VStats

java.lang.Object
- VStats

public final class VStats
extends java.lang.Object

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`computeA(double[] indVar, double[] depVar)` Returns the y-intercept of the least-squares regression line (LSRL) equation, in a `double` format.
`static double`	`computeB(double[] indVar, double[] depVar)` Returns the slope of the least-squares regression line (LSRL) equation, in a `double` format.
`static double`	`computeBinomialCdfProb(int numTrials, int inputLBound, int inputHBound, double pSuccess)` Returns the binomial probability of an interval of x-values, in a `double` format.
`static double`	`computeBinomialPdfProb(int numTrials, int xVal, double pSuccess)` Returns the binomial probability of a single x-value, in a `double` format.
`static double`	`computeChiSquareCDF(double lowerBound, double upperBound, int degFree)` Returns the area (probability) under the chi-square function between 2 chi-square values.
`static java.lang.String`	`computeChiSquareGOFTest(double[] observed, double[] expected, double alpha)` Returns the final decision and p-value of the chi-square goodness of fit (GOF) test.
`static double`	`computeChiSquarePDF(double chiSqrValue, int degFree)` Returns the output of the chi-square function when provided a chi-square value and the degrees of freedom.
`static java.lang.String`	`computeChiSquareTwoWayTest(double[][] observed, double alpha)` Returns the final decision and p-value of a two-way chi-square test.
`static double`	`computeColumnProduct(double[][] inputData, int col)` Returns the product of the elements of a column in a 2D array (0-based index), as a `double` format.
`static double`	`computeColumnSum(double[][] inputData, int col)` Returns the sum of the elements of a column in a 2D array (0-based index), as a `double` format.
`static int`	`computeCombinations(int n, int r)` Returns the number of combinations (in `int` format) possible when given the n-value and r-value (with respect to the format: nCr).
`static double`	`computeDiscreteExpectedValue(double[] inputDataArray, double[] probabilitiesArray)` Returns the expected value of a discrete random variable, in a `double` format.
`static double`	`computeDiscreteStandardDeviation(double[] inputDataArray, double[] probabilitiesArray)` Returns the standard deviation of a discrete random variable, in a `double` format.
`static double`	`computeDiscreteVariance(double[] inputDataArray, double[] probabilitiesArray)` Returns the variance of a discrete random variable, in a `double` format.
`static int`	`computeFactorial(int inputVal)` Returns the factorial (in `int` format) of an `int`.
`static double`	`computeGammaFunction(double inputZ)` Returns the an approximation of the gamma function when given an input.
`static double`	`computeGeometricCdfProb(double pSuccess, int inputLowBound, int inputHighBound)` Returns the geometric probability of an interval of x-values, in a `double` format.
`static double`	`computeGeometricPdfProb(int xVal, double pSuccess)` Returns the geometric probability of a single x-value, in a `double` format.
`static double`	`computeInverseNormalApprox(double input)` Returns the corresponding z-score with respect to the left area under the probability density function (for normal distributions).
`static double`	`computeIQR(double[] inputData)` Returns the interquartile range (IQR) of a `double` array, in a `double` format.
`static java.lang.String`	`computeLinRegTTestNegativeSlope(double[] indVar, double[] depVar, double alpha)` Returns the final decision and p-value of a linear regression t-test.
`static java.lang.String`	`computeLinRegTTestPositiveSlope(double[] indVar, double[] depVar, double alpha)` Returns the final decision and p-value of a linear regression t-test.
`static java.lang.String`	`computeLinRegTTestUnequalSlope(double[] indVar, double[] depVar, double alpha)` Returns the final decision and p-value of a linear regression t-test.
`static double`	`computeLSRLOutput(double[] indVar, double[] depVar, double input)` Returns a `double` which represents the predicted y-value (ŷ) when an x-value is inputted into the least-squares regression line (LSRL).
`static double`	`computeMAD(double[] inputData)` Returns the mean absolute deviation (MAD) of a `double` array, in a `double` format.
`static double[][]`	`computeMatrixAddition(double[][] arr1, double[][] arr2)` Returns a `double` 2D array containing the sum of the 2 parameter matrices (2D arrays).
`static double[][]`	`computeMatrixMultiplicationByScalar(double[][] arr, double scalar)` Returns a `double` 2D array containing the product of a matrix and a scalar.
`static double[][]`	`computeMatrixSubtraction(double[][] arr1, double[][] arr2)` Returns a `double` 2D array containing the difference of the 2 parameter matrices (2D arrays).
`static double`	`computeMaximum(double[] inputData)` Returns the maximum value of a `double` array, in a `double` format.
`static double`	`computeMean(double[] inputData)` Returns the mean (average) of a `double` array, in a `double` format.
`static double`	`computeMedian(double[] inputData)` Returns the median (second quartile) of a `double` array, in a `double` format.
`static double`	`computeMinimum(double[] inputData)` Returns the minimum value of a `double` array, in a `double` format.
`static double`	`computeMode(double[] inputData)` Returns the mode (most occurring value) of a `double` array, in a `double` format.
`static double`	`computeNormalPDF(double inputZ)` Returns the output (in a `double` format) of the probability density function (for normal distributions).
`static java.lang.String`	`computeOneMeanTTestHaGreaterThanValue(double mu, double sampleMean, double sampleSD, int sampleSize, double alpha)` Returns the final decision and p-value of a significance test, utilizing the t-distribution.
`static java.lang.String`	`computeOneMeanTTestHaLessThanValue(double mu, double sampleMean, double sampleSD, int sampleSize, double alpha)` Returns the final decision and p-value of a significance test, utilizing the t-distribution.
`static java.lang.String`	`computeOneMeanTTestHaNotEqualToValue(double mu, double sampleMean, double sampleSD, int sampleSize, double alpha)` Returns the final decision and p-value of a significance test, utilizing the t-distribution.
`static java.lang.String`	`computeOneMeanZConfInt(double mu, double sigma, int sampleSize, double confidenceLevel)` Returns a `String` which represents the confidence interval for a single mean, making use of the z-distribution.
`static java.lang.String`	`computeOneMeanZTestHaGreaterThanValue(double mu, double sigma, double sampleMean, int sampleSize, double alpha)` Returns the final decision (a `String`) of the significance test for a single mean, utilizing the z-distribution.
`static java.lang.String`	`computeOneMeanZTestHaLessThanValue(double mu, double sigma, double sampleMean, int sampleSize, double alpha)` Returns the final decision (a `String`) of the significance test for a single mean, utilizing the z-distribution.
`static java.lang.String`	`computeOneMeanZTestHaNotEqualToValue(double mu, double sigma, double sampleMean, int sampleSize, double alpha)` Returns the final decision (a `String`) of the significance test for a single mean, utilizing the z-distribution.
`static java.lang.String`	`computeOnePropZConfInt(double pHat, int sampleSize, double confidenceLevel)` Returns a `String` which represents the confidence interval for estimating a single population proportion.
`static java.lang.String`	`computeOnePropZTestP0GreaterThanValue(double pHat, double pNought, double sampleSize, double alpha)` Returns the final decision (a `String`) of the significance test for a single proportion, utilizing the z-distribution.
`static java.lang.String`	`computeOnePropZTestP0LessThanValue(double pHat, double pNought, double sampleSize, double alpha)` Returns the final decision (a `String`) of the significance test for a single proportion, utilizing the z-distribution.
`static java.lang.String`	`computeOnePropZTestP0NotEqualToValue(double pHat, double pNought, double sampleSize, double alpha)` Returns the final decision (a `String`) of the significance test for a single proportion, utilizing the z-distribution.
`static java.util.ArrayList<java.lang.Double>`	`computeOutliers(double[] inputData)` Returns a `double` `ArrayList` containing any possible outliers in a `double` array.
`static int`	`computePermutations(int n, int r)` Returns an `int` which represents the number of possible permutations, when the inputs are the n-value and the r-value.
`static double`	`computeQuartile1(double[] inputData)` Returns the first quartile of a `double` array, in a `double` format.
`static double`	`computeQuartile3(double[] inputData)` Returns the third quartile of a `double` array, in a `double` format.
`static double`	`computeR(double[] indVar, double[] depVar)` Returns the correlation coefficient (r-value) of the relationship between the independent and dependent variables, in a `double` format.
`static double`	`computeRange(double[] inputData)` Returns the range (maximum value - minimum value) of a `double` array, in a `double` format.
`static double[]`	`computeResidualValues(double[] indVar, double[] depVar)` Returns a `double` array containing the residual values.
`static double`	`computeRowProduct(double[][] inputData, int row)` Returns the product of the elements of a row in a 2D array (0-based index), as a `double` format.
`static double`	`computeRowSum(double[][] inputData, int row)` Returns the sum of the elements of a row in a 2D array (0-based index), as a `double` format.
`static double`	`computeRSquared(double[] indVar, double[] depVar)` Returns the r^2-value of the relationship between the independent and dependent variables, in a `double` format.
`static double`	`computeSe(double[] indVar, double[] depVar)` Returns the standard error (Se) of the residuals, in a `double` format.
`static double`	`computeSeb(double[] indVar, double[] depVar)` Returns the standard error of the slope.
`static double`	`computeStandardDeviation(double[] inputData)` Returns the standard deviation of a `double` array, in a `double` format.
`static double`	`computeSumOfResidualsSquared(double[] indVar, double[] depVar)` Returns the sum of the residuals squared, in a `double` format.
`static double`	`computeSumValues(double[] inputData)` Returns the sum of the values of a `double` array, in a `double` format.
`static double`	`computeTCDF(double lowBound, double highBound, int degFree)` Returns the area (probability) under the t-distribution function between two t-values.
`static double`	`computeTPDF(double inputVal, int degFree)` Returns the output of the Student's t-distribution function when given the input value and degrees of freedom.
`static java.lang.String`	`computeTwoPropZTestP1GreaterThanP2(int successes1, int sampleSize1, int successes2, int sampleSize2, double alpha)` Returns the final decision (a `String`) of the significance test for 2 proportions, utilizing the z-distribution.
`static java.lang.String`	`computeTwoPropZTestP1LessThanP2(int successes1, int sampleSize1, int successes2, int sampleSize2, double alpha)` Returns the final decision (a `String`) of the significance test for 2 proportions, utilizing the z-distribution.
`static java.lang.String`	`computeTwoPropZTestP1NotEqualToP2(int successes1, int sampleSize1, int successes2, int sampleSize2, double alpha)` Returns the final decision (a `String`) of the significance test for 2 proportions, utilizing the z-distribution.
`static double`	`computeVariance(double[] inputData)` Returns the variance of a `double` array, in a `double` format.
`static double[]`	`computeYPredictedValues(double[] indVar, double[] depVar)` Returns a `double` array containing the predicted y-values (ŷ).
`static double`	`computeZProbAvgLeftRightRiemann(double inputZLow, double inputZHigh)` Returns the (highly accurate) probability approximation between two z-scores for the probability density function (for normal distributions) using the average of a left-endpoint & right-endpoint Riemann sum.
`static double`	`computeZProbLeftRiemann(double inputZLow, double inputZHigh)` Returns the (highly accurate) probability approximation between two z-scores for the probability density function (for normal distributions) using a left-endpoint Riemann sum.
`static double`	`computeZProbMidpointRiemann(double inputZLow, double inputZHigh)` Returns the probability approximation between two z-scores for the probability density function (for normal distributions) using a midpoint Riemann sum (accurate to about 6 decimal places).
`static double`	`computeZProbRightRiemann(double inputZLow, double inputZHigh)` Returns the (highly accurate) probability approximation between two z-scores for the probability density function (for normal distributions) using a right-endpoint Riemann sum.
`static double`	`computeZProbTrapezoidRiemann(double inputZLow, double inputZHigh)` Returns the probability approximation between two z-scores for the probability density function (for normal distributions) using a trapezoidal Riemann sum.
`static double`	`computeZStar(double inputConfidenceLevel)` Returns a `double` which represents the z-star (z-critical) value when a confidence level is inputted.
`static java.lang.String`	`displayLSRLEquation(double[] indVar, double[] depVar)` Returns the least-squares regression line (LSRL) equation, in a `String` format.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Method Detail
  - computeMean
```
public static double computeMean(double[] inputData)
```
    Returns the mean (average) of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the mean of inputData.
  - computeMAD
```
public static double computeMAD(double[] inputData)
```
    Returns the mean absolute deviation (MAD) of a double array, in a double format.
    The MAD of an array is the average distance (absolute value) from each value in the array to the mean.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the mean absolute deviation of inputData.
  - computeMedian
```
public static double computeMedian(double[] inputData)
```
    Returns the median (second quartile) of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the median of inputData.
  - computeMinimum
```
public static double computeMinimum(double[] inputData)
```
    Returns the minimum value of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the minimum value of inputData.
  - computeMaximum
```
public static double computeMaximum(double[] inputData)
```
    Returns the maximum value of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the maximum value of inputData.
  - computeRange
```
public static double computeRange(double[] inputData)
```
    Returns the range (maximum value - minimum value) of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the range of inputData.
  - computeVariance
```
public static double computeVariance(double[] inputData)
```
    Returns the variance of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the variance of inputData.
  - computeStandardDeviation
```
public static double computeStandardDeviation(double[] inputData)
```
    Returns the standard deviation of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the standard deviation of inputData.
  - computeQuartile1
```
public static double computeQuartile1(double[] inputData)
```
    Returns the first quartile of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the first quartile of inputData.
  - computeQuartile3
```
public static double computeQuartile3(double[] inputData)
```
    Returns the third quartile of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the third quartile of inputData.
  - computeMode
```
public static double computeMode(double[] inputData)
```
    Returns the mode (most occurring value) of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the mode of inputData.
  - computeSumValues
```
public static double computeSumValues(double[] inputData)
```
    Returns the sum of the values of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the sum of the values in inputData.
  - computeIQR
```
public static double computeIQR(double[] inputData)
```
    Returns the interquartile range (IQR) of a double array, in a double format.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    the IQR of inputData.
  - computeOutliers
```
public static java.util.ArrayList<java.lang.Double> computeOutliers(double[] inputData)
```
    Returns a double ArrayList containing any possible outliers in a double array.
    
    Parameters:
    
    inputData - a double array.
    
    Returns:
    
    an ArrayList which contains any possible outliers in inputData.
  - computeFactorial
```
public static int computeFactorial(int inputVal)
```
    Returns the factorial (in int format) of an int.
    
    Parameters:
    
    inputVal - an int.
    
    Returns:
    
    the factorial of inputVal.
  - computeCombinations
```
public static int computeCombinations(int n,
                                      int r)
```
    Returns the number of combinations (in int format) possible when given the n-value and r-value (with respect to the format: nCr).
    
    Parameters:
    
    n - the n-value in the format "nCr."
    
    r - the r-value in the format "nCr."
    
    Returns:
    
    the number of combinations possible, with respect to n and r.
  - computeBinomialPdfProb
```
public static double computeBinomialPdfProb(int numTrials,
                                            int xVal,
                                            double pSuccess)
```
    Returns the binomial probability of a single x-value, in a double format.
    
    Parameters:
    
    numTrials - the number of trials.
    
    xVal - the x-value of interest.
    
    pSuccess - the probability of success.
    
    Returns:
    
    the probability of xVal occurring.
  - computeBinomialCdfProb
```
public static double computeBinomialCdfProb(int numTrials,
                                            int inputLBound,
                                            int inputHBound,
                                            double pSuccess)
```
    Returns the binomial probability of an interval of x-values, in a double format.
    
    Parameters:
    
    numTrials - the number of trials.
    
    inputLBound - the low bound x-value.
    
    inputHBound - the high bound x-value.
    
    pSuccess - the probability of success.
    
    Returns:
    
    the probability of obtaining an x-value between inputLBound and inputHBound, inclusive.
  - computeGeometricPdfProb
```
public static double computeGeometricPdfProb(int xVal,
                                             double pSuccess)
```
    Returns the geometric probability of a single x-value, in a double format.
    
    Parameters:
    
    xVal - the x-value of interest.
    
    pSuccess - the probability of success.
    
    Returns:
    
    the probability of the event occurring on the xValth try.
  - computeGeometricCdfProb
```
public static double computeGeometricCdfProb(double pSuccess,
                                             int inputLowBound,
                                             int inputHighBound)
```
    Returns the geometric probability of an interval of x-values, in a double format.
    
    Parameters:
    
    pSuccess - the probability of success.
    
    inputLowBound - the low bound x-value.
    
    inputHighBound - the high bound x-value.
    
    Returns:
    
    the probability of the event occurring on between the inputLowBoundth and inputHighBoundth try, inclusive.
  - computeNormalPDF
```
public static double computeNormalPDF(double inputZ)
```
    Returns the output (in a double format) of the probability density function (for normal distributions).
    This method assumes that µ=0 and σ=1.
    
    Parameters:
    
    inputZ - the input value.
    
    Returns:
    
    the normal probability density function's output when inputZ is the input.
  - computeZProbLeftRiemann
```
public static double computeZProbLeftRiemann(double inputZLow,
                                             double inputZHigh)
```
    Returns the (highly accurate) probability approximation between two z-scores for the probability density function (for normal distributions) using a left-endpoint Riemann sum.
    This method assumes that µ=0 and σ=1.
    Enter large absolute value z-scores for the bounds, for improper integral approximation.
    
    Parameters:
    
    inputZLow - the low bound z-score.
    
    inputZHigh - the high bound z-score.
    
    Returns:
    
    the probability between inputZLow and inputZHigh.
  - computeZProbRightRiemann
```
public static double computeZProbRightRiemann(double inputZLow,
                                              double inputZHigh)
```
    Returns the (highly accurate) probability approximation between two z-scores for the probability density function (for normal distributions) using a right-endpoint Riemann sum.
    This method assumes that µ=0 and σ=1.
    Enter large absolute value z-scores for the bounds, for improper integral approximation.
    
    Parameters:
    
    inputZLow - the low bound z-score.
    
    inputZHigh - the high bound z-score.
    
    Returns:
    
    the probability between inputZLow and inputZHigh.
  - computeZProbAvgLeftRightRiemann
```
public static double computeZProbAvgLeftRightRiemann(double inputZLow,
                                                     double inputZHigh)
```
    Returns the (highly accurate) probability approximation between two z-scores for the probability density function (for normal distributions) using the average of a left-endpoint & right-endpoint Riemann sum.
    This method assumes that µ=0 and σ=1.
    Enter large absolute value z-scores for the bounds, for improper integral approximation.
    
    Parameters:
    
    inputZLow - the low bound z-score.
    
    inputZHigh - the high bound z-score.
    
    Returns:
    
    the probability between inputZLow and inputZHigh.
  - computeZProbMidpointRiemann
```
public static double computeZProbMidpointRiemann(double inputZLow,
                                                 double inputZHigh)
```
    Returns the probability approximation between two z-scores for the probability density function (for normal distributions) using a midpoint Riemann sum (accurate to about 6 decimal places).
    This method assumes that µ=0 and σ=1.
    Enter large absolute value z-scores for the bounds, for improper integral approximation.
    
    Parameters:
    
    inputZLow - the low bound z-score.
    
    inputZHigh - the high bound z-score.
    
    Returns:
    
    the probability between inputZLow and inputZHigh.
  - computeZProbTrapezoidRiemann
```
public static double computeZProbTrapezoidRiemann(double inputZLow,
                                                  double inputZHigh)
```
    Returns the probability approximation between two z-scores for the probability density function (for normal distributions) using a trapezoidal Riemann sum.
    This method assumes that µ=0 and σ=1.
    Enter large absolute value z-scores for the bounds, for improper integral approximation.
    
    Parameters:
    
    inputZLow - the low bound z-score.
    
    inputZHigh - the high bound z-score.
    
    Returns:
    
    the probability between inputZLow and inputZHigh.
  - computeInverseNormalApprox
```
public static double computeInverseNormalApprox(double input)
```
    Returns the corresponding z-score with respect to the left area under the probability density function (for normal distributions).
    This method assumes that µ=0 and σ=1.
    Method is only an approximation, and does not return an exact value.
    
    Parameters:
    
    input - the area under the probability density function (to the left of the desired z-score).
    
    Returns:
    
    the corresponding z-score to the input area.
  - computePermutations
```
public static int computePermutations(int n,
                                      int r)
```
    Returns an int which represents the number of possible permutations, when the inputs are the n-value and the r-value.
    
    Parameters:
    
    n - the n-value in the form "nPr."
    
    r - the r-value in the form "nPr."
    
    Returns:
    
    the number of permutations possible, with respect to n and r.
  - computeDiscreteExpectedValue
```
public static double computeDiscreteExpectedValue(double[] inputDataArray,
                                                  double[] probabilitiesArray)
```
    Returns the expected value of a discrete random variable, in a double format.
    
    Parameters:
    
    inputDataArray - an array containing the possible outcomes of the random variable.
    
    probabilitiesArray - an array containing the probabilities of the respective possible outcomes of the random variable.
    
    Returns:
    
    the expected value (µX) of the random variable.
  - computeDiscreteVariance
```
public static double computeDiscreteVariance(double[] inputDataArray,
                                             double[] probabilitiesArray)
```
    Returns the variance of a discrete random variable, in a double format.
    
    Parameters:
    
    inputDataArray - an array containing the possible outcomes of the random variable.
    
    probabilitiesArray - an array containing the probabilities of the respective possible outcomes of the random variable.
    
    Returns:
    
    the variance (the square of σX) of the random variable.
  - computeDiscreteStandardDeviation
```
public static double computeDiscreteStandardDeviation(double[] inputDataArray,
                                                      double[] probabilitiesArray)
```
    Returns the standard deviation of a discrete random variable, in a double format.
    
    Parameters:
    
    inputDataArray - an array containing the possible outcomes of the random variable.
    
    probabilitiesArray - an array containing the probabilities of the respective possible outcomes of the random variable.
    
    Returns:
    
    the standard deviation (σX) of the random variable.
  - computeRowSum
```
public static double computeRowSum(double[][] inputData,
                                   int row)
```
    Returns the sum of the elements of a row in a 2D array (0-based index), as a double format.
    
    Parameters:
    
    inputData - a 2D array.
    
    row - the row of interest.
    
    Returns:
    
    the sum of the elements in row.
  - computeColumnSum
```
public static double computeColumnSum(double[][] inputData,
                                      int col)
```
    Returns the sum of the elements of a column in a 2D array (0-based index), as a double format.
    
    Parameters:
    
    inputData - a 2D array.
    
    col - the column of interest.
    
    Returns:
    
    the sum of the elements in col.
  - computeRowProduct
```
public static double computeRowProduct(double[][] inputData,
                                       int row)
```
    Returns the product of the elements of a row in a 2D array (0-based index), as a double format.
    
    Parameters:
    
    inputData - a 2D array.
    
    row - the row of interest.
    
    Returns:
    
    the product of the elements in row.
  - computeColumnProduct
```
public static double computeColumnProduct(double[][] inputData,
                                          int col)
```
    Returns the product of the elements of a column in a 2D array (0-based index), as a double format.
    
    Parameters:
    
    inputData - a 2D array.
    
    col - the column of interest.
    
    Returns:
    
    the product of the elements in col.
  - computeMatrixAddition
```
public static double[][] computeMatrixAddition(double[][] arr1,
                                               double[][] arr2)
```
    Returns a double 2D array containing the sum of the 2 parameter matrices (2D arrays).
    The matrices must have the same dimensions.
    
    Parameters:
    
    arr1 - a 2D array.
    
    arr2 - another 2D array.
    
    Returns:
    
    the sum of arr1 and arr2, in a 2D array.
  - computeMatrixSubtraction
```
public static double[][] computeMatrixSubtraction(double[][] arr1,
                                                  double[][] arr2)
```
    Returns a double 2D array containing the difference of the 2 parameter matrices (2D arrays).
    The matrices must have the same dimensions.
    
    Parameters:
    
    arr1 - a 2D array.
    
    arr2 - another 2D array.
    
    Returns:
    
    the difference of arr1 and arr2, in a 2D array.
  - computeMatrixMultiplicationByScalar
```
public static double[][] computeMatrixMultiplicationByScalar(double[][] arr,
                                                             double scalar)
```
    Returns a double 2D array containing the product of a matrix and a scalar.
    
    Parameters:
    
    arr - a 2D array.
    
    scalar - the scalar.
    
    Returns:
    
    the product of arr and scalar.
  - computeSe
```
public static double computeSe(double[] indVar,
                               double[] depVar)
```
    Returns the standard error (Se) of the residuals, in a double format.
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    Returns:
    
    Se with respect to indVar and depVar.
  - computeSumOfResidualsSquared
```
public static double computeSumOfResidualsSquared(double[] indVar,
                                                  double[] depVar)
```
    Returns the sum of the residuals squared, in a double format.
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    Returns:
    
    sum of the residuals squared with respect to indVar and depVar.
  - computeResidualValues
```
public static double[] computeResidualValues(double[] indVar,
                                             double[] depVar)
```
    Returns a double array containing the residual values.
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    Returns:
    
    an array containing the residual values with respect to indVar and depVar.
  - computeYPredictedValues
```
public static double[] computeYPredictedValues(double[] indVar,
                                               double[] depVar)
```
    Returns a double array containing the predicted y-values (ŷ).
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    Returns:
    
    an array containing the predicted y-values with respect to indVar and depVar.
  - computeLSRLOutput
```
public static double computeLSRLOutput(double[] indVar,
                                       double[] depVar,
                                       double input)
```
    Returns a double which represents the predicted y-value (ŷ) when an x-value is inputted into the least-squares regression line (LSRL).
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    input - a double which is the value to be inputted into the LSRL function.
    
    Returns:
    
    the predicted y-value when input is the input x-value to the LSRL function (with respect to indVar and depVar).
  - displayLSRLEquation
```
public static java.lang.String displayLSRLEquation(double[] indVar,
                                                   double[] depVar)
```
    Returns the least-squares regression line (LSRL) equation, in a String format.
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    Returns:
    
    the LSRL equation with respect to indVar and depVar.
  - computeA
```
public static double computeA(double[] indVar,
                              double[] depVar)
```
    Returns the y-intercept of the least-squares regression line (LSRL) equation, in a double format.
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    Returns:
    
    the y-intercept of the LSRL equation, with respect to indVar and depVar.
  - computeB
```
public static double computeB(double[] indVar,
                              double[] depVar)
```
    Returns the slope of the least-squares regression line (LSRL) equation, in a double format.
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    Returns:
    
    the slope of the LSRL equation, with respect to indVar and depVar.
  - computeR
```
public static double computeR(double[] indVar,
                              double[] depVar)
```
    Returns the correlation coefficient (r-value) of the relationship between the independent and dependent variables, in a double format.
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    Returns:
    
    the r-value of the LSRL, with respect to indVar and depVar.
  - computeRSquared
```
public static double computeRSquared(double[] indVar,
                                     double[] depVar)
```
    Returns the r^2-value of the relationship between the independent and dependent variables, in a double format.
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - a double array containing the independent variable values.
    
    depVar - a double array containing the dependent variable values.
    
    Returns:
    
    the r^2-value of the LSRL, with respect to indVar and depVar.
  - computeZStar
```
public static double computeZStar(double inputConfidenceLevel)
```
    Returns a double which represents the z-star (z-critical) value when a confidence level is inputted.
    This method is only an approximation.
    
    Parameters:
    
    inputConfidenceLevel - a double representing the input confidence level.
    
    Returns:
    
    the z-star value with respect to inputConfidenceLevel.
  - computeOneMeanZConfInt
```
public static java.lang.String computeOneMeanZConfInt(double mu,
                                                      double sigma,
                                                      int sampleSize,
                                                      double confidenceLevel)
```
    Returns a String which represents the confidence interval for a single mean, making use of the z-distribution.
    This method assumes that µ=0 and σ=1.
    This method is only an approximation.
    
    Parameters:
    
    mu - the mean of the sample.
    
    sigma - the standard deviation of the population.
    
    sampleSize - the size of the sample.
    
    confidenceLevel - the input confidence level.
    
    Returns:
    
    the confidence interval for a single mean.
  - computeOneMeanZTestHaGreaterThanValue
```
public static java.lang.String computeOneMeanZTestHaGreaterThanValue(double mu,
                                                                     double sigma,
                                                                     double sampleMean,
                                                                     int sampleSize,
                                                                     double alpha)
```
    Returns the final decision (a String) of the significance test for a single mean, utilizing the z-distribution.
    For this method:
    - the null hypothesis should state that the population mean is equal to a certain value.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    Parameters:
    
    mu - the population mean to be tested.
    
    sigma - the population standard deviation.
    
    sampleMean - the mean of the sample.
    
    sampleSize - the size of the sample.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision of the significance test.
  - computeOneMeanZTestHaLessThanValue
```
public static java.lang.String computeOneMeanZTestHaLessThanValue(double mu,
                                                                  double sigma,
                                                                  double sampleMean,
                                                                  int sampleSize,
                                                                  double alpha)
```
    Returns the final decision (a String) of the significance test for a single mean, utilizing the z-distribution.
    For this method:
    - the null hypothesis should state that the population mean is equal to a certain value.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    Parameters:
    
    mu - the population mean to be tested.
    
    sigma - the population standard deviation.
    
    sampleMean - the mean of the sample.
    
    sampleSize - the size of the sample.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision of the significance test.
  - computeOneMeanZTestHaNotEqualToValue
```
public static java.lang.String computeOneMeanZTestHaNotEqualToValue(double mu,
                                                                    double sigma,
                                                                    double sampleMean,
                                                                    int sampleSize,
                                                                    double alpha)
```
    Returns the final decision (a String) of the significance test for a single mean, utilizing the z-distribution.
    For this method:
    - the null hypothesis should state that the population mean is equal to a certain value.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    Parameters:
    
    mu - the population mean to be tested.
    
    sigma - the population standard deviation.
    
    sampleMean - the mean of the sample.
    
    sampleSize - the size of the sample.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision of the significance test.
  - computeOnePropZConfInt
```
public static java.lang.String computeOnePropZConfInt(double pHat,
                                                      int sampleSize,
                                                      double confidenceLevel)
```
    Returns a String which represents the confidence interval for estimating a single population proportion.
    This method is only an approximation.
    
    Parameters:
    
    pHat - the sample proportion.
    
    sampleSize - the size of the sample.
    
    confidenceLevel - the confidence level needed.
    
    Returns:
    
    the confidence interval, where pHat is the center of the interval.
  - computeOnePropZTestP0LessThanValue
```
public static java.lang.String computeOnePropZTestP0LessThanValue(double pHat,
                                                                  double pNought,
                                                                  double sampleSize,
                                                                  double alpha)
```
    Returns the final decision (a String) of the significance test for a single proportion, utilizing the z-distribution.
    For this method:
    - the null hypothesis should state that the population proportion is equal to a certain value.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    Parameters:
    
    pHat - the sample proportion.
    
    pNought - the population proportion to be tested.
    
    sampleSize - the size of the sample.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision of the significance test.
  - computeOnePropZTestP0GreaterThanValue
```
public static java.lang.String computeOnePropZTestP0GreaterThanValue(double pHat,
                                                                     double pNought,
                                                                     double sampleSize,
                                                                     double alpha)
```
    Returns the final decision (a String) of the significance test for a single proportion, utilizing the z-distribution.
    For this method:
    - the null hypothesis should state that the population proportion is equal to a certain value.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    Parameters:
    
    pHat - the sample proportion.
    
    pNought - the population proportion to be tested.
    
    sampleSize - the size of the sample.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision of the significance test.
  - computeOnePropZTestP0NotEqualToValue
```
public static java.lang.String computeOnePropZTestP0NotEqualToValue(double pHat,
                                                                    double pNought,
                                                                    double sampleSize,
                                                                    double alpha)
```
    Returns the final decision (a String) of the significance test for a single proportion, utilizing the z-distribution.
    For this method:
    - the null hypothesis should state that the population proportion is equal to a certain value.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    Parameters:
    
    pHat - the sample proportion.
    
    pNought - the population proportion to be tested.
    
    sampleSize - the size of the sample.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision of the significance test.
  - computeTwoPropZTestP1LessThanP2
```
public static java.lang.String computeTwoPropZTestP1LessThanP2(int successes1,
                                                               int sampleSize1,
                                                               int successes2,
                                                               int sampleSize2,
                                                               double alpha)
```
    Returns the final decision (a String) of the significance test for 2 proportions, utilizing the z-distribution.
    For this method:
    - the null hypothesis should state that the population proportions are equal to each other.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    Parameters:
    
    successes1 - the number of successes in the sample, with respect to p1.
    
    sampleSize1 - the size of the sample, with respect to p1.
    
    successes2 - the number of successes in the sample, with respect to p2.
    
    sampleSize2 - the size of the sample, with respect to p2.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision of the significance test.
  - computeTwoPropZTestP1GreaterThanP2
```
public static java.lang.String computeTwoPropZTestP1GreaterThanP2(int successes1,
                                                                  int sampleSize1,
                                                                  int successes2,
                                                                  int sampleSize2,
                                                                  double alpha)
```
    Returns the final decision (a String) of the significance test for 2 proportions, utilizing the z-distribution.
    For this method:
    - the null hypothesis should state that the population proportions are equal to each other.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    Parameters:
    
    successes1 - the number of successes in the sample, with respect to p1.
    
    sampleSize1 - the size of the sample, with respect to p1.
    
    successes2 - the number of successes in the sample, with respect to p2.
    
    sampleSize2 - the size of the sample, with respect to p2.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision of the significance test.
  - computeTwoPropZTestP1NotEqualToP2
```
public static java.lang.String computeTwoPropZTestP1NotEqualToP2(int successes1,
                                                                 int sampleSize1,
                                                                 int successes2,
                                                                 int sampleSize2,
                                                                 double alpha)
```
    Returns the final decision (a String) of the significance test for 2 proportions, utilizing the z-distribution.
    For this method:
    - the null hypothesis should state that the population proportions are equal to each other.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    Parameters:
    
    successes1 - the number of successes in the sample, with respect to p1.
    
    sampleSize1 - the size of the sample, with respect to p1.
    
    successes2 - the number of successes in the sample, with respect to p2.
    
    sampleSize2 - the size of the sample, with respect to p2.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision of the significance test.
  - computeGammaFunction
```
public static double computeGammaFunction(double inputZ)
```
    Returns the an approximation of the gamma function when given an input.
    This method makes use of Stirling's approximation of the gamma function.
    
    Parameters:
    
    inputZ - the input value.
    
    Returns:
    
    the output of the gamma function when inputZ is the input.
  - computeChiSquarePDF
```
public static double computeChiSquarePDF(double chiSqrValue,
                                         int degFree)
```
    Returns the output of the chi-square function when provided a chi-square value and the degrees of freedom.
    
    Parameters:
    
    chiSqrValue - the input chi-square value.
    
    degFree - the degrees of freedom.
    
    Returns:
    
    the output of the chi-square function when the inputs are chiSqrValue and degFree.
  - computeChiSquareCDF
```
public static double computeChiSquareCDF(double lowerBound,
                                         double upperBound,
                                         int degFree)
```
    Returns the area (probability) under the chi-square function between 2 chi-square values.
    
    Parameters:
    
    lowerBound - the lower bound chi-square value.
    
    upperBound - the upper bound chi-square value.
    
    degFree - the degrees of freedom.
    
    Returns:
    
    the area (probability) under the chi-square function between lowerBound and upperBound.
  - computeChiSquareGOFTest
```
public static java.lang.String computeChiSquareGOFTest(double[] observed,
                                                       double[] expected,
                                                       double alpha)
```
    Returns the final decision and p-value of the chi-square goodness of fit (GOF) test.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    The degrees of freedom will be automatically registered as one less than the number of categories.
    
    Parameters:
    
    observed - the array containing the observed values.
    
    expected - the array containing the expected values.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision and p-value of the GOF test.
  - computeChiSquareTwoWayTest
```
public static java.lang.String computeChiSquareTwoWayTest(double[][] observed,
                                                          double alpha)
```
    Returns the final decision and p-value of a two-way chi-square test.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    The degrees of freedom will automatically be registered as (# of rows - 1) * (# of columns - 1).
    
    Parameters:
    
    observed - the observed matrix (do not include cells for the row totals and column totals).
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision and p-value of the two-way test.
  - computeTPDF
```
public static double computeTPDF(double inputVal,
                                 int degFree)
```
    Returns the output of the Student's t-distribution function when given the input value and degrees of freedom.
    
    Parameters:
    
    inputVal - the input value.
    
    degFree - the degrees of freedom.
    
    Returns:
    
    the output of the t-distribution function when given inputVal and degFree.
  - computeTCDF
```
public static double computeTCDF(double lowBound,
                                 double highBound,
                                 int degFree)
```
    Returns the area (probability) under the t-distribution function between two t-values.
    
    Parameters:
    
    lowBound - the lower bound t-value.
    
    highBound - the higher bound t-value.
    
    degFree - the degrees of freedom.
    
    Returns:
    
    the the area (probability) under the t-distribution function between lowBound and highBound.
  - computeOneMeanTTestHaLessThanValue
```
public static java.lang.String computeOneMeanTTestHaLessThanValue(double mu,
                                                                  double sampleMean,
                                                                  double sampleSD,
                                                                  int sampleSize,
                                                                  double alpha)
```
    Returns the final decision and p-value of a significance test, utilizing the t-distribution.
    The alternate hypothesis must state that the population mean is less than a value.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    The degrees of freedom will automatically be registered as one less than the sample size.
    
    Parameters:
    
    mu - the population mean to be tested.
    
    sampleMean - the mean of the sample.
    
    sampleSD - the standard deviation of the sample.
    
    sampleSize - the size of the sample.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision and p-value of the significance test.
  - computeOneMeanTTestHaGreaterThanValue
```
public static java.lang.String computeOneMeanTTestHaGreaterThanValue(double mu,
                                                                     double sampleMean,
                                                                     double sampleSD,
                                                                     int sampleSize,
                                                                     double alpha)
```
    Returns the final decision and p-value of a significance test, utilizing the t-distribution.
    The alternate hypothesis must state that the population mean is greater than a value.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    The degrees of freedom will automatically be registered as one less than the sample size.
    
    Parameters:
    
    mu - the population mean to be tested.
    
    sampleMean - the mean of the sample.
    
    sampleSD - the standard deviation of the sample.
    
    sampleSize - the size of the sample.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision and p-value of the significance test.
  - computeOneMeanTTestHaNotEqualToValue
```
public static java.lang.String computeOneMeanTTestHaNotEqualToValue(double mu,
                                                                    double sampleMean,
                                                                    double sampleSD,
                                                                    int sampleSize,
                                                                    double alpha)
```
    Returns the final decision and p-value of a significance test, utilizing the t-distribution.
    The alternate hypothesis must state that the population mean is not equal to a value.
    The decision could be to either reject the null hypothesis or fail to reject the null hypothesis.
    The degrees of freedom will automatically be registered as one less than the sample size.
    
    Parameters:
    
    mu - the population mean to be tested.
    
    sampleMean - the mean of the sample.
    
    sampleSD - the standard deviation of the sample.
    
    sampleSize - the size of the sample.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision and p-value of the significance test.
  - computeSeb
```
public static double computeSeb(double[] indVar,
                                double[] depVar)
```
    Returns the standard error of the slope.
    This method uses linear regression to model the relationship between the 2 variables (least-squares regression line format: ŷ = a + bx).
    
    Parameters:
    
    indVar - the independent variable.
    
    depVar - the dependent variable.
    
    Returns:
    
    the standard error of the slope, with respect to indVar and depVar.
  - computeLinRegTTestNegativeSlope
```
public static java.lang.String computeLinRegTTestNegativeSlope(double[] indVar,
                                                               double[] depVar,
                                                               double alpha)
```
    Returns the final decision and p-value of a linear regression t-test.
    This method tests whether or not the population slope is negative.
    The degrees of freedom will automatically be registered as 2 less than the number of data values.
    
    Parameters:
    
    indVar - the independent variable.
    
    depVar - the dependent variable.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision and p-value of the test.
  - computeLinRegTTestPositiveSlope
```
public static java.lang.String computeLinRegTTestPositiveSlope(double[] indVar,
                                                               double[] depVar,
                                                               double alpha)
```
    Returns the final decision and p-value of a linear regression t-test.
    This method tests whether or not the population slope is positive.
    The degrees of freedom will automatically be registered as 2 less than the number of data values.
    
    Parameters:
    
    indVar - the independent variable.
    
    depVar - the dependent variable.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision and p-value of the test.
  - computeLinRegTTestUnequalSlope
```
public static java.lang.String computeLinRegTTestUnequalSlope(double[] indVar,
                                                              double[] depVar,
                                                              double alpha)
```
    Returns the final decision and p-value of a linear regression t-test.
    This method tests whether or not the population slope is not equal to 0.
    The degrees of freedom will automatically be registered as 2 less than the number of data values.
    
    Parameters:
    
    indVar - the independent variable.
    
    depVar - the dependent variable.
    
    alpha - the significance level (α) of the test.
    
    Returns:
    
    the final decision and p-value of the test.

Class VStats

Method Summary

Methods inherited from class java.lang.Object

Method Detail

computeMean

computeMAD

computeMedian

computeMinimum

computeMaximum

computeRange

computeVariance

computeStandardDeviation

computeQuartile1

computeQuartile3

computeMode

computeSumValues

computeIQR

computeOutliers

computeFactorial

computeCombinations

computeBinomialPdfProb

computeBinomialCdfProb

computeGeometricPdfProb

computeGeometricCdfProb

computeNormalPDF

computeZProbLeftRiemann

computeZProbRightRiemann

computeZProbAvgLeftRightRiemann

computeZProbMidpointRiemann

computeZProbTrapezoidRiemann

computeInverseNormalApprox

computePermutations

computeDiscreteExpectedValue

computeDiscreteVariance

computeDiscreteStandardDeviation

computeRowSum

computeColumnSum

computeRowProduct

computeColumnProduct

computeMatrixAddition

computeMatrixSubtraction

computeMatrixMultiplicationByScalar

computeSe

computeSumOfResidualsSquared

computeResidualValues

computeYPredictedValues

computeLSRLOutput

displayLSRLEquation

computeA

computeB

computeR

computeRSquared

computeZStar

computeOneMeanZConfInt

computeOneMeanZTestHaGreaterThanValue

computeOneMeanZTestHaLessThanValue

computeOneMeanZTestHaNotEqualToValue

computeOnePropZConfInt

computeOnePropZTestP0LessThanValue

computeOnePropZTestP0GreaterThanValue

computeOnePropZTestP0NotEqualToValue

computeTwoPropZTestP1LessThanP2

computeTwoPropZTestP1GreaterThanP2

computeTwoPropZTestP1NotEqualToP2

computeGammaFunction

computeChiSquarePDF

computeChiSquareCDF

computeChiSquareGOFTest

computeChiSquareTwoWayTest

computeTPDF

computeTCDF

computeOneMeanTTestHaLessThanValue

computeOneMeanTTestHaGreaterThanValue

computeOneMeanTTestHaNotEqualToValue

computeSeb

computeLinRegTTestNegativeSlope

computeLinRegTTestPositiveSlope

computeLinRegTTestUnequalSlope