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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> import org.apache.commons.math.MathRuntimeException;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.distribution.ChiSquaredDistribution;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.distribution.ChiSquaredDistributionImpl;<a name="line.22"></a> <FONT color="green">023</FONT> <a name="line.23"></a> <FONT color="green">024</FONT> /**<a name="line.24"></a> <FONT color="green">025</FONT> * Implements Chi-Square test statistics defined in the<a name="line.25"></a> <FONT color="green">026</FONT> * {@link UnknownDistributionChiSquareTest} interface.<a name="line.26"></a> <FONT color="green">027</FONT> *<a name="line.27"></a> <FONT color="green">028</FONT> * @version $Revision: 811833 $ $Date: 2009-09-06 12:27:50 -0400 (Sun, 06 Sep 2009) $<a name="line.28"></a> <FONT color="green">029</FONT> */<a name="line.29"></a> <FONT color="green">030</FONT> public class ChiSquareTestImpl implements UnknownDistributionChiSquareTest {<a name="line.30"></a> <FONT color="green">031</FONT> <a name="line.31"></a> <FONT color="green">032</FONT> /** Distribution used to compute inference statistics. */<a name="line.32"></a> <FONT color="green">033</FONT> private ChiSquaredDistribution distribution;<a name="line.33"></a> <FONT color="green">034</FONT> <a name="line.34"></a> <FONT color="green">035</FONT> /**<a name="line.35"></a> <FONT color="green">036</FONT> * Construct a ChiSquareTestImpl<a name="line.36"></a> <FONT color="green">037</FONT> */<a name="line.37"></a> <FONT color="green">038</FONT> public ChiSquareTestImpl() {<a name="line.38"></a> <FONT color="green">039</FONT> this(new ChiSquaredDistributionImpl(1.0));<a name="line.39"></a> <FONT color="green">040</FONT> }<a name="line.40"></a> <FONT color="green">041</FONT> <a name="line.41"></a> <FONT color="green">042</FONT> /**<a name="line.42"></a> <FONT color="green">043</FONT> * Create a test instance using the given distribution for computing<a name="line.43"></a> <FONT color="green">044</FONT> * inference statistics.<a name="line.44"></a> <FONT color="green">045</FONT> * @param x distribution used to compute inference statistics.<a name="line.45"></a> <FONT color="green">046</FONT> * @since 1.2<a name="line.46"></a> <FONT color="green">047</FONT> */<a name="line.47"></a> <FONT color="green">048</FONT> public ChiSquareTestImpl(ChiSquaredDistribution x) {<a name="line.48"></a> <FONT color="green">049</FONT> super();<a name="line.49"></a> <FONT color="green">050</FONT> setDistribution(x);<a name="line.50"></a> <FONT color="green">051</FONT> }<a name="line.51"></a> <FONT color="green">052</FONT> /**<a name="line.52"></a> <FONT color="green">053</FONT> * {@inheritDoc}<a name="line.53"></a> <FONT color="green">054</FONT> * <p><strong>Note: </strong>This implementation rescales the<a name="line.54"></a> <FONT color="green">055</FONT> * <code>expected</code> array if necessary to ensure that the sum of the<a name="line.55"></a> <FONT color="green">056</FONT> * expected and observed counts are equal.</p><a name="line.56"></a> <FONT color="green">057</FONT> *<a name="line.57"></a> <FONT color="green">058</FONT> * @param observed array of observed frequency counts<a name="line.58"></a> <FONT color="green">059</FONT> * @param expected array of expected frequency counts<a name="line.59"></a> <FONT color="green">060</FONT> * @return chi-square test statistic<a name="line.60"></a> <FONT color="green">061</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.61"></a> <FONT color="green">062</FONT> * or length is less than 2<a name="line.62"></a> <FONT color="green">063</FONT> */<a name="line.63"></a> <FONT color="green">064</FONT> public double chiSquare(double[] expected, long[] observed)<a name="line.64"></a> <FONT color="green">065</FONT> throws IllegalArgumentException {<a name="line.65"></a> <FONT color="green">066</FONT> if (expected.length < 2) {<a name="line.66"></a> <FONT color="green">067</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.67"></a> <FONT color="green">068</FONT> "expected array length = {0}, must be at least 2",<a name="line.68"></a> <FONT color="green">069</FONT> expected.length);<a name="line.69"></a> <FONT color="green">070</FONT> }<a name="line.70"></a> <FONT color="green">071</FONT> if (expected.length != observed.length) {<a name="line.71"></a> <FONT color="green">072</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.72"></a> <FONT color="green">073</FONT> "dimension mismatch {0} != {1}", expected.length, observed.length);<a name="line.73"></a> <FONT color="green">074</FONT> }<a name="line.74"></a> <FONT color="green">075</FONT> checkPositive(expected);<a name="line.75"></a> <FONT color="green">076</FONT> checkNonNegative(observed);<a name="line.76"></a> <FONT color="green">077</FONT> double sumExpected = 0d;<a name="line.77"></a> <FONT color="green">078</FONT> double sumObserved = 0d;<a name="line.78"></a> <FONT color="green">079</FONT> for (int i = 0; i < observed.length; i++) {<a name="line.79"></a> <FONT color="green">080</FONT> sumExpected += expected[i];<a name="line.80"></a> <FONT color="green">081</FONT> sumObserved += observed[i];<a name="line.81"></a> <FONT color="green">082</FONT> }<a name="line.82"></a> <FONT color="green">083</FONT> double ratio = 1.0d;<a name="line.83"></a> <FONT color="green">084</FONT> boolean rescale = false;<a name="line.84"></a> <FONT color="green">085</FONT> if (Math.abs(sumExpected - sumObserved) > 10E-6) {<a name="line.85"></a> <FONT color="green">086</FONT> ratio = sumObserved / sumExpected;<a name="line.86"></a> <FONT color="green">087</FONT> rescale = true;<a name="line.87"></a> <FONT color="green">088</FONT> }<a name="line.88"></a> <FONT color="green">089</FONT> double sumSq = 0.0d;<a name="line.89"></a> <FONT color="green">090</FONT> for (int i = 0; i < observed.length; i++) {<a name="line.90"></a> <FONT color="green">091</FONT> if (rescale) {<a name="line.91"></a> <FONT color="green">092</FONT> final double dev = observed[i] - ratio * expected[i];<a name="line.92"></a> <FONT color="green">093</FONT> sumSq += dev * dev / (ratio * expected[i]);<a name="line.93"></a> <FONT color="green">094</FONT> } else {<a name="line.94"></a> <FONT color="green">095</FONT> final double dev = observed[i] - expected[i];<a name="line.95"></a> <FONT color="green">096</FONT> sumSq += dev * dev / expected[i];<a name="line.96"></a> <FONT color="green">097</FONT> }<a name="line.97"></a> <FONT color="green">098</FONT> }<a name="line.98"></a> <FONT color="green">099</FONT> return sumSq;<a name="line.99"></a> <FONT color="green">100</FONT> }<a name="line.100"></a> <FONT color="green">101</FONT> <a name="line.101"></a> <FONT color="green">102</FONT> /**<a name="line.102"></a> <FONT color="green">103</FONT> * {@inheritDoc}<a name="line.103"></a> <FONT color="green">104</FONT> * <p><strong>Note: </strong>This implementation rescales the<a name="line.104"></a> <FONT color="green">105</FONT> * <code>expected</code> array if necessary to ensure that the sum of the<a name="line.105"></a> <FONT color="green">106</FONT> * expected and observed counts are equal.</p><a name="line.106"></a> <FONT color="green">107</FONT> *<a name="line.107"></a> <FONT color="green">108</FONT> * @param observed array of observed frequency counts<a name="line.108"></a> <FONT color="green">109</FONT> * @param expected array of expected frequency counts<a name="line.109"></a> <FONT color="green">110</FONT> * @return p-value<a name="line.110"></a> <FONT color="green">111</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.111"></a> <FONT color="green">112</FONT> * @throws MathException if an error occurs computing the p-value<a name="line.112"></a> <FONT color="green">113</FONT> */<a name="line.113"></a> <FONT color="green">114</FONT> public double chiSquareTest(double[] expected, long[] observed)<a name="line.114"></a> <FONT color="green">115</FONT> throws IllegalArgumentException, MathException {<a name="line.115"></a> <FONT color="green">116</FONT> distribution.setDegreesOfFreedom(expected.length - 1.0);<a name="line.116"></a> <FONT color="green">117</FONT> return 1.0 - distribution.cumulativeProbability(<a name="line.117"></a> <FONT color="green">118</FONT> chiSquare(expected, observed));<a name="line.118"></a> <FONT color="green">119</FONT> }<a name="line.119"></a> <FONT color="green">120</FONT> <a name="line.120"></a> <FONT color="green">121</FONT> /**<a name="line.121"></a> <FONT color="green">122</FONT> * {@inheritDoc}<a name="line.122"></a> <FONT color="green">123</FONT> * <p><strong>Note: </strong>This implementation rescales the<a name="line.123"></a> <FONT color="green">124</FONT> * <code>expected</code> array if necessary to ensure that the sum of the<a name="line.124"></a> <FONT color="green">125</FONT> * expected and observed counts are equal.</p><a name="line.125"></a> <FONT color="green">126</FONT> *<a name="line.126"></a> <FONT color="green">127</FONT> * @param observed array of observed frequency counts<a name="line.127"></a> <FONT color="green">128</FONT> * @param expected array of expected frequency counts<a name="line.128"></a> <FONT color="green">129</FONT> * @param alpha significance level of the test<a name="line.129"></a> <FONT color="green">130</FONT> * @return true iff null hypothesis can be rejected with confidence<a name="line.130"></a> <FONT color="green">131</FONT> * 1 - alpha<a name="line.131"></a> <FONT color="green">132</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.132"></a> <FONT color="green">133</FONT> * @throws MathException if an error occurs performing the test<a name="line.133"></a> <FONT color="green">134</FONT> */<a name="line.134"></a> <FONT color="green">135</FONT> public boolean chiSquareTest(double[] expected, long[] observed,<a name="line.135"></a> <FONT color="green">136</FONT> double alpha) throws IllegalArgumentException, MathException {<a name="line.136"></a> <FONT color="green">137</FONT> if ((alpha <= 0) || (alpha > 0.5)) {<a name="line.137"></a> <FONT color="green">138</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.138"></a> <FONT color="green">139</FONT> "out of bounds significance level {0}, must be between {1} and {2}",<a name="line.139"></a> <FONT color="green">140</FONT> alpha, 0, 0.5);<a name="line.140"></a> <FONT color="green">141</FONT> }<a name="line.141"></a> <FONT color="green">142</FONT> return chiSquareTest(expected, observed) < alpha;<a name="line.142"></a> <FONT color="green">143</FONT> }<a name="line.143"></a> <FONT color="green">144</FONT> <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 chi-square test 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> public double chiSquare(long[][] counts) throws IllegalArgumentException {<a name="line.150"></a> <FONT color="green">151</FONT> <a name="line.151"></a> <FONT color="green">152</FONT> checkArray(counts);<a name="line.152"></a> <FONT color="green">153</FONT> int nRows = counts.length;<a name="line.153"></a> <FONT color="green">154</FONT> int nCols = counts[0].length;<a name="line.154"></a> <FONT color="green">155</FONT> <a name="line.155"></a> <FONT color="green">156</FONT> // compute row, column and total sums<a name="line.156"></a> <FONT color="green">157</FONT> double[] rowSum = new double[nRows];<a name="line.157"></a> <FONT color="green">158</FONT> double[] colSum = new double[nCols];<a name="line.158"></a> <FONT color="green">159</FONT> double total = 0.0d;<a name="line.159"></a> <FONT color="green">160</FONT> for (int row = 0; row < nRows; row++) {<a name="line.160"></a> <FONT color="green">161</FONT> for (int col = 0; col < nCols; col++) {<a name="line.161"></a> <FONT color="green">162</FONT> rowSum[row] += counts[row][col];<a name="line.162"></a> <FONT color="green">163</FONT> colSum[col] += counts[row][col];<a name="line.163"></a> <FONT color="green">164</FONT> total += counts[row][col];<a name="line.164"></a> <FONT color="green">165</FONT> }<a name="line.165"></a> <FONT color="green">166</FONT> }<a name="line.166"></a> <FONT color="green">167</FONT> <a name="line.167"></a> <FONT color="green">168</FONT> // compute expected counts and chi-square<a name="line.168"></a> <FONT color="green">169</FONT> double sumSq = 0.0d;<a name="line.169"></a> <FONT color="green">170</FONT> double expected = 0.0d;<a name="line.170"></a> <FONT color="green">171</FONT> for (int row = 0; row < nRows; row++) {<a name="line.171"></a> <FONT color="green">172</FONT> for (int col = 0; col < nCols; col++) {<a name="line.172"></a> <FONT color="green">173</FONT> expected = (rowSum[row] * colSum[col]) / total;<a name="line.173"></a> <FONT color="green">174</FONT> sumSq += ((counts[row][col] - expected) *<a name="line.174"></a> <FONT color="green">175</FONT> (counts[row][col] - expected)) / expected;<a name="line.175"></a> <FONT color="green">176</FONT> }<a name="line.176"></a> <FONT color="green">177</FONT> }<a name="line.177"></a> <FONT color="green">178</FONT> return sumSq;<a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> <a name="line.180"></a> <FONT color="green">181</FONT> /**<a name="line.181"></a> <FONT color="green">182</FONT> * @param counts array representation of 2-way table<a name="line.182"></a> <FONT color="green">183</FONT> * @return p-value<a name="line.183"></a> <FONT color="green">184</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.184"></a> <FONT color="green">185</FONT> * @throws MathException if an error occurs computing the p-value<a name="line.185"></a> <FONT color="green">186</FONT> */<a name="line.186"></a> <FONT color="green">187</FONT> public double chiSquareTest(long[][] counts)<a name="line.187"></a> <FONT color="green">188</FONT> throws IllegalArgumentException, MathException {<a name="line.188"></a> <FONT color="green">189</FONT> checkArray(counts);<a name="line.189"></a> <FONT color="green">190</FONT> double df = ((double) counts.length -1) * ((double) counts[0].length - 1);<a name="line.190"></a> <FONT color="green">191</FONT> distribution.setDegreesOfFreedom(df);<a name="line.191"></a> <FONT color="green">192</FONT> return 1 - distribution.cumulativeProbability(chiSquare(counts));<a name="line.192"></a> <FONT color="green">193</FONT> }<a name="line.193"></a> <FONT color="green">194</FONT> <a name="line.194"></a> <FONT color="green">195</FONT> /**<a name="line.195"></a> <FONT color="green">196</FONT> * @param counts array representation of 2-way table<a name="line.196"></a> <FONT color="green">197</FONT> * @param alpha significance level of the test<a name="line.197"></a> <FONT color="green">198</FONT> * @return true iff null hypothesis can be rejected with confidence<a name="line.198"></a> <FONT color="green">199</FONT> * 1 - alpha<a name="line.199"></a> <FONT color="green">200</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.200"></a> <FONT color="green">201</FONT> * @throws MathException if an error occurs performing the test<a name="line.201"></a> <FONT color="green">202</FONT> */<a name="line.202"></a> <FONT color="green">203</FONT> public boolean chiSquareTest(long[][] counts, double alpha)<a name="line.203"></a> <FONT color="green">204</FONT> throws IllegalArgumentException, MathException {<a name="line.204"></a> <FONT color="green">205</FONT> if ((alpha <= 0) || (alpha > 0.5)) {<a name="line.205"></a> <FONT color="green">206</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.206"></a> <FONT color="green">207</FONT> "out of bounds significance level {0}, must be between {1} and {2}",<a name="line.207"></a> <FONT color="green">208</FONT> alpha, 0.0, 0.5);<a name="line.208"></a> <FONT color="green">209</FONT> }<a name="line.209"></a> <FONT color="green">210</FONT> return chiSquareTest(counts) < alpha;<a name="line.210"></a> <FONT color="green">211</FONT> }<a name="line.211"></a> <FONT color="green">212</FONT> <a name="line.212"></a> <FONT color="green">213</FONT> /**<a name="line.213"></a> <FONT color="green">214</FONT> * @param observed1 array of observed frequency counts of the first data set<a name="line.214"></a> <FONT color="green">215</FONT> * @param observed2 array of observed frequency counts of the second data set<a name="line.215"></a> <FONT color="green">216</FONT> * @return chi-square test statistic<a name="line.216"></a> <FONT color="green">217</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.217"></a> <FONT color="green">218</FONT> * @since 1.2<a name="line.218"></a> <FONT color="green">219</FONT> */<a name="line.219"></a> <FONT color="green">220</FONT> public double chiSquareDataSetsComparison(long[] observed1, long[] observed2)<a name="line.220"></a> <FONT color="green">221</FONT> throws IllegalArgumentException {<a name="line.221"></a> <FONT color="green">222</FONT> <a name="line.222"></a> <FONT color="green">223</FONT> // Make sure lengths are same<a name="line.223"></a> <FONT color="green">224</FONT> if (observed1.length < 2) {<a name="line.224"></a> <FONT color="green">225</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.225"></a> <FONT color="green">226</FONT> "observed array length = {0}, must be at least 2",<a name="line.226"></a> <FONT color="green">227</FONT> observed1.length);<a name="line.227"></a> <FONT color="green">228</FONT> }<a name="line.228"></a> <FONT color="green">229</FONT> if (observed1.length != observed2.length) {<a name="line.229"></a> <FONT color="green">230</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.230"></a> <FONT color="green">231</FONT> "dimension mismatch {0} != {1}",<a name="line.231"></a> <FONT color="green">232</FONT> observed1.length, observed2.length);<a name="line.232"></a> <FONT color="green">233</FONT> }<a name="line.233"></a> <FONT color="green">234</FONT> <a name="line.234"></a> <FONT color="green">235</FONT> // Ensure non-negative counts<a name="line.235"></a> <FONT color="green">236</FONT> checkNonNegative(observed1);<a name="line.236"></a> <FONT color="green">237</FONT> checkNonNegative(observed2);<a name="line.237"></a> <FONT color="green">238</FONT> <a name="line.238"></a> <FONT color="green">239</FONT> // Compute and compare count sums<a name="line.239"></a> <FONT color="green">240</FONT> long countSum1 = 0;<a name="line.240"></a> <FONT color="green">241</FONT> long countSum2 = 0;<a name="line.241"></a> <FONT color="green">242</FONT> boolean unequalCounts = false;<a name="line.242"></a> <FONT color="green">243</FONT> double weight = 0.0;<a name="line.243"></a> <FONT color="green">244</FONT> for (int i = 0; i < observed1.length; i++) {<a name="line.244"></a> <FONT color="green">245</FONT> countSum1 += observed1[i];<a name="line.245"></a> <FONT color="green">246</FONT> countSum2 += observed2[i];<a name="line.246"></a> <FONT color="green">247</FONT> }<a name="line.247"></a> <FONT color="green">248</FONT> // Ensure neither sample is uniformly 0<a name="line.248"></a> <FONT color="green">249</FONT> if (countSum1 == 0) {<a name="line.249"></a> <FONT color="green">250</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.250"></a> <FONT color="green">251</FONT> "observed counts are all 0 in first observed array");<a name="line.251"></a> <FONT color="green">252</FONT> }<a name="line.252"></a> <FONT color="green">253</FONT> if (countSum2 == 0) {<a name="line.253"></a> <FONT color="green">254</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.254"></a> <FONT color="green">255</FONT> "observed counts are all 0 in second observed array");<a name="line.255"></a> <FONT color="green">256</FONT> }<a name="line.256"></a> <FONT color="green">257</FONT> // Compare and compute weight only if different<a name="line.257"></a> <FONT color="green">258</FONT> unequalCounts = countSum1 != countSum2;<a name="line.258"></a> <FONT color="green">259</FONT> if (unequalCounts) {<a name="line.259"></a> <FONT color="green">260</FONT> weight = Math.sqrt((double) countSum1 / (double) countSum2);<a name="line.260"></a> <FONT color="green">261</FONT> }<a name="line.261"></a> <FONT color="green">262</FONT> // Compute ChiSquare statistic<a name="line.262"></a> <FONT color="green">263</FONT> double sumSq = 0.0d;<a name="line.263"></a> <FONT color="green">264</FONT> double dev = 0.0d;<a name="line.264"></a> <FONT color="green">265</FONT> double obs1 = 0.0d;<a name="line.265"></a> <FONT color="green">266</FONT> double obs2 = 0.0d;<a name="line.266"></a> <FONT color="green">267</FONT> for (int i = 0; i < observed1.length; i++) {<a name="line.267"></a> <FONT color="green">268</FONT> if (observed1[i] == 0 && observed2[i] == 0) {<a name="line.268"></a> <FONT color="green">269</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.269"></a> <FONT color="green">270</FONT> "observed counts are both zero for entry {0}", i);<a name="line.270"></a> <FONT color="green">271</FONT> } else {<a name="line.271"></a> <FONT color="green">272</FONT> obs1 = observed1[i];<a name="line.272"></a> <FONT color="green">273</FONT> obs2 = observed2[i];<a name="line.273"></a> <FONT color="green">274</FONT> if (unequalCounts) { // apply weights<a name="line.274"></a> <FONT color="green">275</FONT> dev = obs1/weight - obs2 * weight;<a name="line.275"></a> <FONT color="green">276</FONT> } else {<a name="line.276"></a> <FONT color="green">277</FONT> dev = obs1 - obs2;<a name="line.277"></a> <FONT color="green">278</FONT> }<a name="line.278"></a> <FONT color="green">279</FONT> sumSq += (dev * dev) / (obs1 + obs2);<a name="line.279"></a> <FONT color="green">280</FONT> }<a name="line.280"></a> <FONT color="green">281</FONT> }<a name="line.281"></a> <FONT color="green">282</FONT> return sumSq;<a name="line.282"></a> <FONT color="green">283</FONT> }<a name="line.283"></a> <FONT color="green">284</FONT> <a name="line.284"></a> <FONT color="green">285</FONT> /**<a name="line.285"></a> <FONT color="green">286</FONT> * @param observed1 array of observed frequency counts of the first data set<a name="line.286"></a> <FONT color="green">287</FONT> * @param observed2 array of observed frequency counts of the second data set<a name="line.287"></a> <FONT color="green">288</FONT> * @return p-value<a name="line.288"></a> <FONT color="green">289</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.289"></a> <FONT color="green">290</FONT> * @throws MathException if an error occurs computing the p-value<a name="line.290"></a> <FONT color="green">291</FONT> * @since 1.2<a name="line.291"></a> <FONT color="green">292</FONT> */<a name="line.292"></a> <FONT color="green">293</FONT> public double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)<a name="line.293"></a> <FONT color="green">294</FONT> throws IllegalArgumentException, MathException {<a name="line.294"></a> <FONT color="green">295</FONT> distribution.setDegreesOfFreedom((double) observed1.length - 1);<a name="line.295"></a> <FONT color="green">296</FONT> return 1 - distribution.cumulativeProbability(<a name="line.296"></a> <FONT color="green">297</FONT> chiSquareDataSetsComparison(observed1, observed2));<a name="line.297"></a> <FONT color="green">298</FONT> }<a name="line.298"></a> <FONT color="green">299</FONT> <a name="line.299"></a> <FONT color="green">300</FONT> /**<a name="line.300"></a> <FONT color="green">301</FONT> * @param observed1 array of observed frequency counts of the first data set<a name="line.301"></a> <FONT color="green">302</FONT> * @param observed2 array of observed frequency counts of the second data set<a name="line.302"></a> <FONT color="green">303</FONT> * @param alpha significance level of the test<a name="line.303"></a> <FONT color="green">304</FONT> * @return true iff null hypothesis can be rejected with confidence<a name="line.304"></a> <FONT color="green">305</FONT> * 1 - alpha<a name="line.305"></a> <FONT color="green">306</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.306"></a> <FONT color="green">307</FONT> * @throws MathException if an error occurs performing the test<a name="line.307"></a> <FONT color="green">308</FONT> * @since 1.2<a name="line.308"></a> <FONT color="green">309</FONT> */<a name="line.309"></a> <FONT color="green">310</FONT> public boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2,<a name="line.310"></a> <FONT color="green">311</FONT> double alpha) throws IllegalArgumentException, MathException {<a name="line.311"></a> <FONT color="green">312</FONT> if ((alpha <= 0) || (alpha > 0.5)) {<a name="line.312"></a> <FONT color="green">313</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.313"></a> <FONT color="green">314</FONT> "out of bounds significance level {0}, must be between {1} and {2}",<a name="line.314"></a> <FONT color="green">315</FONT> alpha, 0.0, 0.5);<a name="line.315"></a> <FONT color="green">316</FONT> }<a name="line.316"></a> <FONT color="green">317</FONT> return chiSquareTestDataSetsComparison(observed1, observed2) < alpha;<a name="line.317"></a> <FONT color="green">318</FONT> }<a name="line.318"></a> <FONT color="green">319</FONT> <a name="line.319"></a> <FONT color="green">320</FONT> /**<a name="line.320"></a> <FONT color="green">321</FONT> * Checks to make sure that the input long[][] array is rectangular,<a name="line.321"></a> <FONT color="green">322</FONT> * has at least 2 rows and 2 columns, and has all non-negative entries,<a name="line.322"></a> <FONT color="green">323</FONT> * throwing IllegalArgumentException if any of these checks fail.<a name="line.323"></a> <FONT color="green">324</FONT> *<a name="line.324"></a> <FONT color="green">325</FONT> * @param in input 2-way table to check<a name="line.325"></a> <FONT color="green">326</FONT> * @throws IllegalArgumentException if the array is not valid<a name="line.326"></a> <FONT color="green">327</FONT> */<a name="line.327"></a> <FONT color="green">328</FONT> private void checkArray(long[][] in) throws IllegalArgumentException {<a name="line.328"></a> <FONT color="green">329</FONT> <a name="line.329"></a> <FONT color="green">330</FONT> if (in.length < 2) {<a name="line.330"></a> <FONT color="green">331</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.331"></a> <FONT color="green">332</FONT> "invalid row dimension: {0} (must be at least 2)",<a name="line.332"></a> <FONT color="green">333</FONT> in.length);<a name="line.333"></a> <FONT color="green">334</FONT> }<a name="line.334"></a> <FONT color="green">335</FONT> <a name="line.335"></a> <FONT color="green">336</FONT> if (in[0].length < 2) {<a name="line.336"></a> <FONT color="green">337</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.337"></a> <FONT color="green">338</FONT> "invalid column dimension: {0} (must be at least 2)",<a name="line.338"></a> <FONT color="green">339</FONT> in[0].length);<a name="line.339"></a> <FONT color="green">340</FONT> }<a name="line.340"></a> <FONT color="green">341</FONT> <a name="line.341"></a> <FONT color="green">342</FONT> checkRectangular(in);<a name="line.342"></a> <FONT color="green">343</FONT> checkNonNegative(in);<a name="line.343"></a> <FONT color="green">344</FONT> <a name="line.344"></a> <FONT color="green">345</FONT> }<a name="line.345"></a> <FONT color="green">346</FONT> <a name="line.346"></a> <FONT color="green">347</FONT> //--------------------- Private array methods -- should find a utility home for these<a name="line.347"></a> <FONT color="green">348</FONT> <a name="line.348"></a> <FONT color="green">349</FONT> /**<a name="line.349"></a> <FONT color="green">350</FONT> * Throws IllegalArgumentException if the input array is not rectangular.<a name="line.350"></a> <FONT color="green">351</FONT> *<a name="line.351"></a> <FONT color="green">352</FONT> * @param in array to be tested<a name="line.352"></a> <FONT color="green">353</FONT> * @throws NullPointerException if input array is null<a name="line.353"></a> <FONT color="green">354</FONT> * @throws IllegalArgumentException if input array is not rectangular<a name="line.354"></a> <FONT color="green">355</FONT> */<a name="line.355"></a> <FONT color="green">356</FONT> private void checkRectangular(long[][] in) {<a name="line.356"></a> <FONT color="green">357</FONT> for (int i = 1; i < in.length; i++) {<a name="line.357"></a> <FONT color="green">358</FONT> if (in[i].length != in[0].length) {<a name="line.358"></a> <FONT color="green">359</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.359"></a> <FONT color="green">360</FONT> "some rows have length {0} while others have length {1}",<a name="line.360"></a> <FONT color="green">361</FONT> in[i].length, in[0].length);<a name="line.361"></a> <FONT color="green">362</FONT> }<a name="line.362"></a> <FONT color="green">363</FONT> }<a name="line.363"></a> <FONT color="green">364</FONT> }<a name="line.364"></a> <FONT color="green">365</FONT> <a name="line.365"></a> <FONT color="green">366</FONT> /**<a name="line.366"></a> <FONT color="green">367</FONT> * Check all entries of the input array are > 0.<a name="line.367"></a> <FONT color="green">368</FONT> *<a name="line.368"></a> <FONT color="green">369</FONT> * @param in array to be tested<a name="line.369"></a> <FONT color="green">370</FONT> * @exception IllegalArgumentException if one entry is not positive<a name="line.370"></a> <FONT color="green">371</FONT> */<a name="line.371"></a> <FONT color="green">372</FONT> private void checkPositive(double[] in) throws IllegalArgumentException {<a name="line.372"></a> <FONT color="green">373</FONT> for (int i = 0; i < in.length; i++) {<a name="line.373"></a> <FONT color="green">374</FONT> if (in[i] <= 0) {<a name="line.374"></a> <FONT color="green">375</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.375"></a> <FONT color="green">376</FONT> "element {0} is not positive: {1}",<a name="line.376"></a> <FONT color="green">377</FONT> i, in[i]);<a name="line.377"></a> <FONT color="green">378</FONT> }<a name="line.378"></a> <FONT color="green">379</FONT> }<a name="line.379"></a> <FONT color="green">380</FONT> }<a name="line.380"></a> <FONT color="green">381</FONT> <a name="line.381"></a> <FONT color="green">382</FONT> /**<a name="line.382"></a> <FONT color="green">383</FONT> * Check all entries of the input array are >= 0.<a name="line.383"></a> <FONT color="green">384</FONT> *<a name="line.384"></a> <FONT color="green">385</FONT> * @param in array to be tested<a name="line.385"></a> <FONT color="green">386</FONT> * @exception IllegalArgumentException if one entry is negative<a name="line.386"></a> <FONT color="green">387</FONT> */<a name="line.387"></a> <FONT color="green">388</FONT> private void checkNonNegative(long[] in) throws IllegalArgumentException {<a name="line.388"></a> <FONT color="green">389</FONT> for (int i = 0; i < in.length; i++) {<a name="line.389"></a> <FONT color="green">390</FONT> if (in[i] < 0) {<a name="line.390"></a> <FONT color="green">391</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.391"></a> <FONT color="green">392</FONT> "element {0} is negative: {1}",<a name="line.392"></a> <FONT color="green">393</FONT> i, in[i]);<a name="line.393"></a> <FONT color="green">394</FONT> }<a name="line.394"></a> <FONT color="green">395</FONT> }<a name="line.395"></a> <FONT color="green">396</FONT> }<a name="line.396"></a> <FONT color="green">397</FONT> <a name="line.397"></a> <FONT color="green">398</FONT> /**<a name="line.398"></a> <FONT color="green">399</FONT> * Check all entries of the input array are >= 0.<a name="line.399"></a> <FONT color="green">400</FONT> *<a name="line.400"></a> <FONT color="green">401</FONT> * @param in array to be tested<a name="line.401"></a> <FONT color="green">402</FONT> * @exception IllegalArgumentException if one entry is negative<a name="line.402"></a> <FONT color="green">403</FONT> */<a name="line.403"></a> <FONT color="green">404</FONT> private void checkNonNegative(long[][] in) throws IllegalArgumentException {<a name="line.404"></a> <FONT color="green">405</FONT> for (int i = 0; i < in.length; i ++) {<a name="line.405"></a> <FONT color="green">406</FONT> for (int j = 0; j < in[i].length; j++) {<a name="line.406"></a> <FONT color="green">407</FONT> if (in[i][j] < 0) {<a name="line.407"></a> <FONT color="green">408</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.408"></a> <FONT color="green">409</FONT> "element ({0}, {1}) is negative: {2}",<a name="line.409"></a> <FONT color="green">410</FONT> i, j, in[i][j]);<a name="line.410"></a> <FONT color="green">411</FONT> }<a name="line.411"></a> <FONT color="green">412</FONT> }<a name="line.412"></a> <FONT color="green">413</FONT> }<a name="line.413"></a> <FONT color="green">414</FONT> }<a name="line.414"></a> <FONT color="green">415</FONT> <a name="line.415"></a> <FONT color="green">416</FONT> /**<a name="line.416"></a> <FONT color="green">417</FONT> * Modify the distribution used to compute inference statistics.<a name="line.417"></a> <FONT color="green">418</FONT> *<a name="line.418"></a> <FONT color="green">419</FONT> * @param value<a name="line.419"></a> <FONT color="green">420</FONT> * the new distribution<a name="line.420"></a> <FONT color="green">421</FONT> * @since 1.2<a name="line.421"></a> <FONT color="green">422</FONT> */<a name="line.422"></a> <FONT color="green">423</FONT> public void setDistribution(ChiSquaredDistribution value) {<a name="line.423"></a> <FONT color="green">424</FONT> distribution = value;<a name="line.424"></a> <FONT color="green">425</FONT> }<a name="line.425"></a> <FONT color="green">426</FONT> }<a name="line.426"></a> </PRE> </BODY> </HTML>