Fixed userguide typos.
Thanks to Matt Adereth for the patch. JIRA: MATH-1048 git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1536265 13f79535-47bb-0310-9956-ffa450edef68
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Luc Maisonobe
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@ -302,7 +302,7 @@ double totalSampleSum = aggregatedStats.getSum();
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Strings, integers, longs and chars are all supported as value types,
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as well as instances of any class that implements <code>Comparable.</code>
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The ordering of values used in computing cumulative frequencies is by
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default the <i>natural ordering,</i> but this can be overriden by supplying a
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default the <i>natural ordering,</i> but this can be overridden by supplying a
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<code>Comparator</code> to the constructor. Adding values that are not
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comparable to those that have already been added results in an
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<code>IllegalArgumentException.</code>
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@ -385,7 +385,7 @@ System.out.println(f.getCumPct("z")); // displays 1
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<li> When there are fewer than two observations in the model, or when
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there is no variation in the x values (i.e. all x values are the same)
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all statistics return <code>NaN</code>. At least two observations with
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different x coordinates are requred to estimate a bivariate regression
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different x coordinates are required to estimate a bivariate regression
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model.</li>
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<li> getters for the statistics always compute values based on the current
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set of observations -- i.e., you can get statistics, then add more data
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@ -529,7 +529,7 @@ System.out.println(regression.getInterceptStdErr() );
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OLSMultipleLinearRegression</a> provides Ordinary Least Squares Regression, and
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<a href="../apidocs/org/apache/commons/math3/stat/regression/GLSMultipleLinearRegression.html">
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GLSMultipleLinearRegression</a> implements Generalized Least Squares. See the javadoc for these
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classes for details on the algorithms and forumlas used.
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classes for details on the algorithms and formulas used.
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</p>
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<p>
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Data for OLS models can be loaded in a single double[] array, consisting of concatenated rows of data, each containing
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@ -864,7 +864,7 @@ new PearsonsCorrelation().correlation(ranking.rank(x), ranking.rank(y))
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assumptions of the parametric t-test procedure, as discussed
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<a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
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here</a></li>
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<li>p-values returned by t-, chi-square and Anova tests are exact, based
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<li>p-values returned by t-, chi-square and ANOVA tests are exact, based
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on numerical approximations to the t-, chi-square and F distributions in the
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<code>distributions</code> package. </li>
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<li>The G test implementation provides two p-values:
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@ -893,7 +893,7 @@ double[] observed = {1d, 2d, 3d};
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double mu = 2.5d;
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System.out.println(TestUtils.t(mu, observed));
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</source>
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The code above will display the t-statisitic associated with a one-sample
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The code above will display the t-statistic associated with a one-sample
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t-test comparing the mean of the <code>observed</code> values against
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<code>mu.</code>
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</dd>
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@ -1026,7 +1026,7 @@ TestUtils.chiSquareTest(expected, observed);
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</source>
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</dd>
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<dd> To test the null hypothesis that <code>observed</code> conforms to
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<code>expected</code> with <code>alpha</code> siginficance level
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<code>expected</code> with <code>alpha</code> significance level
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(equiv. <code>100 * (1-alpha)%</code> confidence) where <code>
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0 < alpha < 1 </code> use:
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<source>
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@ -1058,7 +1058,7 @@ TestUtils.chiSquareTest(counts);
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</source>
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</dd>
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<dd>To perform a chi-square test of independence with <code>alpha</code>
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siginficance level (equiv. <code>100 * (1-alpha)%</code> confidence)
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significance level (equiv. <code>100 * (1-alpha)%</code> confidence)
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where <code>0 < alpha < 1 </code> use:
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<source>
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TestUtils.chiSquareTest(counts, alpha);
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@ -1070,12 +1070,12 @@ TestUtils.chiSquareTest(counts, alpha);
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<dt><strong>G tests</strong></dt>
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<br></br>
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<dd>G tests are an alternative to chi-square tests that are recommended
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when observed counts are small and / or incidence probabillities for
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when observed counts are small and / or incidence probabilities for
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some cells are small. See Ted Dunning's paper,
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<a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.5962">
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Accurate Methods for the Statistics of Surprise and Coincidence</a> for
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background and an empirical analysis showing now chi-square
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statistics can be misldeading in the presence of low incidence probabilities.
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statistics can be misleading in the presence of low incidence probabilities.
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This paper also derives the formulas used in computing G statistics and the
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root log likelihood ratio provided by the <code>GTest</code> class.</dd>
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<dd>
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@ -1116,7 +1116,7 @@ System.out.println(TestUtils.gDataSetsComparison(obs1, obs2)); // G statistic
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System.out.println(TestUtils.gTestDataSetsComparison(obs1, obs2)); // p-value
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</source>
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</dd>
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<dd>For 2 x 2 designs, the <code>rootLogLikelihoodRaio</code> method
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<dd>For 2 x 2 designs, the <code>rootLogLikelihoodRatio</code> method
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computes the
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<a href="http://tdunning.blogspot.com/2008/03/surprise-and-coincidence.html">
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signed root log likelihood ratio.</a> For example, suppose that for two events
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@ -1129,7 +1129,7 @@ new GTest().rootLogLikelihoodRatio(5, 1995, 0, 100000);
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and B are independent.
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</dd>
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<br></br>
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<dt><strong>One-Way Anova tests</strong></dt>
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<dt><strong>One-Way ANOVA tests</strong></dt>
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<br></br>
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<source>
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double[] classA =
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@ -1151,7 +1151,7 @@ classes.add(classC);
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double fStatistic = TestUtils.oneWayAnovaFValue(classes); // F-value
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double pValue = TestUtils.oneWayAnovaPValue(classes); // P-value
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</source>
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To test perform a One-Way Anova test with signficance level set at 0.01
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To test perform a One-Way ANOVA test with significance level set at 0.01
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(so the test will, assuming assumptions are met, reject the null
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hypothesis incorrectly only about one in 100 times), use
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<source>
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