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comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/stat/inference/ChiSquareTest.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.<a name="line.22"></a>
26 <FONT color="green">023</FONT> * &lt;p&gt;This interface handles only known distributions. If the distribution is<a name="line.23"></a>
27 <FONT color="green">024</FONT> * unknown and should be provided by a sample, then the {@link UnknownDistributionChiSquareTest<a name="line.24"></a>
28 <FONT color="green">025</FONT> * UnknownDistributionChiSquareTest} extended interface should be used instead.&lt;/p&gt;<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> */<a name="line.27"></a>
31 <FONT color="green">028</FONT> public interface ChiSquareTest {<a name="line.28"></a>
32 <FONT color="green">029</FONT> <a name="line.29"></a>
33 <FONT color="green">030</FONT> /**<a name="line.30"></a>
34 <FONT color="green">031</FONT> * Computes the &lt;a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"&gt;<a name="line.31"></a>
35 <FONT color="green">032</FONT> * Chi-Square statistic&lt;/a&gt; comparing &lt;code&gt;observed&lt;/code&gt; and &lt;code&gt;expected&lt;/code&gt;<a name="line.32"></a>
36 <FONT color="green">033</FONT> * frequency counts.<a name="line.33"></a>
37 <FONT color="green">034</FONT> * &lt;p&gt;<a name="line.34"></a>
38 <FONT color="green">035</FONT> * This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that<a name="line.35"></a>
39 <FONT color="green">036</FONT> * the observed counts follow the expected distribution.&lt;/p&gt;<a name="line.36"></a>
40 <FONT color="green">037</FONT> * &lt;p&gt;<a name="line.37"></a>
41 <FONT color="green">038</FONT> * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.38"></a>
42 <FONT color="green">039</FONT> * &lt;li&gt;Expected counts must all be positive.<a name="line.39"></a>
43 <FONT color="green">040</FONT> * &lt;/li&gt;<a name="line.40"></a>
44 <FONT color="green">041</FONT> * &lt;li&gt;Observed counts must all be &gt;= 0.<a name="line.41"></a>
45 <FONT color="green">042</FONT> * &lt;/li&gt;<a name="line.42"></a>
46 <FONT color="green">043</FONT> * &lt;li&gt;The observed and expected arrays must have the same length and<a name="line.43"></a>
47 <FONT color="green">044</FONT> * their common length must be at least 2.<a name="line.44"></a>
48 <FONT color="green">045</FONT> * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.45"></a>
49 <FONT color="green">046</FONT> * If any of the preconditions are not met, an<a name="line.46"></a>
50 <FONT color="green">047</FONT> * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.47"></a>
51 <FONT color="green">048</FONT> *<a name="line.48"></a>
52 <FONT color="green">049</FONT> * @param observed array of observed frequency counts<a name="line.49"></a>
53 <FONT color="green">050</FONT> * @param expected array of expected frequency counts<a name="line.50"></a>
54 <FONT color="green">051</FONT> * @return chiSquare statistic<a name="line.51"></a>
55 <FONT color="green">052</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.52"></a>
56 <FONT color="green">053</FONT> */<a name="line.53"></a>
57 <FONT color="green">054</FONT> double chiSquare(double[] expected, long[] observed)<a name="line.54"></a>
58 <FONT color="green">055</FONT> throws IllegalArgumentException;<a name="line.55"></a>
59 <FONT color="green">056</FONT> <a name="line.56"></a>
60 <FONT color="green">057</FONT> /**<a name="line.57"></a>
61 <FONT color="green">058</FONT> * Returns the &lt;i&gt;observed significance level&lt;/i&gt;, or &lt;a href=<a name="line.58"></a>
62 <FONT color="green">059</FONT> * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"&gt;<a name="line.59"></a>
63 <FONT color="green">060</FONT> * p-value&lt;/a&gt;, associated with a<a name="line.60"></a>
64 <FONT color="green">061</FONT> * &lt;a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"&gt;<a name="line.61"></a>
65 <FONT color="green">062</FONT> * Chi-square goodness of fit test&lt;/a&gt; comparing the &lt;code&gt;observed&lt;/code&gt;<a name="line.62"></a>
66 <FONT color="green">063</FONT> * frequency counts to those in the &lt;code&gt;expected&lt;/code&gt; array.<a name="line.63"></a>
67 <FONT color="green">064</FONT> * &lt;p&gt;<a name="line.64"></a>
68 <FONT color="green">065</FONT> * The number returned is the smallest significance level at which one can reject<a name="line.65"></a>
69 <FONT color="green">066</FONT> * the null hypothesis that the observed counts conform to the frequency distribution<a name="line.66"></a>
70 <FONT color="green">067</FONT> * described by the expected counts.&lt;/p&gt;<a name="line.67"></a>
71 <FONT color="green">068</FONT> * &lt;p&gt;<a name="line.68"></a>
72 <FONT color="green">069</FONT> * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.69"></a>
73 <FONT color="green">070</FONT> * &lt;li&gt;Expected counts must all be positive.<a name="line.70"></a>
74 <FONT color="green">071</FONT> * &lt;/li&gt;<a name="line.71"></a>
75 <FONT color="green">072</FONT> * &lt;li&gt;Observed counts must all be &gt;= 0.<a name="line.72"></a>
76 <FONT color="green">073</FONT> * &lt;/li&gt;<a name="line.73"></a>
77 <FONT color="green">074</FONT> * &lt;li&gt;The observed and expected arrays must have the same length and<a name="line.74"></a>
78 <FONT color="green">075</FONT> * their common length must be at least 2.<a name="line.75"></a>
79 <FONT color="green">076</FONT> * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.76"></a>
80 <FONT color="green">077</FONT> * If any of the preconditions are not met, an<a name="line.77"></a>
81 <FONT color="green">078</FONT> * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.78"></a>
82 <FONT color="green">079</FONT> *<a name="line.79"></a>
83 <FONT color="green">080</FONT> * @param observed array of observed frequency counts<a name="line.80"></a>
84 <FONT color="green">081</FONT> * @param expected array of expected frequency counts<a name="line.81"></a>
85 <FONT color="green">082</FONT> * @return p-value<a name="line.82"></a>
86 <FONT color="green">083</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.83"></a>
87 <FONT color="green">084</FONT> * @throws MathException if an error occurs computing the p-value<a name="line.84"></a>
88 <FONT color="green">085</FONT> */<a name="line.85"></a>
89 <FONT color="green">086</FONT> double chiSquareTest(double[] expected, long[] observed)<a name="line.86"></a>
90 <FONT color="green">087</FONT> throws IllegalArgumentException, MathException;<a name="line.87"></a>
91 <FONT color="green">088</FONT> <a name="line.88"></a>
92 <FONT color="green">089</FONT> /**<a name="line.89"></a>
93 <FONT color="green">090</FONT> * Performs a &lt;a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"&gt;<a name="line.90"></a>
94 <FONT color="green">091</FONT> * Chi-square goodness of fit test&lt;/a&gt; evaluating the null hypothesis that the observed counts<a name="line.91"></a>
95 <FONT color="green">092</FONT> * conform to the frequency distribution described by the expected counts, with<a name="line.92"></a>
96 <FONT color="green">093</FONT> * significance level &lt;code&gt;alpha&lt;/code&gt;. Returns true iff the null hypothesis can be rejected<a name="line.93"></a>
97 <FONT color="green">094</FONT> * with 100 * (1 - alpha) percent confidence.<a name="line.94"></a>
98 <FONT color="green">095</FONT> * &lt;p&gt;<a name="line.95"></a>
99 <FONT color="green">096</FONT> * &lt;strong&gt;Example:&lt;/strong&gt;&lt;br&gt;<a name="line.96"></a>
100 <FONT color="green">097</FONT> * To test the hypothesis that &lt;code&gt;observed&lt;/code&gt; follows<a name="line.97"></a>
101 <FONT color="green">098</FONT> * &lt;code&gt;expected&lt;/code&gt; at the 99% level, use &lt;/p&gt;&lt;p&gt;<a name="line.98"></a>
102 <FONT color="green">099</FONT> * &lt;code&gt;chiSquareTest(expected, observed, 0.01) &lt;/code&gt;&lt;/p&gt;<a name="line.99"></a>
103 <FONT color="green">100</FONT> * &lt;p&gt;<a name="line.100"></a>
104 <FONT color="green">101</FONT> * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.101"></a>
105 <FONT color="green">102</FONT> * &lt;li&gt;Expected counts must all be positive.<a name="line.102"></a>
106 <FONT color="green">103</FONT> * &lt;/li&gt;<a name="line.103"></a>
107 <FONT color="green">104</FONT> * &lt;li&gt;Observed counts must all be &gt;= 0.<a name="line.104"></a>
108 <FONT color="green">105</FONT> * &lt;/li&gt;<a name="line.105"></a>
109 <FONT color="green">106</FONT> * &lt;li&gt;The observed and expected arrays must have the same length and<a name="line.106"></a>
110 <FONT color="green">107</FONT> * their common length must be at least 2.<a name="line.107"></a>
111 <FONT color="green">108</FONT> * &lt;li&gt; &lt;code&gt; 0 &lt; alpha &lt; 0.5 &lt;/code&gt;<a name="line.108"></a>
112 <FONT color="green">109</FONT> * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.109"></a>
113 <FONT color="green">110</FONT> * If any of the preconditions are not met, an<a name="line.110"></a>
114 <FONT color="green">111</FONT> * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.111"></a>
115 <FONT color="green">112</FONT> *<a name="line.112"></a>
116 <FONT color="green">113</FONT> * @param observed array of observed frequency counts<a name="line.113"></a>
117 <FONT color="green">114</FONT> * @param expected array of expected frequency counts<a name="line.114"></a>
118 <FONT color="green">115</FONT> * @param alpha significance level of the test<a name="line.115"></a>
119 <FONT color="green">116</FONT> * @return true iff null hypothesis can be rejected with confidence<a name="line.116"></a>
120 <FONT color="green">117</FONT> * 1 - alpha<a name="line.117"></a>
121 <FONT color="green">118</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.118"></a>
122 <FONT color="green">119</FONT> * @throws MathException if an error occurs performing the test<a name="line.119"></a>
123 <FONT color="green">120</FONT> */<a name="line.120"></a>
124 <FONT color="green">121</FONT> boolean chiSquareTest(double[] expected, long[] observed, double alpha)<a name="line.121"></a>
125 <FONT color="green">122</FONT> throws IllegalArgumentException, MathException;<a name="line.122"></a>
126 <FONT color="green">123</FONT> <a name="line.123"></a>
127 <FONT color="green">124</FONT> /**<a name="line.124"></a>
128 <FONT color="green">125</FONT> * Computes the Chi-Square statistic associated with a<a name="line.125"></a>
129 <FONT color="green">126</FONT> * &lt;a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"&gt;<a name="line.126"></a>
130 <FONT color="green">127</FONT> * chi-square test of independence&lt;/a&gt; based on the input &lt;code&gt;counts&lt;/code&gt;<a name="line.127"></a>
131 <FONT color="green">128</FONT> * array, viewed as a two-way table.<a name="line.128"></a>
132 <FONT color="green">129</FONT> * &lt;p&gt;<a name="line.129"></a>
133 <FONT color="green">130</FONT> * The rows of the 2-way table are<a name="line.130"></a>
134 <FONT color="green">131</FONT> * &lt;code&gt;count[0], ... , count[count.length - 1] &lt;/code&gt;&lt;/p&gt;<a name="line.131"></a>
135 <FONT color="green">132</FONT> * &lt;p&gt;<a name="line.132"></a>
136 <FONT color="green">133</FONT> * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.133"></a>
137 <FONT color="green">134</FONT> * &lt;li&gt;All counts must be &gt;= 0.<a name="line.134"></a>
138 <FONT color="green">135</FONT> * &lt;/li&gt;<a name="line.135"></a>
139 <FONT color="green">136</FONT> * &lt;li&gt;The count array must be rectangular (i.e. all count[i] subarrays<a name="line.136"></a>
140 <FONT color="green">137</FONT> * must have the same length).<a name="line.137"></a>
141 <FONT color="green">138</FONT> * &lt;/li&gt;<a name="line.138"></a>
142 <FONT color="green">139</FONT> * &lt;li&gt;The 2-way table represented by &lt;code&gt;counts&lt;/code&gt; must have at<a name="line.139"></a>
143 <FONT color="green">140</FONT> * least 2 columns and at least 2 rows.<a name="line.140"></a>
144 <FONT color="green">141</FONT> * &lt;/li&gt;<a name="line.141"></a>
145 <FONT color="green">142</FONT> * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.142"></a>
146 <FONT color="green">143</FONT> * If any of the preconditions are not met, an<a name="line.143"></a>
147 <FONT color="green">144</FONT> * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.144"></a>
148 <FONT color="green">145</FONT> *<a name="line.145"></a>
149 <FONT color="green">146</FONT> * @param counts array representation of 2-way table<a name="line.146"></a>
150 <FONT color="green">147</FONT> * @return chiSquare statistic<a name="line.147"></a>
151 <FONT color="green">148</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.148"></a>
152 <FONT color="green">149</FONT> */<a name="line.149"></a>
153 <FONT color="green">150</FONT> double chiSquare(long[][] counts)<a name="line.150"></a>
154 <FONT color="green">151</FONT> throws IllegalArgumentException;<a name="line.151"></a>
155 <FONT color="green">152</FONT> <a name="line.152"></a>
156 <FONT color="green">153</FONT> /**<a name="line.153"></a>
157 <FONT color="green">154</FONT> * Returns the &lt;i&gt;observed significance level&lt;/i&gt;, or &lt;a href=<a name="line.154"></a>
158 <FONT color="green">155</FONT> * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"&gt;<a name="line.155"></a>
159 <FONT color="green">156</FONT> * p-value&lt;/a&gt;, associated with a<a name="line.156"></a>
160 <FONT color="green">157</FONT> * &lt;a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"&gt;<a name="line.157"></a>
161 <FONT color="green">158</FONT> * chi-square test of independence&lt;/a&gt; based on the input &lt;code&gt;counts&lt;/code&gt;<a name="line.158"></a>
162 <FONT color="green">159</FONT> * array, viewed as a two-way table.<a name="line.159"></a>
163 <FONT color="green">160</FONT> * &lt;p&gt;<a name="line.160"></a>
164 <FONT color="green">161</FONT> * The rows of the 2-way table are<a name="line.161"></a>
165 <FONT color="green">162</FONT> * &lt;code&gt;count[0], ... , count[count.length - 1] &lt;/code&gt;&lt;/p&gt;<a name="line.162"></a>
166 <FONT color="green">163</FONT> * &lt;p&gt;<a name="line.163"></a>
167 <FONT color="green">164</FONT> * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.164"></a>
168 <FONT color="green">165</FONT> * &lt;li&gt;All counts must be &gt;= 0.<a name="line.165"></a>
169 <FONT color="green">166</FONT> * &lt;/li&gt;<a name="line.166"></a>
170 <FONT color="green">167</FONT> * &lt;li&gt;The count array must be rectangular (i.e. all count[i] subarrays must have the same length).<a name="line.167"></a>
171 <FONT color="green">168</FONT> * &lt;/li&gt;<a name="line.168"></a>
172 <FONT color="green">169</FONT> * &lt;li&gt;The 2-way table represented by &lt;code&gt;counts&lt;/code&gt; must have at least 2 columns and<a name="line.169"></a>
173 <FONT color="green">170</FONT> * at least 2 rows.<a name="line.170"></a>
174 <FONT color="green">171</FONT> * &lt;/li&gt;<a name="line.171"></a>
175 <FONT color="green">172</FONT> * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.172"></a>
176 <FONT color="green">173</FONT> * If any of the preconditions are not met, an<a name="line.173"></a>
177 <FONT color="green">174</FONT> * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.174"></a>
178 <FONT color="green">175</FONT> *<a name="line.175"></a>
179 <FONT color="green">176</FONT> * @param counts array representation of 2-way table<a name="line.176"></a>
180 <FONT color="green">177</FONT> * @return p-value<a name="line.177"></a>
181 <FONT color="green">178</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.178"></a>
182 <FONT color="green">179</FONT> * @throws MathException if an error occurs computing the p-value<a name="line.179"></a>
183 <FONT color="green">180</FONT> */<a name="line.180"></a>
184 <FONT color="green">181</FONT> double chiSquareTest(long[][] counts)<a name="line.181"></a>
185 <FONT color="green">182</FONT> throws IllegalArgumentException, MathException;<a name="line.182"></a>
186 <FONT color="green">183</FONT> <a name="line.183"></a>
187 <FONT color="green">184</FONT> /**<a name="line.184"></a>
188 <FONT color="green">185</FONT> * Performs a &lt;a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"&gt;<a name="line.185"></a>
189 <FONT color="green">186</FONT> * chi-square test of independence&lt;/a&gt; evaluating the null hypothesis that the classifications<a name="line.186"></a>
190 <FONT color="green">187</FONT> * represented by the counts in the columns of the input 2-way table are independent of the rows,<a name="line.187"></a>
191 <FONT color="green">188</FONT> * with significance level &lt;code&gt;alpha&lt;/code&gt;. Returns true iff the null hypothesis can be rejected<a name="line.188"></a>
192 <FONT color="green">189</FONT> * with 100 * (1 - alpha) percent confidence.<a name="line.189"></a>
193 <FONT color="green">190</FONT> * &lt;p&gt;<a name="line.190"></a>
194 <FONT color="green">191</FONT> * The rows of the 2-way table are<a name="line.191"></a>
195 <FONT color="green">192</FONT> * &lt;code&gt;count[0], ... , count[count.length - 1] &lt;/code&gt;&lt;/p&gt;<a name="line.192"></a>
196 <FONT color="green">193</FONT> * &lt;p&gt;<a name="line.193"></a>
197 <FONT color="green">194</FONT> * &lt;strong&gt;Example:&lt;/strong&gt;&lt;br&gt;<a name="line.194"></a>
198 <FONT color="green">195</FONT> * To test the null hypothesis that the counts in<a name="line.195"></a>
199 <FONT color="green">196</FONT> * &lt;code&gt;count[0], ... , count[count.length - 1] &lt;/code&gt;<a name="line.196"></a>
200 <FONT color="green">197</FONT> * all correspond to the same underlying probability distribution at the 99% level, use &lt;/p&gt;&lt;p&gt;<a name="line.197"></a>
201 <FONT color="green">198</FONT> * &lt;code&gt;chiSquareTest(counts, 0.01) &lt;/code&gt;&lt;/p&gt;<a name="line.198"></a>
202 <FONT color="green">199</FONT> * &lt;p&gt;<a name="line.199"></a>
203 <FONT color="green">200</FONT> * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.200"></a>
204 <FONT color="green">201</FONT> * &lt;li&gt;All counts must be &gt;= 0.<a name="line.201"></a>
205 <FONT color="green">202</FONT> * &lt;/li&gt;<a name="line.202"></a>
206 <FONT color="green">203</FONT> * &lt;li&gt;The count array must be rectangular (i.e. all count[i] subarrays must have the same length).<a name="line.203"></a>
207 <FONT color="green">204</FONT> * &lt;/li&gt;<a name="line.204"></a>
208 <FONT color="green">205</FONT> * &lt;li&gt;The 2-way table represented by &lt;code&gt;counts&lt;/code&gt; must have at least 2 columns and<a name="line.205"></a>
209 <FONT color="green">206</FONT> * at least 2 rows.<a name="line.206"></a>
210 <FONT color="green">207</FONT> * &lt;/li&gt;<a name="line.207"></a>
211 <FONT color="green">208</FONT> * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.208"></a>
212 <FONT color="green">209</FONT> * If any of the preconditions are not met, an<a name="line.209"></a>
213 <FONT color="green">210</FONT> * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.210"></a>
214 <FONT color="green">211</FONT> *<a name="line.211"></a>
215 <FONT color="green">212</FONT> * @param counts array representation of 2-way table<a name="line.212"></a>
216 <FONT color="green">213</FONT> * @param alpha significance level of the test<a name="line.213"></a>
217 <FONT color="green">214</FONT> * @return true iff null hypothesis can be rejected with confidence<a name="line.214"></a>
218 <FONT color="green">215</FONT> * 1 - alpha<a name="line.215"></a>
219 <FONT color="green">216</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.216"></a>
220 <FONT color="green">217</FONT> * @throws MathException if an error occurs performing the test<a name="line.217"></a>
221 <FONT color="green">218</FONT> */<a name="line.218"></a>
222 <FONT color="green">219</FONT> boolean chiSquareTest(long[][] counts, double alpha)<a name="line.219"></a>
223 <FONT color="green">220</FONT> throws IllegalArgumentException, MathException;<a name="line.220"></a>
224 <FONT color="green">221</FONT> <a name="line.221"></a>
225 <FONT color="green">222</FONT> }<a name="line.222"></a>
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286 </PRE>
287 </BODY>
288 </HTML>