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33      * frequency counts.
36 * the observed counts follow the expected distribution.</p>
39 * <li>Expected counts must all be positive.
41 * <li>Observed counts must all be >= 0.
49 * @param observed array of observed frequency counts
50 * @param expected array of expected frequency counts
63 * frequency counts to those in the <code>expected</code> array.
66 * the null hypothesis that the observed counts conform to the frequency distribution
67 * described by the expected counts.</p>
70 * <li>Expected counts must all be positive.
72 * <li>Observed counts must all be >= 0.
80 * @param observed array of observed frequency counts
81 * @param expected array of expected frequency counts
91 * Chi-square goodness of fit test</a> evaluating the null hypothesis that the observed counts
92 * conform to the frequency distribution described by the expected counts, with
102 * <li>Expected counts must all be positive.
104 * <li>Observed counts must all be >= 0.
113 * @param observed array of observed frequency counts
114 * @param expected array of expected frequency counts
127 * chi-square test of independence</a> based on the input <code>counts</code>
134 * <li>All counts must be >= 0.
139 * <li>The 2-way table represented by <code>counts</code> must have at
146 * @param counts array representation of 2-way table
150 double chiSquare(long[][] counts)
158 * chi-square test of independence</a> based on the input <code>counts</code>
165 * <li>All counts must be >= 0.
169 * <li>The 2-way table represented by <code>counts</code> must have at least 2 columns and
176 * @param counts array representation of 2-way table
181 double chiSquareTest(long[][] counts)
187 * represented by the counts in the columns of the input 2-way table are independent of the rows,
195 * To test the null hypothesis that the counts in
198 * <code>chiSquareTest(counts, 0.01) </code></p>
201 * <li>All counts must be >= 0.
205 * <li>The 2-way table represented by <code>counts</code> must have at least 2 columns and
212 * @param counts array representation of 2-way table
219 boolean chiSquareTest(long[][] counts, double alpha)