AQStat (OpenAPI)

```
public interface AQStat
```

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method and Description
`double[]`	`ANOVA(double[][] x)` Calculates one way ANOVA for incoming series of arrays [link]
`boolean`	`ANOVATest(double[][] x, double significanceLevel)` Performs one way ANOVA Test for incoming series of arrays [link]
`double[]`	`bins(double[] x, int binNumber)` Sorts incoming data into user defined number of uniformly spaced bins [link]
`double`	`Chi2(double[] expected, long[] observed)` Performs a Pearson's Chi² test on incoming array.
`double[][]`	`correlation(double[][] x)` Calculates correlation matrix of incoming double precision MxN array.
`double`	`correlation(double[] x, double[] y)` Calculates the Pearson's correlation coefficient from 2 data sets, and the associated t-test and p-values.
`double[][]`	`covariance(double[][] x)` Calculates covariance matrix of incoming double precision MxN array [link]
`double`	`covariance(double[] x, double[] y)` Calculates the covariance coefficient from 2 data sets [link]
`double`	`cumNormalDist(double z)` Calculates value of cumulative normal distribution at z [link]
`double[][]`	`frequency(double[] x)` Calculates values to be displayed in frequency table.
`java.lang.String`	`frequencyTable(double[] x)` Calculates frequency table for incoming array.
`double`	`geometricMean(double[] in)` Calculates geometric mean of incoming array.
`double`	`harmonicMean(double[] in)` Calculates harmonic mean of incoming array.
`double`	`interquartilerange(double[] in)` Calculates difference between 25th and 75th quartile of incoming array.
`double`	`kruskalWallis(double[][] x)` Performs Kruskal-Wallis one way ANOVA.
`double`	`kurtosis(double[] in)` Calculates kurtosis of incoming array.
`double[]`	`mannWhitneyU(double[] x, double[] y)` Performs Mann-Whitney U test.
`double`	`max(double[] in)` Calculates maximum value in incoming array.
`double`	`mean(double[] in)` Calculates the arithmetic mean of incoming array.
`double`	`median(double[] in)` Calculates median value in incoming array.
`double`	`min(double[] in)` Calculates minimum value in incoming array.
`double`	`mode(double[] in)` Calculates mode of incoming array.
`double`	`pairedTTest(double[] x, double[] y)` Performs a paired sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean 0 and unknown variance, against the alternative that the mean is not 0.
`double`	`percentile(double[] in, double k)` Calculates value of kth percentile of incoming array [link]
`double`	`range(double[] in)` Calculates range of incoming array.
`double`	`rSquared(double[] x, double[] y)` Calculates coefficient of determination (R²).
`double`	`signedRank(double[] x, double M)` Performs a signed rank test (Wilcoxon signed rank) of the null hypothesis that data in the vector x comes from a continuous, symmetric distribution with median M, against the alternative that the distribution does not have median M.
`double`	`signedRank(double[] x, double[] y)` Performs a paired, signed rank test (Wilcoxon signed rank) of the null hypothesis that data in the vector x-y come from a continuous, symmetric distribution with equal medians, against the alternative that the distribution does not have equal medians.
`double`	`skew(double[] in)` Calculates skew (symmetry) of incoming array.
`double`	`spearman(double[] x, double[] y)` Calculates the Spearman rank correlation coefficient from 2 data sets [link]
`double`	`sse(double[] in)` Calculates the sum squared error of incoming array.
`double`	`std(double[] in)` Calculates standard deviation of incoming array.
`double`	`tTest(double[] x)` Performs a single sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean 0 and unknown variance, against the alternative that the mean is not 0.
`double`	`tTest(double[] x, double m)` Performs a single sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean m and unknown variance, against the alternative that the mean is not m.
`double`	`tTest(double[] x, double[] y)` performs a t-test of the null hypothesis that data in the vectors x and y are independent random samples from normal distributions with equal means and equal but unknown variances, against the alternative that the means are not equal.
`double`	`variance(double[] in)` Calculates variance of incoming array.
`double[]`	`zscore(double[] in)` Calculates z-scores of incoming array.
`double`	`ztest(double[] x, double mu, double sigma)` Performs a z-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean m and standard deviation sigma, against the alternative that the mean is not m.

- Method Detail
  - mean
```
double mean(double[] in)
```
    Calculates the arithmetic mean of incoming array. [link]
    
    Parameters:
    
    in - A double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - range
```
double range(double[] in)
```
    Calculates range of incoming array. Differece between min and max values. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - std
```
double std(double[] in)
```
    Calculates standard deviation of incoming array. Measures variability of incoming data. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - variance
```
double variance(double[] in)
```
    Calculates variance of incoming array. Measures variability of incoming data. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - kurtosis
```
double kurtosis(double[] in)
```
    Calculates kurtosis of incoming array. Degree to which data departs from a normal distribution, in terms of "peakedness." A normal distribution has kurtosis of 1. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - skew
```
double skew(double[] in)
```
    Calculates skew (symmetry) of incoming array. Degree to which data is centered about the mean. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - median
```
double median(double[] in)
```
    Calculates median value in incoming array. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - mode
```
double mode(double[] in)
```
    Calculates mode of incoming array. Most commonly occurring value. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - max
```
double max(double[] in)
```
    Calculates maximum value in incoming array.
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - min
```
double min(double[] in)
```
    Calculates minimum value in incoming array.
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - sse
```
double sse(double[] in)
```
    Calculates the sum squared error of incoming array. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - harmonicMean
```
double harmonicMean(double[] in)
```
    Calculates harmonic mean of incoming array. The reciprocal of the average of the reciprocals of incoming data points. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - geometricMean
```
double geometricMean(double[] in)
```
    Calculates geometric mean of incoming array. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - zscore
```
double[] zscore(double[] in)
```
    Calculates z-scores of incoming array. Indicates number of standard deviations away from mean a value is. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision array
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - interquartilerange
```
double interquartilerange(double[] in)
```
    Calculates difference between 25th and 75th quartile of incoming array. [link]
    
    Parameters:
    
    in - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - percentile
```
double percentile(double[] in,
                  double k)
```
    Calculates value of kth percentile of incoming array [link]
    
    Parameters:
    
    in - a double precision array.
    
    k - a double value between 0 and 100
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - frequency
```
double[][] frequency(double[] x)
```
    Calculates values to be displayed in frequency table. [link]
    Parameters:
    
    x - a double precision array.
    
    Returns:
    double precision array with 2 columns
    
    out[0] = List of unique values in incoming array
    out[1] = Number of occurrences of each unique value
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - frequencyTable
```
java.lang.String frequencyTable(double[] x)
```
    Calculates frequency table for incoming array. [link]
    Parameters:
    
    x - a double precision array.
    
    Returns:
    String
    
    List of unique values in incoming array
    Number of occurrences of each unique value
    Relative percentage of each unique value
    Cumulative percentage of each unique value
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - rSquared
```
double rSquared(double[] x,
                double[] y)
```
    Calculates coefficient of determination (R²). Indicates proportion of variance of one variable that can be predicted from a second variable. [link]
    - Indicates proportion of variance of one variable that can be predicted from a second variable.
    - also used to indicate goodness of fit for regressions and least-squares fittings.
    Parameters:
    
    x - a double precision array.
    
    y - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - tTest
```
double tTest(double[] x)
```
    Performs a single sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean 0 and unknown variance, against the alternative that the mean is not 0. [link]
    
    Parameters:
    
    x - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - tTest
```
double tTest(double[] x,
             double m)
```
    Performs a single sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean m and unknown variance, against the alternative that the mean is not m. I.e. T tests determine whether data sets are likely to have come from populations having the same mean, assuming normal distribution. [link]
    
    Parameters:
    
    x - a double precision array.
    
    m - a double value
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - pairedTTest
```
double pairedTTest(double[] x,
                   double[] y)
```
    Performs a paired sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean 0 and unknown variance, against the alternative that the mean is not 0. [link]
    
    Parameters:
    
    x - a double precision array.
    
    y - a double precision array
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - tTest
```
double tTest(double[] x,
             double[] y)
```
    performs a t-test of the null hypothesis that data in the vectors x and y are independent random samples from normal distributions with equal means and equal but unknown variances, against the alternative that the means are not equal. [link]
    
    Parameters:
    
    x - a double precision array.
    
    y - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - ztest
```
double ztest(double[] x,
             double mu,
             double sigma)
```
    Performs a z-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean m and standard deviation sigma, against the alternative that the mean is not m. [link]
    
    Parameters:
    
    x - a double precision array.
    
    mu - a double precision value
    
    sigma - a double precision value
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - signedRank
```
double signedRank(double[] x,
                  double M)
```
    Performs a signed rank test (Wilcoxon signed rank) of the null hypothesis that data in the vector x comes from a continuous, symmetric distribution with median M, against the alternative that the distribution does not have median M. [link]
    
    Parameters:
    
    x - a double precision array.
    
    M - a double precision value
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - signedRank
```
double signedRank(double[] x,
                  double[] y)
```
    Performs a paired, signed rank test (Wilcoxon signed rank) of the null hypothesis that data in the vector x-y come from a continuous, symmetric distribution with equal medians, against the alternative that the distribution does not have equal medians. [link]
    
    Parameters:
    
    x - a double precision array.
    
    y - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - correlation
```
double correlation(double[] x,
                   double[] y)
```
    Calculates the Pearson's correlation coefficient from 2 data sets, and the associated t-test and p-values. 1 indicates proportionality. -1 indicates negative proportionality. 0 indicates no correlation. [link]
    
    Parameters:
    
    x - a double precision array.
    
    y - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - correlation
```
double[][] correlation(double[][] x)
```
    Calculates correlation matrix of incoming double precision MxN array. [link]
    Parameters:
    x - an MxN double precision array.
    
    columns = variables
    rows = observations
    Returns:
    
    NxN double precision array
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - covariance
```
double covariance(double[] x,
                  double[] y)
```
    Calculates the covariance coefficient from 2 data sets [link]
    
    Parameters:
    
    x - a double precision array.
    
    y - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - covariance
```
double[][] covariance(double[][] x)
```
    Calculates covariance matrix of incoming double precision MxN array [link]
    Parameters:
    x - an MxN double precision array.
    
    columns = variables
    rows = observations
    Returns:
    
    NxN double precision array
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - spearman
```
double spearman(double[] x,
                double[] y)
```
    Calculates the Spearman rank correlation coefficient from 2 data sets [link]
    
    Parameters:
    
    x - a double precision array.
    
    y - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - kruskalWallis
```
double kruskalWallis(double[][] x)
```
    Performs Kruskal-Wallis one way ANOVA. Kruskal Wallis ANOVA is a non-parametric method for testing equality of population medians among groups. It is an extension of the Mann Whitney U test to 3 or more groups. [link]
    
    Parameters:
    
    x - an MxN double precision array, M data arrays of length N.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - ANOVA
```
double[] ANOVA(double[][] x)
```
    Calculates one way ANOVA for incoming series of arrays [link]
    Parameters:
    
    x - a double precision array, M (number of data sets) X N (length of each set)
    
    Returns:
    double precision array
    
    out[0] = ANOVA P-value
    out[1] = ANOVA F-value
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - ANOVATest
```
boolean ANOVATest(double[][] x,
                  double significanceLevel)
```
    Performs one way ANOVA Test for incoming series of arrays [link]
    Parameters:
    
    x - a double precision array, M (number of data sets) X N (length of each set)
    
    significanceLevel - a double precision value (0<significanceLevel<= 0.5).
    
    Returns:
    Boolean
    
    False if no significant difference among means of incoming arrays (null hypothesis)
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - Chi2
```
double Chi2(double[] expected,
            long[] observed)
```
    Performs a Pearson's Chi² test on incoming array. Calcuates p-value. [link]
    - The chi-squared statistic compares the "expected" frequency of a sample with the actual, or "observed" frequency.
    - measure of "goodness of fit" between predicted and observed data sets
    - measure of independence between data sets
    Parameters:
    
    expected - a double precision array.
    
    observed - a long array
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - bins
```
double[] bins(double[] x,
              int binNumber)
```
    Sorts incoming data into user defined number of uniformly spaced bins [link]
    
    Parameters:
    
    x - a double precision array.
    
    binNumber - an integer
    
    Returns:
    
    double precision array
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - mannWhitneyU
```
double[] mannWhitneyU(double[] x,
                      double[] y)
```
    Performs Mann-Whitney U test. It's non-parametric test for assessing whether two independent samples of observations come from the same distribution. [link]
    Parameters:
    
    x - a double precision array.
    
    y - a double precision array.
    
    Returns:
    2XN double precision array
    
    U value
    z value
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty
  - cumNormalDist
```
double cumNormalDist(double z)
```
    Calculates value of cumulative normal distribution at z [link]
    
    Parameters:
    
    z - a double precision array.
    
    Returns:
    
    double precision value
    
    Throws:
    
    java.lang.IllegalArgumentException - if the incoming array is empty

Interface AQStat

Method Summary

Method Detail

mean

range

std

variance

kurtosis

skew

median

mode

max

min

sse

harmonicMean

geometricMean

zscore

interquartilerange

percentile

frequency

frequencyTable

rSquared

tTest

tTest

pairedTTest

tTest

ztest

signedRank

signedRank

correlation

correlation

covariance

covariance

spearman

kruskalWallis

ANOVA

ANOVATest

Chi2

bins

mannWhitneyU

cumNormalDist