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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 for unknown distributions.<a name="line.22"></a> <FONT color="green">023</FONT> * <p>Two samples tests are used when the distribution is unknown <i>a priori</i><a name="line.23"></a> <FONT color="green">024</FONT> * but provided by one sample. We compare the second sample against the first.</p><a name="line.24"></a> <FONT color="green">025</FONT> *<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> * @since 1.2<a name="line.27"></a> <FONT color="green">028</FONT> */<a name="line.28"></a> <FONT color="green">029</FONT> public interface UnknownDistributionChiSquareTest extends ChiSquareTest {<a name="line.29"></a> <FONT color="green">030</FONT> <a name="line.30"></a> <FONT color="green">031</FONT> /**<a name="line.31"></a> <FONT color="green">032</FONT> * <p>Computes a<a name="line.32"></a> <FONT color="green">033</FONT> * <a href="http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/chi2samp.htm"><a name="line.33"></a> <FONT color="green">034</FONT> * Chi-Square two sample test statistic</a> comparing bin frequency counts<a name="line.34"></a> <FONT color="green">035</FONT> * in <code>observed1</code> and <code>observed2</code>. The<a name="line.35"></a> <FONT color="green">036</FONT> * sums of frequency counts in the two samples are not required to be the<a name="line.36"></a> <FONT color="green">037</FONT> * same. The formula used to compute the test statistic is</p><a name="line.37"></a> <FONT color="green">038</FONT> * <code><a name="line.38"></a> <FONT color="green">039</FONT> * &sum;[(K * observed1[i] - observed2[i]/K)<sup>2</sup> / (observed1[i] + observed2[i])]<a name="line.39"></a> <FONT color="green">040</FONT> * </code> where<a name="line.40"></a> <FONT color="green">041</FONT> * <br/><code>K = &sqrt;[&sum(observed2 / &sum;(observed1)]</code><a name="line.41"></a> <FONT color="green">042</FONT> * </p><a name="line.42"></a> <FONT color="green">043</FONT> * <p>This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that<a name="line.43"></a> <FONT color="green">044</FONT> * both observed counts follow the same distribution.</p><a name="line.44"></a> <FONT color="green">045</FONT> * <p><a name="line.45"></a> <FONT color="green">046</FONT> * <strong>Preconditions</strong>: <ul><a name="line.46"></a> <FONT color="green">047</FONT> * <li>Observed counts must be non-negative.<a name="line.47"></a> <FONT color="green">048</FONT> * </li><a name="line.48"></a> <FONT color="green">049</FONT> * <li>Observed counts for a specific bin must not both be zero.<a name="line.49"></a> <FONT color="green">050</FONT> * </li><a name="line.50"></a> <FONT color="green">051</FONT> * <li>Observed counts for a specific sample must not all be 0.<a name="line.51"></a> <FONT color="green">052</FONT> * </li><a name="line.52"></a> <FONT color="green">053</FONT> * <li>The arrays <code>observed1</code> and <code>observed2</code> must have the same length and<a name="line.53"></a> <FONT color="green">054</FONT> * their common length must be at least 2.<a name="line.54"></a> <FONT color="green">055</FONT> * </li></ul></p><p><a name="line.55"></a> <FONT color="green">056</FONT> * If any of the preconditions are not met, an<a name="line.56"></a> <FONT color="green">057</FONT> * <code>IllegalArgumentException</code> is thrown.</p><a name="line.57"></a> <FONT color="green">058</FONT> *<a name="line.58"></a> <FONT color="green">059</FONT> * @param observed1 array of observed frequency counts of the first data set<a name="line.59"></a> <FONT color="green">060</FONT> * @param observed2 array of observed frequency counts of the second data set<a name="line.60"></a> <FONT color="green">061</FONT> * @return chiSquare statistic<a name="line.61"></a> <FONT color="green">062</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.62"></a> <FONT color="green">063</FONT> */<a name="line.63"></a> <FONT color="green">064</FONT> double chiSquareDataSetsComparison(long[] observed1, long[] observed2)<a name="line.64"></a> <FONT color="green">065</FONT> throws IllegalArgumentException;<a name="line.65"></a> <FONT color="green">066</FONT> <a name="line.66"></a> <FONT color="green">067</FONT> /**<a name="line.67"></a> <FONT color="green">068</FONT> * <p>Returns the <i>observed significance level</i>, or <a href=<a name="line.68"></a> <FONT color="green">069</FONT> * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"><a name="line.69"></a> <FONT color="green">070</FONT> * p-value</a>, associated with a Chi-Square two sample test comparing<a name="line.70"></a> <FONT color="green">071</FONT> * bin frequency counts in <code>observed1</code> and<a name="line.71"></a> <FONT color="green">072</FONT> * <code>observed2</code>.<a name="line.72"></a> <FONT color="green">073</FONT> * </p><a name="line.73"></a> <FONT color="green">074</FONT> * <p>The number returned is the smallest significance level at which one<a name="line.74"></a> <FONT color="green">075</FONT> * can reject the null hypothesis that the observed counts conform to the<a name="line.75"></a> <FONT color="green">076</FONT> * same distribution.<a name="line.76"></a> <FONT color="green">077</FONT> * </p><a name="line.77"></a> <FONT color="green">078</FONT> * <p>See {@link #chiSquareDataSetsComparison(long[], long[])} for details<a name="line.78"></a> <FONT color="green">079</FONT> * on the formula used to compute the test statistic. The degrees of<a name="line.79"></a> <FONT color="green">080</FONT> * of freedom used to perform the test is one less than the common length<a name="line.80"></a> <FONT color="green">081</FONT> * of the input observed count arrays.<a name="line.81"></a> <FONT color="green">082</FONT> * </p><a name="line.82"></a> <FONT color="green">083</FONT> * <strong>Preconditions</strong>: <ul><a name="line.83"></a> <FONT color="green">084</FONT> * <li>Observed counts must be non-negative.<a name="line.84"></a> <FONT color="green">085</FONT> * </li><a name="line.85"></a> <FONT color="green">086</FONT> * <li>Observed counts for a specific bin must not both be zero.<a name="line.86"></a> <FONT color="green">087</FONT> * </li><a name="line.87"></a> <FONT color="green">088</FONT> * <li>Observed counts for a specific sample must not all be 0.<a name="line.88"></a> <FONT color="green">089</FONT> * </li><a name="line.89"></a> <FONT color="green">090</FONT> * <li>The arrays <code>observed1</code> and <code>observed2</code> must<a name="line.90"></a> <FONT color="green">091</FONT> * have the same length and<a name="line.91"></a> <FONT color="green">092</FONT> * their common length must be at least 2.<a name="line.92"></a> <FONT color="green">093</FONT> * </li></ul><p><a name="line.93"></a> <FONT color="green">094</FONT> * If any of the preconditions are not met, an<a name="line.94"></a> <FONT color="green">095</FONT> * <code>IllegalArgumentException</code> is thrown.</p><a name="line.95"></a> <FONT color="green">096</FONT> *<a name="line.96"></a> <FONT color="green">097</FONT> * @param observed1 array of observed frequency counts of the first data set<a name="line.97"></a> <FONT color="green">098</FONT> * @param observed2 array of observed frequency counts of the second data set<a name="line.98"></a> <FONT color="green">099</FONT> * @return p-value<a name="line.99"></a> <FONT color="green">100</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.100"></a> <FONT color="green">101</FONT> * @throws MathException if an error occurs computing the p-value<a name="line.101"></a> <FONT color="green">102</FONT> */<a name="line.102"></a> <FONT color="green">103</FONT> double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)<a name="line.103"></a> <FONT color="green">104</FONT> throws IllegalArgumentException, MathException;<a name="line.104"></a> <FONT color="green">105</FONT> <a name="line.105"></a> <FONT color="green">106</FONT> /**<a name="line.106"></a> <FONT color="green">107</FONT> * <p>Performs a Chi-Square two sample test comparing two binned data<a name="line.107"></a> <FONT color="green">108</FONT> * sets. The test evaluates the null hypothesis that the two lists of<a name="line.108"></a> <FONT color="green">109</FONT> * observed counts conform to the same frequency distribution, with<a name="line.109"></a> <FONT color="green">110</FONT> * significance level <code>alpha</code>. Returns true iff the null<a name="line.110"></a> <FONT color="green">111</FONT> * hypothesis can be rejected with 100 * (1 - alpha) percent confidence.<a name="line.111"></a> <FONT color="green">112</FONT> * </p><a name="line.112"></a> <FONT color="green">113</FONT> * <p>See {@link #chiSquareDataSetsComparison(long[], long[])} for<a name="line.113"></a> <FONT color="green">114</FONT> * details on the formula used to compute the Chisquare statistic used<a name="line.114"></a> <FONT color="green">115</FONT> * in the test. The degrees of of freedom used to perform the test is<a name="line.115"></a> <FONT color="green">116</FONT> * one less than the common length of the input observed count arrays.<a name="line.116"></a> <FONT color="green">117</FONT> * </p><a name="line.117"></a> <FONT color="green">118</FONT> * <strong>Preconditions</strong>: <ul><a name="line.118"></a> <FONT color="green">119</FONT> * <li>Observed counts must be non-negative.<a name="line.119"></a> <FONT color="green">120</FONT> * </li><a name="line.120"></a> <FONT color="green">121</FONT> * <li>Observed counts for a specific bin must not both be zero.<a name="line.121"></a> <FONT color="green">122</FONT> * </li><a name="line.122"></a> <FONT color="green">123</FONT> * <li>Observed counts for a specific sample must not all be 0.<a name="line.123"></a> <FONT color="green">124</FONT> * </li><a name="line.124"></a> <FONT color="green">125</FONT> * <li>The arrays <code>observed1</code> and <code>observed2</code> must<a name="line.125"></a> <FONT color="green">126</FONT> * have the same length and their common length must be at least 2.<a name="line.126"></a> <FONT color="green">127</FONT> * </li><a name="line.127"></a> <FONT color="green">128</FONT> * <li> <code> 0 < alpha < 0.5 </code><a name="line.128"></a> <FONT color="green">129</FONT> * </li></ul><p><a name="line.129"></a> <FONT color="green">130</FONT> * If any of the preconditions are not met, an<a name="line.130"></a> <FONT color="green">131</FONT> * <code>IllegalArgumentException</code> is thrown.</p><a name="line.131"></a> <FONT color="green">132</FONT> *<a name="line.132"></a> <FONT color="green">133</FONT> * @param observed1 array of observed frequency counts of the first data set<a name="line.133"></a> <FONT color="green">134</FONT> * @param observed2 array of observed frequency counts of the second data set<a name="line.134"></a> <FONT color="green">135</FONT> * @param alpha significance level of the test<a name="line.135"></a> <FONT color="green">136</FONT> * @return true iff null hypothesis can be rejected with confidence<a name="line.136"></a> <FONT color="green">137</FONT> * 1 - alpha<a name="line.137"></a> <FONT color="green">138</FONT> * @throws IllegalArgumentException if preconditions are not met<a name="line.138"></a> <FONT color="green">139</FONT> * @throws MathException if an error occurs performing the test<a name="line.139"></a> <FONT color="green">140</FONT> */<a name="line.140"></a> <FONT color="green">141</FONT> boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)<a name="line.141"></a> <FONT color="green">142</FONT> throws IllegalArgumentException, MathException;<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> </PRE> </BODY> </HTML>