# Class Statistics

java.lang.Object
org.cicirello.math.stats.Statistics

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

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`
`stdev(double[] data)`
Computes the sample standard deviation.
`static double`
`stdev(int[] data)`
Computes the sample standard deviation.
`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 Details

• ### 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.
• ### stdev

public static double stdev(int[] data)
Computes the sample standard deviation.
Parameters:
`data` - The dataset.
Returns:
the sample standard deviation.
• ### stdev

public static double stdev(double[] data)
Computes the sample standard deviation.
Parameters:
`data` - The dataset.
Returns:
the sample standard deviation.
• ### 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).