>
99 <FONT color="green">096</FONT> *<a name="line.96"></a>
100 <FONT color="green">097</FONT> * @param observed1 array of observed frequency counts of the first data set<a name="line.97"></a>
101 <FONT color="green">098</FONT> * @param observed2 array of observed frequency counts of the second data set<a name="line.98"></a>
102 <FONT color="green">099</FONT> * @return p-value<a name="line.99"></a>
103 <FONT color="green">100</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.100"></a>
104 <FONT color="green">101</FONT> * @throws MathException if an error occurs computing the p-value<a name="line.101"></a>
105 <FONT color="green">102</FONT> */<a name="line.102"></a>
106 <FONT color="green">103</FONT> double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)<a name="line.103"></a>
107 <FONT color="green">104</FONT> throws IllegalArgumentException, MathException;<a name="line.104"></a>
108 <FONT color="green">105</FONT> <a name="line.105"></a>
109 <FONT color="green">106</FONT> /**<a name="line.106"></a>
110 <FONT color="green">107</FONT> * &lt;p&gt;Performs a Chi-Square two sample test comparing two binned data<a name="line.107"></a>
111 <FONT color="green">108</FONT> * sets. The test evaluates the null hypothesis that the two lists of<a name="line.108"></a>
112 <FONT color="green">109</FONT> * observed counts conform to the same frequency distribution, with<a name="line.109"></a>
113 <FONT color="green">110</FONT> * significance level &lt;code&gt;alpha&lt;/code&gt;. Returns true iff the null<a name="line.110"></a>
114 <FONT color="green">111</FONT> * hypothesis can be rejected with 100 * (1 - alpha) percent confidence.<a name="line.111"></a>
115 <FONT color="green">112</FONT> * &lt;/p&gt;<a name="line.112"></a>
116 <FONT color="green">113</FONT> * &lt;p&gt;See {@link #chiSquareDataSetsComparison(long[], long[])} for<a name="line.113"></a>
117 <FONT color="green">114</FONT> * details on the formula used to compute the Chisquare statistic used<a name="line.114"></a>
118 <FONT color="green">115</FONT> * in the test. The degrees of of freedom used to perform the test is<a name="line.115"></a>
119 <FONT color="green">116</FONT> * one less than the common length of the input observed count arrays.<a name="line.116"></a>
120 <FONT color="green">117</FONT> * &lt;/p&gt;<a name="line.117"></a>
121 <FONT color="green">118</FONT> * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.118"></a>
122 <FONT color="green">119</FONT> * &lt;li&gt;Observed counts must be non-negative.<a name="line.119"></a>
123 <FONT color="green">120</FONT> * &lt;/li&gt;<a name="line.120"></a>
124 <FONT color="green">121</FONT> * &lt;li&gt;Observed counts for a specific bin must not both be zero.<a name="line.121"></a>
125 <FONT color="green">122</FONT> * &lt;/li&gt;<a name="line.122"></a>
126 <FONT color="green">123</FONT> * &lt;li&gt;Observed counts for a specific sample must not all be 0.<a name="line.123"></a>
127 <FONT color="green">124</FONT> * &lt;/li&gt;<a name="line.124"></a>
128 <FONT color="green">125</FONT> * &lt;li&gt;The arrays &lt;code&gt;observed1&lt;/code&gt; and &lt;code&gt;observed2&lt;/code&gt; must<a name="line.125"></a>
129 <FONT color="green">126</FONT> * have the same length and their common length must be at least 2.<a name="line.126"></a>
130 <FONT color="green">127</FONT> * &lt;/li&gt;<a name="line.127"></a>
131 <FONT color="green">128</FONT> * &lt;li&gt; &lt;code&gt; 0 &lt; alpha &lt; 0.5 &lt;/code&gt;<a name="line.128"></a>
132 <FONT color="green">129</FONT> * &lt;/li&gt;&lt;/ul&gt;&lt;p&gt;<a name="line.129"></a>
133 <FONT color="green">130</FONT> * If any of the preconditions are not met, an<a name="line.130"></a>
134 <FONT color="green">131</FONT> * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.131"></a>
135 <FONT color="green">132</FONT> *<a name="line.132"></a>
136 <FONT color="green">133</FONT> * @param observed1 array of observed frequency counts of the first data set<a name="line.133"></a>
137 <FONT color="green">134</FONT> * @param observed2 array of observed frequency counts of the second data set<a name="line.134"></a>
138 <FONT color="green">135</FONT> * @param alpha significance level of the test<a name="line.135"></a>
139 <FONT color="green">136</FONT> * @return true iff null hypothesis can be rejected with confidence<a name="line.136"></a>
140 <FONT color="green">137</FONT> * 1 - alpha<a name="line.137"></a>
141 <FONT color="green">138</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.138"></a>
142 <FONT color="green">139</FONT> * @throws MathException if an error occurs performing the test<a name="line.139"></a>
143 <FONT color="green">140</FONT> */<a name="line.140"></a>
144 <FONT color="green">141</FONT> boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)<a name="line.141"></a>
145 <FONT color="green">142</FONT> throws IllegalArgumentException, MathException;<a name="line.142"></a>
146 <FONT color="green">143</FONT> <a name="line.143"></a>
147 <FONT color="green">144</FONT> }<a name="line.144"></a>
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