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Fixed some errors, improved content. 

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@764343 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Phil Steitz 2009-04-12 23:55:45 +00:00
parent 9f0ea4e9c4
commit 6206817ffb
1 changed files with 25 additions and 16 deletions
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41
src/site/xdoc/userguide/stat.xml
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@ -513,13 +513,13 @@ regression.addData(y, x, omega); // we do need covariance
where <code>E(X)</code> is the mean of <code>X</code> and <code>E(Y)</code>
is the mean of the <code>Y</code> values. Non-bias-corrected estimates use
<code>n</code> in place of <code>n - 1.</code> Whether or not covariances are
bias-corrected is determined by the optional constructor parameter,
"biasCorrected," which defaults to <code>true.</code>
bias-corrected is determined by the optional parameter, "biasCorrected," which
defaults to <code>true.</code>
</li>
<li>
<a href="../apidocs/org/apache/commons/math/stat/correlation/PearsonsCorrelation.html">
PearsonsCorrelation</a> computes corralations defined by the formula <br></br>
<code>cor(X, Y) = sum[(x<sub>i</sub> - E(X))(y<sub>i</sub> - E(Y))] / [(n - 1)s(X)s(Y)]</code>
PearsonsCorrelation</a> computes correlations defined by the formula <br></br>
<code>cor(X, Y) = sum[(x<sub>i</sub> - E(X))(y<sub>i</sub> - E(Y))] / [(n - 1)s(X)s(Y)]</code><br/>
where <code>E(X)</code> and <code>E(Y)</code> are means of <code>X</code> and <code>Y</code>
and <code>s(X)</code>, <code>s(Y)</code> are standard deviations.
</li>
@ -579,8 +579,8 @@ new PearsonsCorrelation().computeCorrelationMatrix(data)
<dt><strong>Pearson's correlation significance and standard errors</strong></dt>
<br></br>
<dd> To compute standard errors and/or significances of correlation coefficients
associated with Pearson's correlation coefficients, start by creating a PearsonsCorrelation
instance from the data <code>data</code> using
associated with Pearson's correlation coefficients, start by creating a
<code>PearsonsCorrelation</code> instance
<source>
PearsonsCorrelation correlation = new PearsonsCorrelation(data);
</source>
@ -593,16 +593,25 @@ correlation.getCorrelationStandardErrors();
<code>SE<sub>r</sub> = ((1 - r<sup>2</sup>) / (n - 2))<sup>1/2</sup></code><br/>
where <code>r</code> is the estimated correlation coefficient and
<code>n</code> is the number of observations in the source dataset.<br/><br/>
<strong>p-values</strong> for the null hypothesis that respective coefficients are zero (also known as
<i>significances</i>) populate the <code>RealMatrix</code> returned by
<strong>p-values</strong> for the (2-sided) null hypotheses that elements of
a correlation matrix are zero populate the RealMatrix returned by
<source>
correlation.getCorrelationPValues();
correlation.getCorrelationPValues()
</source>
<code>getCorrelationPValues().getEntry(i,j)</code> is the probability
that a random variable distributed as <code>t<sub>n-2</sub></code> takes
<code>getCorrelationPValues().getEntry(i,j)</code> is the
probability that a random variable distributed as <code>t<sub>n-2</sub></code> takes
a value with absolute value greater than or equal to <br></br>
<code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code>, where <code>r</code>
is the estimated correlation coefficient.
<code>|r<sub>ij</sub>|((n - 2) / (1 - r<sub>ij</sub><sup>2</sup>))<sup>1/2</sup></code>,
where <code>r<sub>ij</sub></code> is the estimated correlation between the ith and jth
columns of the source array or RealMatrix. This is sometimes referred to as the
<i>significance</i> of the coefficient.<br/><br/>
For example, if <code>data</code> is a RealMatrix with 2 columns and 10 rows, then
<source>
new PearsonsCorrelation(data).getCorrelationPValues().getEntry(0,1)
</source>
is the significance of the Pearson's correlation coefficient between the two columns
of <code>data</code>. If this value is less than .01, we can say that the correlation
between the two columns of data is significant at the 99% level.
</dd>
<br></br>
</dl>
@ -691,7 +700,7 @@ correlation.getCorrelationPValues();
<source>
double[] observed = {1d, 2d, 3d};
double mu = 2.5d;
System.out.println(TestUtils.t(mu, observed);
System.out.println(TestUtils.t(mu, observed));
</source>
The code above will display the t-statisitic associated with a one-sample
t-test comparing the mean of the <code>observed</code> values against
@ -708,7 +717,7 @@ sampleStats = SummaryStatistics.newInstance();
for (int i = 0; i &lt; observed.length; i++) {
sampleStats.addValue(observed[i]);
}
System.out.println(TestUtils.t(mu, observed);
System.out.println(TestUtils.t(mu, observed));
</source>
</dd>
<dd>To compute the p-value associated with the null hypothesis that the mean
@ -717,7 +726,7 @@ System.out.println(TestUtils.t(mu, observed);
<source>
double[] observed = {1d, 2d, 3d};
double mu = 2.5d;
System.out.println(TestUtils.tTest(mu, observed);
System.out.println(TestUtils.tTest(mu, observed));
</source>
The snippet above will display the p-value associated with the null
hypothesis that the mean of the population from which the