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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.stat.inference;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import org.apache.commons.math.MathException;<a name="line.19"></a> <FONT color="green">020</FONT> <a name="line.20"></a> <FONT color="green">021</FONT> /**<a name="line.21"></a> <FONT color="green">022</FONT> * An interface for Chi-Square tests.<a name="line.22"></a> <FONT color="green">023</FONT> * <p>This interface handles only known distributions. If the distribution is<a name="line.23"></a> <FONT color="green">024</FONT> * unknown and should be provided by a sample, then the {@link UnknownDistributionChiSquareTest<a name="line.24"></a> <FONT color="green">025</FONT> * UnknownDistributionChiSquareTest} extended interface should be used instead.</p><a name="line.25"></a> <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> <FONT color="green">027</FONT> */<a name="line.27"></a> <FONT color="green">028</FONT> public interface ChiSquareTest {<a name="line.28"></a> <FONT color="green">029</FONT> <a name="line.29"></a> <FONT color="green">030</FONT> /**<a name="line.30"></a> <FONT color="green">031</FONT> * Computes the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"><a name="line.31"></a> <FONT color="green">032</FONT> * Chi-Square statistic</a> comparing <code>observed</code> and <code>expected</code><a name="line.32"></a> <FONT color="green">033</FONT> * frequency counts.<a name="line.33"></a> <FONT color="green">034</FONT> * <p><a name="line.34"></a> <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> <FONT color="green">036</FONT> * the observed counts follow the expected distribution.</p><a name="line.36"></a> <FONT color="green">037</FONT> * <p><a name="line.37"></a> <FONT color="green">038</FONT> * <strong>Preconditions</strong>: <ul><a name="line.38"></a> <FONT color="green">039</FONT> * <li>Expected counts must all be positive.<a name="line.39"></a> <FONT color="green">040</FONT> * </li><a name="line.40"></a> <FONT color="green">041</FONT> * <li>Observed counts must all be >= 0.<a name="line.41"></a> <FONT color="green">042</FONT> * </li><a name="line.42"></a> <FONT color="green">043</FONT> * <li>The observed and expected arrays must have the same length and<a name="line.43"></a> <FONT color="green">044</FONT> * their common length must be at least 2.<a name="line.44"></a> <FONT color="green">045</FONT> * </li></ul></p><p><a name="line.45"></a> <FONT color="green">046</FONT> * If any of the preconditions are not met, an<a name="line.46"></a> <FONT color="green">047</FONT> * <code>IllegalArgumentException</code> is thrown.</p><a name="line.47"></a> <FONT color="green">048</FONT> *<a name="line.48"></a> <FONT color="green">049</FONT> * @param observed array of observed frequency counts<a name="line.49"></a> <FONT color="green">050</FONT> * @param expected array of expected frequency counts<a name="line.50"></a> <FONT color="green">051</FONT> * @return chiSquare statistic<a name="line.51"></a> <FONT color="green">052</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.52"></a> <FONT color="green">053</FONT> */<a name="line.53"></a> <FONT color="green">054</FONT> double chiSquare(double[] expected, long[] observed)<a name="line.54"></a> <FONT color="green">055</FONT> throws IllegalArgumentException;<a name="line.55"></a> <FONT color="green">056</FONT> <a name="line.56"></a> <FONT color="green">057</FONT> /**<a name="line.57"></a> <FONT color="green">058</FONT> * Returns the <i>observed significance level</i>, or <a href=<a name="line.58"></a> <FONT color="green">059</FONT> * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"><a name="line.59"></a> <FONT color="green">060</FONT> * p-value</a>, associated with a<a name="line.60"></a> <FONT color="green">061</FONT> * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"><a name="line.61"></a> <FONT color="green">062</FONT> * Chi-square goodness of fit test</a> comparing the <code>observed</code><a name="line.62"></a> <FONT color="green">063</FONT> * frequency counts to those in the <code>expected</code> array.<a name="line.63"></a> <FONT color="green">064</FONT> * <p><a name="line.64"></a> <FONT color="green">065</FONT> * The number returned is the smallest significance level at which one can reject<a name="line.65"></a> <FONT color="green">066</FONT> * the null hypothesis that the observed counts conform to the frequency distribution<a name="line.66"></a> <FONT color="green">067</FONT> * described by the expected counts.</p><a name="line.67"></a> <FONT color="green">068</FONT> * <p><a name="line.68"></a> <FONT color="green">069</FONT> * <strong>Preconditions</strong>: <ul><a name="line.69"></a> <FONT color="green">070</FONT> * <li>Expected counts must all be positive.<a name="line.70"></a> <FONT color="green">071</FONT> * </li><a name="line.71"></a> <FONT color="green">072</FONT> * <li>Observed counts must all be >= 0.<a name="line.72"></a> <FONT color="green">073</FONT> * </li><a name="line.73"></a> <FONT color="green">074</FONT> * <li>The observed and expected arrays must have the same length and<a name="line.74"></a> <FONT color="green">075</FONT> * their common length must be at least 2.<a name="line.75"></a> <FONT color="green">076</FONT> * </li></ul></p><p><a name="line.76"></a> <FONT color="green">077</FONT> * If any of the preconditions are not met, an<a name="line.77"></a> <FONT color="green">078</FONT> * <code>IllegalArgumentException</code> is thrown.</p><a name="line.78"></a> <FONT color="green">079</FONT> *<a name="line.79"></a> <FONT color="green">080</FONT> * @param observed array of observed frequency counts<a name="line.80"></a> <FONT color="green">081</FONT> * @param expected array of expected frequency counts<a name="line.81"></a> <FONT color="green">082</FONT> * @return p-value<a name="line.82"></a> <FONT color="green">083</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.83"></a> <FONT color="green">084</FONT> * @throws MathException if an error occurs computing the p-value<a name="line.84"></a> <FONT color="green">085</FONT> */<a name="line.85"></a> <FONT color="green">086</FONT> double chiSquareTest(double[] expected, long[] observed)<a name="line.86"></a> <FONT color="green">087</FONT> throws IllegalArgumentException, MathException;<a name="line.87"></a> <FONT color="green">088</FONT> <a name="line.88"></a> <FONT color="green">089</FONT> /**<a name="line.89"></a> <FONT color="green">090</FONT> * Performs a <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"><a name="line.90"></a> <FONT color="green">091</FONT> * Chi-square goodness of fit test</a> evaluating the null hypothesis that the observed counts<a name="line.91"></a> <FONT color="green">092</FONT> * conform to the frequency distribution described by the expected counts, with<a name="line.92"></a> <FONT color="green">093</FONT> * significance level <code>alpha</code>. Returns true iff the null hypothesis can be rejected<a name="line.93"></a> <FONT color="green">094</FONT> * with 100 * (1 - alpha) percent confidence.<a name="line.94"></a> <FONT color="green">095</FONT> * <p><a name="line.95"></a> <FONT color="green">096</FONT> * <strong>Example:</strong><br><a name="line.96"></a> <FONT color="green">097</FONT> * To test the hypothesis that <code>observed</code> follows<a name="line.97"></a> <FONT color="green">098</FONT> * <code>expected</code> at the 99% level, use </p><p><a name="line.98"></a> <FONT color="green">099</FONT> * <code>chiSquareTest(expected, observed, 0.01) </code></p><a name="line.99"></a> <FONT color="green">100</FONT> * <p><a name="line.100"></a> <FONT color="green">101</FONT> * <strong>Preconditions</strong>: <ul><a name="line.101"></a> <FONT color="green">102</FONT> * <li>Expected counts must all be positive.<a name="line.102"></a> <FONT color="green">103</FONT> * </li><a name="line.103"></a> <FONT color="green">104</FONT> * <li>Observed counts must all be >= 0.<a name="line.104"></a> <FONT color="green">105</FONT> * </li><a name="line.105"></a> <FONT color="green">106</FONT> * <li>The observed and expected arrays must have the same length and<a name="line.106"></a> <FONT color="green">107</FONT> * their common length must be at least 2.<a name="line.107"></a> <FONT color="green">108</FONT> * <li> <code> 0 < alpha < 0.5 </code><a name="line.108"></a> <FONT color="green">109</FONT> * </li></ul></p><p><a name="line.109"></a> <FONT color="green">110</FONT> * If any of the preconditions are not met, an<a name="line.110"></a> <FONT color="green">111</FONT> * <code>IllegalArgumentException</code> is thrown.</p><a name="line.111"></a> <FONT color="green">112</FONT> *<a name="line.112"></a> <FONT color="green">113</FONT> * @param observed array of observed frequency counts<a name="line.113"></a> <FONT color="green">114</FONT> * @param expected array of expected frequency counts<a name="line.114"></a> <FONT color="green">115</FONT> * @param alpha significance level of the test<a name="line.115"></a> <FONT color="green">116</FONT> * @return true iff null hypothesis can be rejected with confidence<a name="line.116"></a> <FONT color="green">117</FONT> * 1 - alpha<a name="line.117"></a> <FONT color="green">118</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.118"></a> <FONT color="green">119</FONT> * @throws MathException if an error occurs performing the test<a name="line.119"></a> <FONT color="green">120</FONT> */<a name="line.120"></a> <FONT color="green">121</FONT> boolean chiSquareTest(double[] expected, long[] observed, double alpha)<a name="line.121"></a> <FONT color="green">122</FONT> throws IllegalArgumentException, MathException;<a name="line.122"></a> <FONT color="green">123</FONT> <a name="line.123"></a> <FONT color="green">124</FONT> /**<a name="line.124"></a> <FONT color="green">125</FONT> * Computes the Chi-Square statistic associated with a<a name="line.125"></a> <FONT color="green">126</FONT> * <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"><a name="line.126"></a> <FONT color="green">127</FONT> * chi-square test of independence</a> based on the input <code>counts</code><a name="line.127"></a> <FONT color="green">128</FONT> * array, viewed as a two-way table.<a name="line.128"></a> <FONT color="green">129</FONT> * <p><a name="line.129"></a> <FONT color="green">130</FONT> * The rows of the 2-way table are<a name="line.130"></a> <FONT color="green">131</FONT> * <code>count[0], ... , count[count.length - 1] </code></p><a name="line.131"></a> <FONT color="green">132</FONT> * <p><a name="line.132"></a> <FONT color="green">133</FONT> * <strong>Preconditions</strong>: <ul><a name="line.133"></a> <FONT color="green">134</FONT> * <li>All counts must be >= 0.<a name="line.134"></a> <FONT color="green">135</FONT> * </li><a name="line.135"></a> <FONT color="green">136</FONT> * <li>The count array must be rectangular (i.e. all count[i] subarrays<a name="line.136"></a> <FONT color="green">137</FONT> * must have the same length).<a name="line.137"></a> <FONT color="green">138</FONT> * </li><a name="line.138"></a> <FONT color="green">139</FONT> * <li>The 2-way table represented by <code>counts</code> must have at<a name="line.139"></a> <FONT color="green">140</FONT> * least 2 columns and at least 2 rows.<a name="line.140"></a> <FONT color="green">141</FONT> * </li><a name="line.141"></a> <FONT color="green">142</FONT> * </li></ul></p><p><a name="line.142"></a> <FONT color="green">143</FONT> * If any of the preconditions are not met, an<a name="line.143"></a> <FONT color="green">144</FONT> * <code>IllegalArgumentException</code> is thrown.</p><a name="line.144"></a> <FONT color="green">145</FONT> *<a name="line.145"></a> <FONT color="green">146</FONT> * @param counts array representation of 2-way table<a name="line.146"></a> <FONT color="green">147</FONT> * @return chiSquare statistic<a name="line.147"></a> <FONT color="green">148</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.148"></a> <FONT color="green">149</FONT> */<a name="line.149"></a> <FONT color="green">150</FONT> double chiSquare(long[][] counts)<a name="line.150"></a> <FONT color="green">151</FONT> throws IllegalArgumentException;<a name="line.151"></a> <FONT color="green">152</FONT> <a name="line.152"></a> <FONT color="green">153</FONT> /**<a name="line.153"></a> <FONT color="green">154</FONT> * Returns the <i>observed significance level</i>, or <a href=<a name="line.154"></a> <FONT color="green">155</FONT> * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"><a name="line.155"></a> <FONT color="green">156</FONT> * p-value</a>, associated with a<a name="line.156"></a> <FONT color="green">157</FONT> * <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"><a name="line.157"></a> <FONT color="green">158</FONT> * chi-square test of independence</a> based on the input <code>counts</code><a name="line.158"></a> <FONT color="green">159</FONT> * array, viewed as a two-way table.<a name="line.159"></a> <FONT color="green">160</FONT> * <p><a name="line.160"></a> <FONT color="green">161</FONT> * The rows of the 2-way table are<a name="line.161"></a> <FONT color="green">162</FONT> * <code>count[0], ... , count[count.length - 1] </code></p><a name="line.162"></a> <FONT color="green">163</FONT> * <p><a name="line.163"></a> <FONT color="green">164</FONT> * <strong>Preconditions</strong>: <ul><a name="line.164"></a> <FONT color="green">165</FONT> * <li>All counts must be >= 0.<a name="line.165"></a> <FONT color="green">166</FONT> * </li><a name="line.166"></a> <FONT color="green">167</FONT> * <li>The count array must be rectangular (i.e. all count[i] subarrays must have the same length).<a name="line.167"></a> <FONT color="green">168</FONT> * </li><a name="line.168"></a> <FONT color="green">169</FONT> * <li>The 2-way table represented by <code>counts</code> must have at least 2 columns and<a name="line.169"></a> <FONT color="green">170</FONT> * at least 2 rows.<a name="line.170"></a> <FONT color="green">171</FONT> * </li><a name="line.171"></a> <FONT color="green">172</FONT> * </li></ul></p><p><a name="line.172"></a> <FONT color="green">173</FONT> * If any of the preconditions are not met, an<a name="line.173"></a> <FONT color="green">174</FONT> * <code>IllegalArgumentException</code> is thrown.</p><a name="line.174"></a> <FONT color="green">175</FONT> *<a name="line.175"></a> <FONT color="green">176</FONT> * @param counts array representation of 2-way table<a name="line.176"></a> <FONT color="green">177</FONT> * @return p-value<a name="line.177"></a> <FONT color="green">178</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.178"></a> <FONT color="green">179</FONT> * @throws MathException if an error occurs computing the p-value<a name="line.179"></a> <FONT color="green">180</FONT> */<a name="line.180"></a> <FONT color="green">181</FONT> double chiSquareTest(long[][] counts)<a name="line.181"></a> <FONT color="green">182</FONT> throws IllegalArgumentException, MathException;<a name="line.182"></a> <FONT color="green">183</FONT> <a name="line.183"></a> <FONT color="green">184</FONT> /**<a name="line.184"></a> <FONT color="green">185</FONT> * Performs a <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"><a name="line.185"></a> <FONT color="green">186</FONT> * chi-square test of independence</a> evaluating the null hypothesis that the classifications<a name="line.186"></a> <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> <FONT color="green">188</FONT> * with significance level <code>alpha</code>. Returns true iff the null hypothesis can be rejected<a name="line.188"></a> <FONT color="green">189</FONT> * with 100 * (1 - alpha) percent confidence.<a name="line.189"></a> <FONT color="green">190</FONT> * <p><a name="line.190"></a> <FONT color="green">191</FONT> * The rows of the 2-way table are<a name="line.191"></a> <FONT color="green">192</FONT> * <code>count[0], ... , count[count.length - 1] </code></p><a name="line.192"></a> <FONT color="green">193</FONT> * <p><a name="line.193"></a> <FONT color="green">194</FONT> * <strong>Example:</strong><br><a name="line.194"></a> <FONT color="green">195</FONT> * To test the null hypothesis that the counts in<a name="line.195"></a> <FONT color="green">196</FONT> * <code>count[0], ... , count[count.length - 1] </code><a name="line.196"></a> <FONT color="green">197</FONT> * all correspond to the same underlying probability distribution at the 99% level, use </p><p><a name="line.197"></a> <FONT color="green">198</FONT> * <code>chiSquareTest(counts, 0.01) </code></p><a name="line.198"></a> <FONT color="green">199</FONT> * <p><a name="line.199"></a> <FONT color="green">200</FONT> * <strong>Preconditions</strong>: <ul><a name="line.200"></a> <FONT color="green">201</FONT> * <li>All counts must be >= 0.<a name="line.201"></a> <FONT color="green">202</FONT> * </li><a name="line.202"></a> <FONT color="green">203</FONT> * <li>The count array must be rectangular (i.e. all count[i] subarrays must have the same length).<a name="line.203"></a> <FONT color="green">204</FONT> * </li><a name="line.204"></a> <FONT color="green">205</FONT> * <li>The 2-way table represented by <code>counts</code> must have at least 2 columns and<a name="line.205"></a> <FONT color="green">206</FONT> * at least 2 rows.<a name="line.206"></a> <FONT color="green">207</FONT> * </li><a name="line.207"></a> <FONT color="green">208</FONT> * </li></ul></p><p><a name="line.208"></a> <FONT color="green">209</FONT> * If any of the preconditions are not met, an<a name="line.209"></a> <FONT color="green">210</FONT> * <code>IllegalArgumentException</code> is thrown.</p><a name="line.210"></a> <FONT color="green">211</FONT> *<a name="line.211"></a> <FONT color="green">212</FONT> * @param counts array representation of 2-way table<a name="line.212"></a> <FONT color="green">213</FONT> * @param alpha significance level of the test<a name="line.213"></a> <FONT color="green">214</FONT> * @return true iff null hypothesis can be rejected with confidence<a name="line.214"></a> <FONT color="green">215</FONT> * 1 - alpha<a name="line.215"></a> <FONT color="green">216</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.216"></a> <FONT color="green">217</FONT> * @throws MathException if an error occurs performing the test<a name="line.217"></a> <FONT color="green">218</FONT> */<a name="line.218"></a> <FONT color="green">219</FONT> boolean chiSquareTest(long[][] counts, double alpha)<a name="line.219"></a> <FONT color="green">220</FONT> throws IllegalArgumentException, MathException;<a name="line.220"></a> <FONT color="green">221</FONT> <a name="line.221"></a> <FONT color="green">222</FONT> }<a name="line.222"></a> </PRE> </BODY> </HTML>