## Class Statistics

• ```public final class Statistics
extends Object```
Utility class of basic statistics.
• ### Method Summary

All Methods
Modifier and Type Method Description
`static double` ```correlation​(double[] X, double[] Y)```
Computes correlation coefficient for a pair of random variables.
`static double` ```correlation​(int[] X, int[] Y)```
Computes correlation coefficient for a pair of random variables.
`static double[][]` `correlationMatrix​(double[][] data)`
Computes correlation matrix.
`static double[][]` `correlationMatrix​(int[][] data)`
Computes correlation matrix.
`static double` ```covariance​(double[] X, double[] Y)```
Computes covariance for a pair of random variables.
`static double` ```covariance​(int[] X, int[] Y)```
Computes covariance for a pair of random variables.
`static double` `mean​(double[] data)`
Computes mean of a dataset.
`static double` `mean​(int[] data)`
Computes mean of a dataset.
`static double` ```tTestUnequalVariances​(double[] data1, double[] data2)```
Welch's t-test, also known as t-test with unequal variances.
`static double` ```tTestUnequalVariances​(int[] data1, int[] data2)```
Welch's t-test, also known as t-test with unequal variances.
`static Number[]` ```tTestWelch​(double[] data1, double[] data2)```
Welch's t-test, also known as t-test with unequal variances.
`static Number[]` ```tTestWelch​(int[] data1, int[] data2)```
Welch's t-test, also known as t-test with unequal variances.
`static double` `variance​(double[] data)`
Computes variance of a population.
`static double` `variance​(int[] data)`
Computes variance of a population.
`static double` `varianceSample​(double[] data)`
Computes variance of a sample.
`static double` `varianceSample​(int[] data)`
Computes variance of a sample.
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Method Detail

• #### mean

`public static double mean​(int[] data)`
Computes mean of a dataset.
Parameters:
`data` - The dataset.
Returns:
the mean of the data.
• #### mean

`public static double mean​(double[] data)`
Computes mean of a dataset.
Parameters:
`data` - The dataset.
Returns:
the mean of the data.
• #### variance

`public static double variance​(int[] data)`
Computes variance of a population.
Parameters:
`data` - The dataset.
Returns:
the variance of the data.
• #### variance

`public static double variance​(double[] data)`
Computes variance of a population.
Parameters:
`data` - The dataset.
Returns:
the variance of the data.
• #### varianceSample

`public static double varianceSample​(int[] data)`
Computes variance of a sample.
Parameters:
`data` - The dataset.
Returns:
the variance of the data.
• #### varianceSample

`public static double varianceSample​(double[] data)`
Computes variance of a sample.
Parameters:
`data` - The dataset.
Returns:
the variance of the data.
• #### covariance

```public static double covariance​(int[] X,
int[] Y)```
Computes covariance for a pair of random variables.
Parameters:
`X` - Array of samples of first variable.
`Y` - Array of samples of second variable.
Returns:
the covariance of X and Y.
• #### covariance

```public static double covariance​(double[] X,
double[] Y)```
Computes covariance for a pair of random variables.
Parameters:
`X` - Array of samples of first variable.
`Y` - Array of samples of second variable.
Returns:
the covariance of X and Y.
• #### correlation

```public static double correlation​(int[] X,
int[] Y)```
Computes correlation coefficient for a pair of random variables.
Parameters:
`X` - Array of samples of first variable.
`Y` - Array of samples of second variable.
Returns:
the correlation coefficient of X and Y.
• #### correlation

```public static double correlation​(double[] X,
double[] Y)```
Computes correlation coefficient for a pair of random variables.
Parameters:
`X` - Array of samples of first variable.
`Y` - Array of samples of second variable.
Returns:
the correlation coefficient of X and Y.
• #### correlationMatrix

`public static double[][] correlationMatrix​(int[][] data)`
Computes correlation matrix.
Parameters:
`data` - The data with random variables in rows and samples in columns.
Returns:
the correlation matrix, M, where M[i][j] is the correlation coefficient of data[i] and data[j].
• #### correlationMatrix

`public static double[][] correlationMatrix​(double[][] data)`
Computes correlation matrix.
Parameters:
`data` - The data with random variables in rows and samples in columns.
Returns:
the correlation matrix, M, where M[i][j] is the correlation coefficient of data[i] and data[j].
• #### tTestUnequalVariances

```public static double tTestUnequalVariances​(double[] data1,
double[] data2)```
Welch's t-test, also known as t-test with unequal variances. The Welch's t-test can be used when variances are unequal and is also applicable if sample sizes differ.
Parameters:
`data1` - First dataset.
`data2` - Second dataset.
Returns:
The t statistic.
• #### tTestUnequalVariances

```public static double tTestUnequalVariances​(int[] data1,
int[] data2)```
Welch's t-test, also known as t-test with unequal variances. The Welch's t-test can be used when variances are unequal and is also applicable if sample sizes differ.
Parameters:
`data1` - First dataset.
`data2` - Second dataset.
Returns:
The t statistic.
• #### tTestWelch

```public static Number[] tTestWelch​(double[] data1,
double[] data2)```
Welch's t-test, also known as t-test with unequal variances. The Welch's t-test can be used when variances are unequal and is also applicable if sample sizes differ. This method computes both the t statistic, as well as the approximate degrees of freedom.
Parameters:
`data1` - First dataset.
`data2` - Second dataset.
Returns:
An array, a, of length 2 such that a is the t statistic (as a Double object), and a is the degrees of freedom (as an Integer object).
• #### tTestWelch

```public static Number[] tTestWelch​(int[] data1,
int[] data2)```
Welch's t-test, also known as t-test with unequal variances. The Welch's t-test can be used when variances are unequal and is also applicable if sample sizes differ. This method computes both the t statistic, as well as the approximate degrees of freedom.
Parameters:
`data1` - First dataset.
`data2` - Second dataset.
Returns:
An array, a, of length 2 such that a is the t statistic (as a Double object), and a is the degrees of freedom (as an Integer object).