Michael Thomas Flanagan's Java Scientific Library

ANOVA Class:     Analysis of Variance

      

Last update: 7 January 2012
Main Page of Michael Thomas Flanagan's Java Scientific Library

This class contains methods for:

In this documentation the measurements under analysis will be referred to as responses irrespective of whether the data is scientific, sociological, psychometric, educational etc. and whether the responding agency is human or inanimate.

Responses may be entered as:
from a text file or as a 2D array (double, float, Matrix, BigDecimal, long, int, BigInteger, String, char or boolean).
Great care should be taken in assessing whether your data is appropriate if entering non-parametric data into a parametric test.

import directive: import flanagan.analysis.ANOVA;

SUMMARY OF METHODS
Constructor public ANOVA()
public ANOVA(String dataTitle)
Enter the data Read title, group names
and responses from text file
Enter responses as rows per group		 public void readResponseData()
public void readResponseData(String filename)
Enter data via program
arrays
Enter responses as rows per group		 public void enterResponseData(double[][] responses)
public void enterResponseData(float[][] responses)
public void enterResponseData(long[][] responses)
public void enterResponseData(int[][] responses)
public void enterResponseData(Matrix responses)
public void enterResponseData(BigDecimal[][] responses)
public void enterResponseData(BigInteger[][] responses)
public void enterResponseData(String[][] responses)
public void enterResponseData(char[][] responses)
public void enterResponseData(boolean[][] responses)
Enter data title public void enterTitle(String title)
Enter group names public void enterGroupNames(String[] groupNames)
Dichotomous data pairs public void addDichotomousPair(String falseSign, String trueSign)
public void addDichotomousPair(char falseSign, char trueSign)
public void setDichotomousPairValues(double firstValue, double secondValue)
public double[] getDichotomousPairValues()
Critical significance level public void setCriticalSignificance(double critProb)
public double getCriticalSignificance()
Perform ANOVA With file output public void oneWayAnalysis(String filename)
public void oneWayAnalysisWithPairComparison(String filename)
public void oneWayAnalysisWithPairComparison(int group1, int group2, String filename)
public void oneWayAnalysis()
public void oneWayAnalysisWithPairComparison()
public void oneWayAnalysisWithPairComparison(int group1, int group2)
Without file output public void oneWayANOVA()
public void oneWayANOVAwithPairComparison()
public void oneWayANOVAwithPairComparison(int group1, int group2)
Print Analysis Print to a file public void outputAnalysis(String filename)
public void outputAnalysis()
Output file precision public void numberOfDecimalPlaces(int trunc)
public void numberOfDecimalPlacesAll(int trunc)
F-ratio for between and within groups F-ratio public double oneWayFratio()
public double oneWayFratio(int group1, int group2)
public BigDecimal oneWayFratio_as_BD()
public BigDecimal oneWayFratio_as_BD(int group1, int group2)
Significance public double oneWaySignificance()
public double oneWaySignificance(int group1, int group2)
F-ratio at critical level public double criticalFratio()
public double criticalFratio(int group1, int group2)
Degrees of Freedom Total degrees of freedom public int totalDoF()
public int totalDoF(int group1, int group2)
Degrees of freedom between groups public int betweenGroupsDoF()
public int betweenGroupsDoF(int group1, int group2)
Degrees of freedom within groups public int withinGroupsDoF()
public int withinGroupsDoF(int group1, int group2)
Mean Squares Total mean square public double totalMeanSquare()
public BigDecimal totalMeanSquare_as_BD()
public double totalMeanSquare(int group1, int group2)
public BigDecimal totalMeanSquare_as_BD(int group1, int group2)
Mean square between groups public double betweenGroupsMeanSquare()
public BigDecimal betweenGroupsMeanSquare_as_BD()
public double betweenGroupsMeanSquare(int group1, int group2)
public BigDecimal betweenGroupsMeanSquare_as_BD(int group1, int group2)
Mean square within groups public double withinGroupsMeanSquare()
public BigDecimal withinGroupsMeanSquare_as_BD()
public double withinGroupsMeanSquare(int group1, int group2)
public BigDecimal withinGroupsMeanSquare_as_BD(int group1, int group2)
Sum of Squares Total sum of squares public double totalSumOfSquares()
public BigDecimal totalSumOfSquares_as_BD()
public double totalSumOfSquares(int group1, int group2)
public BigDecimal totalSumOfSquares_as_BD(int group1, int group2)
Sum of squares between groups public double betweenGroupsSumOfSquares()
public BigDecimal betweenGroupsSumOfSquares_as_BD()
public double betweenGroupsSumOfSquares(int group1, int group2)
public BigDecimal betweenGroupsSumOfSquares_as_BD(int group1, int group2)
Sum of squares within groups public double withinGroupsSumOfSquares()
public BigDecimal withinGroupsSumOfSquares_as_BD()
public double withinGroupsSumOfSquares(int group1, int group2)
public BigDecimal withinGroupsSumOfSquares_as_BD(int group1, int group2)
Groups Enter group names public void enterGroupNames(String[] groupNames)
Get group names public String[] getGroupNames()
Get group name for a given index public String[] getGroupName(int i)
Get number of groups public int getNumberOfGroups()
Get number of responses per group public int[] numberOfResponsesPerGroup()
Get group means public double[] groupMeans()
public BigDecimal[] groupMeans_as_BD()
Get group standard deviations public double[] groupStandardDeviations()
Get group standard errors public double[] groupStandardErrors()
Get group mean lower confidence limits public double[] groupMeanLowerConfidenceLimits()
Get group mean upper confidence limits public double[] groupMeanUpperConfidenceLimits()
Get group minima public double[] groupMinima()
public BigDecimal[] groupMinima_as_BD()
Get group maxima public double[] groupMaxima()
public BigDecimal[] groupMaxima_as_BD()
Get group medians public double[] groupMedians()
public BigDecimal[] groupMedians_as_BD()
Get group moment skewnesses public double[] groupMomentSkewnesses()
Get group median skewnesses public double[] groupMedianSkewnesses()
Get group quartile skewnesses public double[] groupQuartileSkewnesses()
public BigDecimal[] groupQuartileSkewnesses_as_BD()
Get group kurtoses public double[] groupKurtoses()
public BigDecimal[] groupKurtoses_as_BD()
Get group excess kurtoses public double[] groupExcessKurtoses()
public BigDecimal[] groupExcessKurtoses_as_BD()
Total Responses Get total mean public double totalMean()
public BigDecimal totalMean_as_BD()
Get total standard deviation public double totalStandardDeviation()
Get total standard error public double totalStandardError()
Get total mean lower confidence limit public double totalMeanLowerConfidenceLimit()
Get total mean upper confidence limits public double totalMeanUpperConfidenceLimit()
Get total minimum public double totalMinimum()
public BigDecimal totalMinimum_as_BD()
Get total maximum public double totalMaximum()
public BigDecimal totalMaximum_as_BD()
Get total median public double totalMedian()
public BigDecimal totalMedian_as_BD()
Get total moment skewness public double totalMomentSkewness()
Get total median skewness public double totalMedianSkewness()
Get total quartile skewness public double totalQuartileSkewness()
public BigDecimal totalQuartileSkewness_as_BD()
Get total kurtosis public double totalKurtosis()
public BigDecimal totalKurtosis_as_BD()
Get total excess kurtosis public double totalExcessKurtosis()
public BigDecimal totalExcessKurtosis_as_BD()
Gaussian Probabilty Plots Groups public double[] groupGPPcorrelationCoefficient()
public double[] groupGPPgradient()
public double[] groupGPPintercept()
public double[] groupGPPmu()
public double[] groupGPPsigma()
Total responses public double totalGPPcorrelationCoefficient()
public double totalGPPgradient()
public double totalGPPintercept()
public double totalGPPmu()
public double totalGPPsigma()
Get Responses Get responses as entered public Object getResponsesAsEntered()
Get responses as double public double[][] getResponses()
public double[][] getResponsesAsdouble()
Get responses as BigDecimal public BigDecimal[][] getResponsesAsBigDecimal()



CONSTRUCTOR

public ANOVA(String dataTitle)
public ANOVA()
Usage:                      ANOVA aov = new ANOVA(dataTitle);
Creates an instance of ANOVA and sets the title of the data to be entered as the String held in dataTitle.

Usage:                      ANOVA aov = new ANOVA();
Creates an instance of ANOVA and sets the title of the data to be entered to the default name, Untitled data.

ENTER DATA

The data may be read from a text file or entered via data arrays and Strings created within your program. The responses should be enetered as rows of responses per each group.

READ THE DATA FROM A TEXT FILE
public void readResponseData()
public void readResponseData(String filename)
Usage:                      aov.readResponseData();
The data is read from a text (.txt) file selected via a dialogue window that will display all directories, and their files, on the user's computer and which opens, displaying the current directory, when this method is called.

Usage:                      aov.readResponseData(filename);
The data is read from the text (.txt) file filename. The file name must include its extension, e.g. .txt. It must either be in the working directory or the file name filename must also include the path to the appropriate directory, e.g. "C:\\AnalysisPrograms\\ScoresAnalyses\\ScoresDataOne.txt".

The text file must be of the following format:

     data title
     number of groups
     group names (one word each), as either a row or a column, e.g.    item1      item2  . . .   itemn
     number of responses per group, as either a row or a column
     response 1 for group 1     response 2 for group 1  . . .   final response for group 1 (all on one line)
     response 1 for group 2     response 2 for group 2  . . .   final response for group 2 (all on one line)
     . . . .
     response 1 for group n     response 2 for group n  . . .   final response for group n (all on one line)

where there are n groups.
Each group may contain a different number of responses.
The group names must be single words. Each response may be a floating point number, an integer number, a single word or a single letter. The group names and responses may be separated from any preceding and/or any following number or word by a single space or several spaces, a comma, a tab, a semicolon, colon or end of line. All responses for a group must be on the same line. The following list shows how the recognised non-numerical responses will be converted to a numeric format.
See Dichotomous Pairs for setting the option of reading dichotomous data with a non-numerical dichotomous pair not listed above and for resetting the numerical values of the dihotomous pair
Great care should be taken in assessing whether your data is appropriate if entering non-parametric data into a parametric test.
Example data file: AnovaExampleInput.txt.

ENTER DATA VIA PROGRAM ARRAYS
The responses must be enetered as rows of responses per group

Enter responses as rows per person
public void enterResponseData(double[][] responses)
public void enterResponseData(float[][] responses)
public void enterResponseData(long[][] responses)
public void enterResponseData(int[][] responses)
public void enterResponseData(Matrix responses)
public void enterResponseData(BigDecimal[][] responses)
public void enterResponseData(BigInteger[][] responses)
public void enterResponseData(String[][] responses)
public void enterResponseData(char[][] responses)
public void enterResponseData(boolean[][] responses)
Usage:                      aov.enterResponseData(responses);
The responses are entered via the two-dimension al array, responses. The array must be ordered in the following manner:

     responses[0][0] - response of person 1 to item 1      responses[0][1] - response of person 1 to item 2  . . .   responses[0][n-1] - response of person 1 to the nth item
     responses[1][0] - response of person 2 to item 1      responses[1][1] - response of person 1 to item 2  . . .   responses[1][n-1] - response of person 2 to the nth item
     . . . .
     responses[m-1][0] - response of person m to item 1      responses[m-1][1] - response of person m to item 2  . . .   responses[m-1][n-1] - response of person m to the nth item
where there are n items and m persons.
The allowed formats of the responses depends on the type of the array:
With the exception of data entered as either BigDecimal or BigInteger all entered data is converted to double before the ANOVA is performed. Data entered as BigInteger is converted to BigDecimal. The ANOVA of data entered as BigDecimal or BigInteger is performed in arbitrary precision arithmetic and the group analyses, for such entered data, is performed in arbitrary precision arithmetic where possible.
Great care should be taken in assessing whether your data is appropriate if entering non-parametric data into a parametric test.



GET RESPONSES
public Object getResponsesAsEntered()
public double[][] getResponses()
public double[][] getResponsesAsdouble()
public BigDecimal[][] getResponsesAsBigDecimal() Get responses as entered
Usage:                      responses = aov.getResponsesAsEntered()
This method returns the entered responses as the data type in which they were entered as an Object.

Get responses as double
Usage:                      responses = aov.getResponses()
                                  responses = aov.getResponsesAsdouble()
These two methods both return the entered responses as a two dimensional array of the data type double.

Get responses as BigDecimal
Usage:                      responses = aov.getResponsesAsEntered()
This method returns the entered responses as a two dimensional array of the data type BigDecimal.



ENTER TITLE
public void enterTitle(String title)
Usage:                      aov.enterTitle(title)
This is an optional method, for use if the responses have been entered via an array within your program. The data title is entered via the String argument title. A second line,
  Program execution initiated at the time on the date
will be automatically added to the entered title.
If this method is not called, and the responses have been entered via an array within your program, a default title,
  Untitled Data
  Program execution initiated at the time on the date
will be created.
These titles will be used as a header to any output file.



CRITICAL SIGNIFICANCE LEVEL
Enter the critcal significance level
public void setCriticalSignificance(double critProb)
Usage:                      aov.setCriticalSignificance(critProb)
This is an optional method, for use if you wish to reset the critical significance level used in displaying the ANOVA results. Enter the required critical significance level, crotProb, as a fraction of 1.0. The default value is 0.05.

Get the critcal significance level
public double getCriticalSignificance()
Usage:                      critProb = aov.getCriticalSignificance()
This method returns the critical significance level as a fraction of 1.0.


GROUP NAMES
Enter the group names
public void enterGroupNames(String[] names)
Usage:                      aov.enterGroupNames(names)
This is an optional method, for use if the responses have been entered via an array within your program. The group names are entered via the String[] argument names. It is suggested that you use short single word descriptors as these names are used as column headers in an output file. If this method is not called, and the responses have been entered via an array within your program, an array of default names,
  group1,  group2,  group3,  group4 . . .
will be created.

See GROUPS for all of the group methods.


DICHOTOMOUS DATA PAIRS
Add additional dichotomous data pairs
public void addDichotomousPair(String falseSign, String trueSign)
public void addDichotomousPair(char falseSign, char trueSign)
Usage:                      aov.addDichotomousPair(falseSign, trueSign)
This method should be called if you wish any of the above appropriate response entry methods to read dichotomous data in which the dichotomous pair is not one of the pairs already recognised by this class. The recognised pairs are (false, false or FALSE)/(true, True or TRUE), (yes, Yes, YES, y or Y)/(no, No, NO, n or N) or any numerical pair. If your pair is not one of the recognised pairs enter the pair via the arguments falseSign and trueSign. Responses equal to the argument falseSign, on data processing, will be converted to -1 and those equal to trueSign will be converted to 1. This method may be called if the data is to be read in from a text file or will be entered via a String[][] array or a char[][] array. If to be called it must be called before the responses are read or entered. The pair may be entered as a pair of String or a pair of char.

Reset the dichotomous pair numerical values
public void setDichotomousPairValues(double firstValue, double secondValue)
public double[] getDichotomousPairValues()
Usage:                      aov.setDichotomousPairValues(firstValue, secondValue)
This method allows the values assigned to dichotomous pairs to be reset to the values entere as firstValue and secondValue. The default values, if this method is not called, are -1.0 and 1.0.

Usage:                      pairValues = aov.getDichotomousPairValues()
This method returns the two dichotomous pair values as the first and second element of an array of doubles.


ANALYSIS OF VARIANCE (ANOVA)


ANOVA of all groups together with NO comparison of individual pairs of groups
public void oneWayAnalysis(String filename)
public void oneWayAnalysis()
public void oneWayANOVA()
Perform a one-way analysis of variance and write the results to a file.
Usage:                      aov.oneWayAnalysis(filename)
This method performs a one way analysis of variance of all the entered groups together. The results of the analysis are vwritten to a file named filename. If you add the ".txt" extension to the name in the the String filename the results will be written to a text file that displays the results in an easily readable format.
If you add the ".xls" extension, the results are written in a format to facilitate display by Microsoft Excel. On opening, with Microsoft Excel, a ".xls" file created by this method Microsoft Excel may ask you to verify that file is Excel readable. Click the "yes" button in the query box.
The output file will be created in the directory in which you are working unless you add a path to filename, e.g. "C:\\AnalysisPrograms\\ANOVA\\AnovaOutput.txt".

The output file will be of the form:
    Title/s
    Input file name if data read from a text file
    This output file name
    Date of execution

    One-Way ANOVA for all groups together:
         Sum of squares
         Degrees of freedom
         Mean square
     all for between groups analysis, within groups analysis and a total analysis
         F-ratio for the between groups and within groups analyses
         F-ratio at the (100 - α)% critical level
         The significance calculated for the F-ratio

    Analysis of each group and of all of the responses:
         Number of responses
         mean
         Standard deviation
         Standard Error
         Lower bound of the α% confidence interval of the mean
         Upper bound of the α% confidence interval of the mean
         Minimum
         Maximum
   where the default value for the critical value, α%, is 95%. The value of α may be altered by calling the method setCriticalSignificance(critProb), where α = 100(1.0 - critProb).

Example output file with no pair comparisons: AnovaExampleOutputOne.txt
See below for details of the precision with which the output values are printed and how this may be reset.

Usage:                      aov.oneWayAnalysis()
This method performs the same analysis as described immediately above and writes the above described analysis to a file of file name, OneWayANOVAoutput.

Usage:                      aov.ANOVA()
This method performs the same analysis as described immediately above but does NOT write the analysis to a file. The results of the analysis may be accessed using the various get methods.

ANOVA of all groups together plus a comparison of all individual pairs of groups
public void oneWayAnalysisWithPairComparison(String filename)
public void oneWayAnalysisWithPairComparison()
public void oneWayANOVAWithPairComparison()
Perform a one-way analysis of variance and write the results to a file.
Usage:                      aov.oneWayAnalysisWithPairComparison(filename)
This method performs a one way analysis of variance of all entered groups together and of all individual pairs of the entered groups. The results of the analysis are written to a file named filename. If you add the ".txt" extension to the name in the the String filename the results will be written to a text file that displays the results in an easily readable format.
If you add the ".xls" extension, the results are written in a format to facilitate display by Microsoft Excel. On opening, with Microsoft Excel, a ".xls" file created by this method Microsoft Excel may ask you to verify that file is Excel readable. Click the "yes" button in the query box.
. Click the "yes" button in the query box.
The output file will be created in the directory in which you are working unless you add a path to filename, e.g. "C:\\AnalysisPrograms\\ANOVA\\AnovaOutput.txt".

The output file will be of the form:
    Title/s
    Input file name if data read from a text file
    This output file name
    Date of execution

    One-Way ANOVA for all groups together:
         Sum of squares
         Degrees of freedom
         Mean square
     all for between groups analysis, within groups analysis and a total analysis
         F-ratio for the between groups and within groups analyses
         F-ratio at the (100 - α)% critical level
         The significance calculated for the F-ratio

    Analysis of each group and of all of the responses:
         Number of responses
         mean
         Standard deviation
         Standard Error
         Lower bound of the α% confidence interval of the mean
         Upper bound of the α% confidence interval of the mean
         Minimum
         Maximum
   where the default value for the critical value, α%, is 95%. The value of α may be altered by calling the method setCriticalSignificance(critProb), where α = 100(1.0 - critProb).

    Pair comparisons:
    A summary of the one way analysis of variance (ANOVA), as described above for all groups together, will be printed here for all pairs of groups.

Example output file with all pairs compared: AnovaExampleOutputTwo.txt
See below for details of the precision with which the output values are printed and how this may be reset.

Usage:                      aov.oneWayAnalysisWithPairComparison()
This method performs the same analysis as described immediately above and writes the above described analysis to a file of file name, OneWayANOVAoutput.

Usage:                      aov.ANOVAWithPairComparison()
This method performs the same analysis as described immediately above but does NOT write the analysis to a file. The results of the analysis may be accessed using the various get methods.

ANOVA of all groups together plus a comparison of a chosen individual pair of groups
public void oneWayAnalysisWithPairComparison(int group1, int group2, String filename)
public void oneWayAnalysisWithPairComparison(int group1, int group2)
public void oneWayANOVAWithPairComparison(int group1, int group2)
Perform a one-way analysis of variance and write the results to a file.
Usage:                      aov.oneWayAnalysisWithPairComparison(group1, group2, filename)
This method performs a one way analysis of variance of all entered groups together and of the pair of entered groups whose indices are the integers, group1 and group1. The indices start at 1, e.g. if group1 corresponds to the first group entered its value will be 1 and if group2 corresponds to the fourth group entered its value will be 4. The results of the analysis are written to a file named filename. If you add the ".txt" extension to the name in the the String filename the results will be written to a text file that displays the results in an easily readable format.
If you add the ".xls" extension, the results are written in a format to facilitate display by Microsoft Excel. On opening, with Microsoft Excel, a ".xls" file created by this method Microsoft Excel may ask you to verify that file is Excel readable. Click the "yes" button in the query box.

The output file will be created in the directory in which you are working unless you add a path to filename, e.g. "C:\\AnalysisPrograms\\ANOVA\\AnovaOutput.txt".

The output file will be of the form:
    Title/s
    Input file name if data read from a text file
    This output file name
    Date of execution

    One-Way ANOVA for all groups together:
         Sum of squares
         Degrees of freedom
         Mean square
     all for between groups analysis, within groups analysis and a total analysis
         F-ratio for the between groups and within groups analyses
         F-ratio at the (100 - α)% critical level
         The significance calculated for the F-ratio

    Analysis of each group and of all of the responses:
         Number of responses
         mean
         Standard deviation
         Standard Error
         Lower bound of the α% confidence interval of the mean
         Upper bound of the α% confidence interval of the mean
         Minimum
         Maximum
   where the default value for the critical value, α%, is 95%. The value of α may be altered by calling the method setCriticalSignificance(critProb), where α = 100(1.0 - critProb).

    Pair comparisons:
    A summary of the one way analysis of variance (ANOVA), as described above for all groups together, will be printed here for the chosen pair of groups.

Example output file with an chosen individual pair comparison: AnovaExampleOutputThree.txt
See below for details of the precision with which the output values are printed and how this may be reset.

Usage:                      aov.oneWayAnalysisWithPairComparison(group1, group2)
This method performs the same analysis as described immediately above and writes the above described analysis to a file of file name, OneWayANOVAoutput.

Usage:                      aov.ANOVAWithPairComparison(group1, group2)
This method performs the same analysis as described immediately above but does NOT write the analysis to a file. The results of the analysis may be accessed using the various get methods.


PRINT THE ANALYSIS TO A FILE

Print ANOVA and Group Statistics
public void outputAnalysis(String filename)
public void outputAnalysis()
Usage:                      aov.outputAnalysis(filename)
This method performs a one way analysis of variance, if an analysis has not already been performed, and writes the results of the analysis to a file named filename. If you add the ".txt" extension to the name in the the String filename the results will be written to a text file that displays the results in an easily readable format.
If you add the ".xls" extension, the results are written in a format to facilitate display by Microsoft Excel. On opening, with Microsoft Excel, a ".xls" file created by this method Microsoft Excel may ask you to verify that file is Excel readable. Click the "yes" button in the query box.
.
The output file will be created in the directory in which you are working unless you add a path to filename, e.g. "C:\\AnalysisPrograms\\ANOVA\\AnovaOutput.txt".

The output file will be of the form:
    Title
    Date of execution

    One-Way ANOVA for all groups together:
         Sum of squares
         Degrees of freedom
         Mean square
     all for between groups analysis, within groups analysis and a total analysis
         F-ratio for the between groups and within groups analyses
         F-ratio at the (100 - α)% critical level
         The significance calculated for the F-ratio

    Analysis of each group:
         Number of responses
         mean
         Standard deviation
         Standard Error
         Lower bound of the α% confidence interval of the mean
         Upper bound of the α% confidence interval of the mean
         Minimum
         Maximum
   where the default value for the critical value, α%, is 95%. The value of α may be altered by calling the method setCriticalSignificance(critProb), where α = 100(1.0 - critProb).

    Pair comparisons:
    If an analysis method with pair comparisons has been chosen a summary of the one way analysis of variance (ANOVA), as described above for all groups together, will be printed here for each chosen pair of groups.

Example output file with no pair comparisons: AnovaExampleOutputOne.txt
Example output file with all pairs compared: AnovaExampleOutputTwo.txt
Example output file with a single pair comparison: AnovaExampleOutputThree.txt

Usage:                      aov.outputAnalysis()
This method performs the same analysis as described immediately above and writes the above described analysis to a file of file name, OneWayANOVAoutput.

Set the precision with which floating point numbers are written
public void numberOfDecimalPlaces(int trunc)
Usage:                      aov.numberOfDecimalPlaces(trunc)
This optional method sets the number of places displayed after the decimal point when floating point numbers are written to an output file. The number of places required is entered via the argument trunc. The default value is 6. The displayed number is the rounded equivalent of the stored number. If the precision of the entered data is greater than the value trunc the output method overides the trunc value and uses the maximum precision of the entered data. Data of precision greater than 15, i.e. in data entered as BigDecimal, will be truncated to a precision of 15 on output to a file. Use the various get methods to obtain results that may be of greater precision. See immediately below (numberOfDecimalPlacesAll) for a method that sets the output precision irrespective of the input precision.

public void numberOfDecimalPlacesAll(int trunc)
Usage:                      aov.numberOfDecimalPlacesAll(trunc)
This optional method sets the number of places displayed after the decimal point when floating point numbers are written to an output file. The number of places required is entered via the argument trunc. The default value is 6. The displayed number is the rounded equivalent of the stored number. The precision set by this method is used in the output irrespective of the precision of the input data. See immediately above (numberOfDecimalPlaces) for a method that sets takes the precision of the entered data into account.


F-RATIO

F-ratio calculated for between and within groups
public double oneWayFratio()
public BigDecimal oneWayFratio_as_BD()
public double oneWayFratio(int groupa, int groupb)
public BigDecimal oneWayFratio_as_BD(int groupa, int groupb)
Usage:                      fratio = aov.oneWayFratio()
This method returns the F-ratio, F, calculated for the mean square between groups and the mean square within groups for a one-way ANOVA of all the entered data,

where






xij is the jth response of the ith group, n is the number of groups and mj is the number of responses in the jth group. The F-ratio value is returned as a double.

Usage:                      fratio = aov.oneWayFratio_as_BD()
This method returns the F-ratio calculated for the mean square between groups and the mean square within groups for a one-way ANOVA of the entered data. The F-ratio value is returned as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Usage:                      fratioab = aov.oneWayFratio(groupa, groupb)
This method returns the F-ratio, F, for the two groups of indices groupa and groupb where the above definitions are unchanged with the exceptions:



dofbetween = 1
dofwithin = ma + mb - 2
where ma and mb are the nubers of responses in the groups of indices groupa and groupb respectively. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4. The F-ratio value is returned as a double.

Usage:                      fratio = aov.oneWayFratio_as_BD(groupa, groupb)
This method returns the F-ratio, F, for the two groups of indices groupa and groupb as described above. The F-ratio value is returned as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

F-ratio significance
public double oneWaySignificance()
public double oneWaySignificance(int groupa, int groupb)
Usage:                      significance = aov.oneWaySignificance()
This method returns the significance calculated for the F-ratio calculated for the mean square between groups and the mean square within groups for a one-way ANOVA of the entered data. The significance value is returned as a double.

Usage:                      significance = aov.oneWaySignificance(groupa, groupb)
This method returns the significance calculated for the F-ratio calculated for the mean square between the two groups and the mean square within the two groups for a one-way ANOVA of the responses in the two groups of indices groupa and groupb. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4. The significance value is returned as a double.

Critical F-ratio
public double criticalFratio()
public double criticalFratio(int groupa, int groupb)
Usage:                      critFratio = aov.criticalFratio()
This method returns the F-ratio calculated to give the chosen critical significance for the degrees of freedom within groups and between groups for all the entered data. The default value of the critical significance is 0.05 (5%). The user may reset the critical significance level (see setCriticalSignificance).

Usage:                      critFratio = aov.criticalFratio(groupa, groupb)
This method returns the F-ratio calculated to give the chosen critical significance for the degrees of freedom within groups and between groups for the two groups of indices groupa and groupb. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4. The default value of the critical significance is 0.05 (5%). The user may reset the critical significance level (see setCriticalSignificance)


DEGREES OF FREEDOM

Total degrees of freedom
public int totalDoF()
public int totalDoF(int groupa, int groupb)
Usage:                      doft = aov.totalDoF()
This method returns the total degrees of freedom, doftotal, for a one-way ANOVA of all the entered data

where n is the number of groups and mi is the number of responses in the ith group.

Usage:                      doftab = aov.totalDoF(groupa, groupb)
This method returns the total degrees of freedom, doftotal, for a one-way ANOVA of the pair of groups of indices groupa and groupb
doftotal = ma + mb - 1
where ma and mb are the number of responses groups of indices groupa and groupb. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4.

Degrees of freedom between groups
public int betweenGroupsDoF()
public int betweenGroupsDoF(int groupa, int groupb)
Usage:                      dofb = aov.betweenGroupsDoF()
This method returns the between groups degrees of freedom, dofbetween, for a one-way ANOVA of all entered data
dofbetween = n - 1
where n is the number of groups.

Usage:                      doftab = aov.betweenDoF(groupa, groupb)
This method returns the between groups degrees of freedom, dofbetween, for a one-way ANOVA of the pair of groups of indices groupa and groupb
dofbetween = 1
The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4.

Degrees of freedom within groups
public int withinGroupsDoF()
public int withinGroupsDoF(int groupa, int groupb)
Usage:                      dofw = aov.withinGroupsDoF()
This method returns the within groups degrees of freedom for a one-way ANOVA of all entered data

where n is the number of groups and mi is the number of responses in the ith group.

Usage:                      doftab = aov.withinDoF(groupa, groupb)
This method returns the within groups degrees of freedom, dofwithin, for a one-way ANOVA of the pair of groups of indices groupa and groupb
dofwithin = ma + mb - 2
where ma and mb are the number of responses groups of indices groupa and groupb. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4.




MEAN SQUARES

Total mean square
public double totalMeanSquare()
public BigDecimal totalMeanSquare_as_BD()
public double totalMeanSquare(int groupa, int groupb)
public BigDecimal totalMeanSquare_as_BD(int groupa, int groupb)
Usage:                      mst = aov.totalMeanSquare()
This method returns the total mean square, MStotal, for all the entered data

where
              
xij is the jth response of the ith group, n is the number of groups and mj is the number of responses in the jth group. The value of MStotal is returned as a double.

Usage:                      mst = aov.totalMeanSquare_as_BD()
This method returns the total mean square, MStotal, as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Usage:                      mstab = aov.totalMeanSquare(groupa, groupb)
This method returns the total mean square, MStotal, for the pair of groups of indices groupa and groupb

where

doftotal = ma + mb - 1
where ma and mb are the nubers of responses in the groups of indices groupa and groupb respectively. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4. The value of MStotal is returned as a double.

Usage:                      mstab = aov.totalMeanSquare_as_BD(groupa, groupb)
This method returns the total mean square, MStotal, for the pair of groups of indices groupa and groupb as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Mean square between groups
public double betweenGroupsMeanSquare()
public BigDecimal betweenGroupsMeanSquare_as_BD()
public double betweenGroupsMeanSquare(int groupa, int groupb)
public BigDecimal betweenGroupsMeanSquare_as_BD(int groupa, int groupb)
Usage:                      msb = aov.betweenGroupsMeanSquare()
This method returns the between groups mean square, MSbetween, for all the entered data

where
                             
xij is the jth response of the ith group, n is the number of groups and mj is the number of responses in the jth group. The value of MSbetween is returned as a double.

Usage:                      msb = aov.betweenGroupsMeanSquare_as_BD()
This method returns the between groups mean square, MSbetween, as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Usage:                      msbab = aov.betweenGroupsMeanSquare(groupa, groupb)
This method returns the between groups mean square, MSbetween, for the pair of groups of indices groupa and groupb


where
              
dofbetween = 1

xij is the jth response of the ith group, ma and mb are the nubers of responses in the groups of indices groupa and groupb respectively. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4. The value of MSbetween is returned as a double.

Usage:                      msbab = aov.betweenGroupsMeanSquare_as_BD(groupa, groupb)
This method returns the between groups mean square, MSbetween, for the pair of groups of indices groupa and groupb as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Mean square within groups
public double withinGroupsMeanSquare()
public BigDecimal withinGroupsMeanSquare_as_BD()
public double withinGroupsMeanSquare(int groupa, int groupb)
public BigDecimal withinGroupsMeanSquare_as_BD(int groupa, int groupb)
Usage:                      msw = aov.withinGroupsMeanSquare()
This method returns the within groups mean square, MSwithin, for all the entered data

where
              
xij is the jth response of the ith group, n is the number of groups and mj is the number of responses in the jth group. The value of MSwithin is returned as a double.

Usage:                      msw = aov.withinGroupsMeanSquare_as_BD()
This method returns the within groups mean square, MSwithin, as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Usage:                      mswab = aov.withinGroupsMeanSquare(groupa, groupb)
This method returns the within groups mean square, MSwithin, for the pair of groups of indices groupa and groupb


where

dofwithin = ma + mb - 2
xij is the jth response of the ith group, ma and mb are the nubers of responses in the groups of indices groupa and groupb respectively. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4. The value of MSwithin is returned as a double.

Usage:                      mswab = aov.withinGroupsMeanSquare_as_BD(groupa, groupb)
This method returns the within groups mean square, MSwithin, for the pair of groups of indices groupa and groupb as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.


SUM OF SQUARES

Total sum of squares
public double totalSumOfSquares()
public BigDecimal totalSumOfSquares_as_BD()
public double totalSumOfSquares(int groupa, int groupb)
public BigDecimal totalSumOfSquares_as_BD(int groupa, int groupb)
Usage:                      sst = aov.totalSumOfSquares()
This method returns the total sum of squares, SStotal, for all the entered data

where

xij is the jth response of the ith group, n is the number of groups and mj is the number of responses in the jth group. The value of SStotal is returned as a double.

Usage:                      sst = aov.totalSumOfSquares_as_BD()
This method returns the total sum of squares, SStotal, as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Usage:                      sstab = aov.totalSumOfSquares(groupa, groupb)
This method returns the total sum of squares, SStotal, for the pair of groups of indices groupa and groupb


where

xij is the jth response of the ith group, ma and mb are the nubers of responses in the groups of indices groupa and groupb respectively. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4. The value of SStotal is returned as a double.

Usage:                      sstab = aov.totalSumOfSquares_as_BD(groupa, groupb)
This method returns the total sum of squares, SStotal, for the pair of groups of indices groupa and groupb as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Between groups sum of squares
public double betweenGroupsSumOfSquares()
public BigDecimal betweenGroupsSumOfSquares_as_BD()
public double betweenGroupsSumOfSquares(int groupa, int groupb)
public BigDecimal betweenGroupsSumOfSquares_as_BD(int groupa, int groupb)
Usage:                      ssb = aov.betweenGroupsSumOfSquares()
This method returns the between groups sum of squares, SSbetween, for all the entered data

where
              
xij is the jth response of the ith group, n is the number of groups and mj is the number of responses in the jth group. The value of SSbetween is returned as a double.

Usage:                      ssb = aov.betweenGroupsSumOfSquares_as_BD()
This method returns the between groups sum of squares, SSbetween, for all the entered data as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Usage:                      ssb = aov.betweenGroupsSumOfSquares(groupa, groupb)
This method returns the between groups sum of squares, SSbetween, for the pair of groups of indices groupa and groupb


where
              
xij is the jth response of the ith group, ma and mb are the nubers of responses in the groups of indices groupa and groupb respectively. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4. The value of SSbetween is returned as a double.

Usage:                      ssb = aov.betweenGroupsSumOfSquares_as_BD(groupa, groupb)
This method returns the between groups sum of squares, SSbetween, for the pair of groups of indices groupa and groupb as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Within groups sum of squares
public double withinGroupsSumOfSquares()
public BigDecimal withinGroupsSumOfSquares_as_BD()
public double withinGroupsSumOfSquares(int groupa, int groupb)
public BigDecimal withinGroupsSumOfSquares_as_BD(int groupa, int groupb)
Usage:                      ssw = aov.withinGroupsSumOfSquares()
This method returns the within groups sum of squares, SSwithin, for all the entered data

where

xij is the jth response of the ith group, n is the number of groups and mj is the number of responses in the jth group. The value of SSwithin is returned as a double.

Usage:                      ssw = aov.withinGroupsSumOfSquares_as_BD()
This method returns, as a BigDecimal, the within groups sum of squares, SSwithin, for all the entered data. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.,br />
Usage:                      ssw = aov.withinGroupsSumOfSquares(groupa, groupb)
This method returns the within groups sum of squares, SSwithin, for the pair of groups of indices groupa and groupb


where

xij is the jth response of the ith group, ma and mb are the nubers of responses in the groups of indices groupa and groupb respectively. The indices start at 1, e.g. if groupa corresponds to the first group entered its value will be 1 and if groupb corresponds to the fourth group entered its value will be 4. The value of SSwithin is returned as a double.

Usage:                      ssw = aov.withinGroupsSumOfSquares_as_BD(groupa, groupb)
This method returns the within groups sum of squares, SSwithin, for the pair of groups of indices groupa and groupb as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.


GROUPS

Enter the group names
public void enterGroupNames(String[] names)
Usage:                      aov.enterGroupNames(names)
This is an optional method, for use if the responses have been entered via an array within your program. The group names are entered via the String[] argument names. It is suggested that you use short single word descriptors as these names are used as column headers in an output file. If this method is not called, and the responses have been entered via an array within your program, an array of default names,
  group1,  group2,  group3,  group4 . . .
will be created.

Get all the entered item names
public String[] getGroupNames()
Usage:                      groupNames = aov.getGroupNames()
This method returns the group names of all the groups entered, i.e. before any item deletions have been made.

Get the name of a group of a given index
public String getGroupName(int index)
Usage:                      name = aov.getGroupName(index)
This method returns the name of the group of index itemN. NOTE!! the indices of the groups starts at 1 NOT at 0.

Get the number of groups
public int getNumberOfGroups()
Usage:                      name = aov.getGroupName(index)
This method returns the name of the group of index index. NOTE!! the indices of the groups starts at 1 NOT at 0.

Get number of responses per group
public int[] numberOfResponsesPerGroup()
Usage:                      nresponses = aov.numberOfResponsesPerGroup()
This method returns the number of responses in each group as an array of int.

Get group means
public double[] groupMeans()
public BigDecimal[] groupMeans_as_BD()
Usage:                      means = aov.groupMeans()
This method returns the means of the groups as an array of double.

Usage:                      means = aov.groupMeans_as_BD()
This method returns the means of the groups as an array of BigDouble. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get group standard deviations
public double[] groupStandarDeviations()
Usage:                      sd = aov.groupStandardDeviations()
This method returns the standard deviations of the groups as an array of double.

Get group standard errors
public double[] groupStandarErrors()
Usage:                      se = aov.groupStandardErrors()
This method returns the standard errors of the groups as an array of double.

Get group mean lower confidence limits
public double[] groupMeanLowerConfidenceLimits()
Usage:                      lci = aov.groupMeanLowerConfidenceLimits()
This method returns the lower limits of the α% confidence interval for the means of the groups as an array of double. The default value for the critical value, α%, is 95%. The value of α may be altered by calling the method setCriticalSignificance(critProb), where α = 100(1.0 - critProb).

Get group mean upper confidence limits
public double[] groupMeanUpperConfidenceLimits()
Usage:                      uci = aov.groupMeanUpperConfidenceLimits()
This method returns the upper limits of the α% confidence interval for the means of the groups as an array of double. The default value for the critical value, α%, is 95%. The value of α may be altered by calling the method setCriticalSignificance(critProb), where α = 100(1.0 - critProb).

Get group minima
public double[] groupMinima()
public BigDecimal[] groupMinima_as_BD()
Usage:                      min = aov.groupMinima()
This method returns the minima of the groups as an array of double.

Usage:                      min = aov.groupMinima_as_BD()
This method returns the minima of the groups as an array of BigDouble. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get group maxima
public double[] groupMaxima()
public BigDecimal[] groupMaxima_as_BD()
Usage:                      meax = aov.groupMaxima()
This method returns the maxima of the groups as an array of double.

Usage:                      max = aov.groupMaxima_as_BD()
This method returns the maxima of the groups as an array of BigDouble. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get group medians
public double[] groupMedians()
public BigDecimal[] groupMedians_as_BD()
Usage:                      med = aov.groupMedians()
This method returns the medians of the groups as an array of double.

Usage:                      med = aov.groupMedians_as_BD()
This method returns the medians of the groups as an array of BigDouble. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get group moment skewnesses
public double[] groupMomentSkewnesses()
Usage:                      momskew = aov.groupMomentSkewnesses()
This method returns the moment skewnesses of the groups as an array of double.

Get group median skewnesses
public double[] groupMedianSkewnesses()
Usage:                      medskew = aov.groupMedianSkewnesses()
This method returns the median skewnesses of the groups as an array of double.

Get group quartile skewnesses
public double[] groupQuartileSkewnesses()
public BigDecimal[] groupQuartileSkewnesses_as_BD()
Usage:                      qskew = aov.groupQuartileSkewnesses()
This method returns the quartile skewnesses of the groups as an array of double.

Usage:                      qskew = aov.groupQuartileSkewnesses_as_BD()
This method returns the quartile skewnesses of the groups as an array of BigDouble. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get group kurtoses
public double[] groupKurtoses()
public BigDecimal[] groupKurtoses_as_BD()
Usage:                      kurt = aov.groupKurtoses()
This method returns the kurtoses of the groups as an array of double.

Usage:                      kurt = aov.groupKurtoses_as_BD()
This method returns the kurtoses of the groups as an array of BigDouble. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get group excess kurtoses
public double[] groupExcessKurtoses()
public BigDecimal[] groupExcessKurtoses_as_BD()
Usage:                      ekurt = aov.groupExcessKurtoses()
This method returns the excess kurtoses of the groups as an array of double.

Usage:                      ekurt = aov.groupExcessKurtoses_as_BD()
This method returns the excess kurtoses of the groups as an array of BigDouble. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.


TOTAL RESPONSES

Get total mean
public double totalMean()
public BigDecimal totalMean_as_BD()
Usage:                      mean = aov.totalMean()
This method returns the mean of the total responses as a double.

Usage:                      mean = aov.totalMean_as_BD()
This method returns the mean of the total responses as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get total standard deviation
public double totalStandarDeviation()
Usage:                      sd = aov.totalStandardDeviation()
This method returns the standard deviation of the total responses as a double.

Get total standard error
public double totalStandarError()
Usage:                      se = aov.totalStandardError()
This method returns the standard error of the total responses as a double.

Get total mean lower confidence limit
public double totalMeanLowerConfidenceLimit()
Usage:                      lci = aov.totalMeanLowerConfidenceLimit()
This method returns the lower limit of the α% confidence interval for the mean of the total responses as a double. The default value for the critical value, α%, is 95%. The value of α may be altered by calling the method setCriticalSignificance(critProb), where α = 100(1.0 - critProb).

Get total mean upper confidence limit
public double totalMeanUpperConfidenceLimit()
Usage:                      uci = aov.totalMeanUpperConfidenceLimit()
This method returns the upper limit of the α% confidence interval for the mean of the total responses as a double. The default value for the critical value, α%, is 95%. The value of α may be altered by calling the method setCriticalSignificance(critProb), where α = 100(1.0 - critProb).

Get total minimum
public double totalMinimum()
public BigDecimal totalMinimum_as_BD()
Usage:                      min = aov.totalMinimum()
This method returns the minimum of the total responses as a double.

Usage:                      min = aov.totalMinimum_as_BD()
This method returns the minimum of the total responses as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get total maximum
public double totalMaximum()
public BigDecimal totalMaximum_as_BD()
Usage:                      meax = aov.totalMaximum()
This method returns the maximum of the total responses as a double.

Usage:                      max = aov.totalMaximum_as_BD()
This method returns the maximum of the total responses as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get total median
public double totalMedian()
public BigDecimal totalMedian_as_BD()
Usage:                      med = aov.totalMedian()
This method returns the median of the total responses as a double.

Usage:                      med = aov.totalMedian_as_BD()
This method returns the median of the total responses as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get total moment skewness
public double totalMomentSkewness()
Usage:                      momskew = aov.totalMomentSkewness()
This method returns the moment skewness of the total responses as a double.

Get total median skewness
public double totalMedianSkewness()
Usage:                      medskew = aov.totalMedianSkewness()
This method returns the median skewness of the total responses as a double.

Get total quartile skewness
public double totalQuartileSkewness()
public BigDecimal totalQuartileSkewness_as_BD()
Usage:                      qskew = aov.totalQuartileSkewness()
This method returns the quartile skewness of the total responses as a double.

Usage:                      qskew = aov.totalQuartileSkewness_as_BD()
This method returns the quartile skewness of the total responses as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get total kurtosis
public double totalKurtosis()
public BigDecimal totalKurtosis_as_BD()
Usage:                      kurt = aov.totalKurtosis()
This method returns the kurtosis of the total responses as a double.

Usage:                      kurt = aov.totalKurtosis_as_BD()
This method returns the kurtosis of the total responses as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.

Get total excess kurtosis
public double totalExcessKurtosis()
public BigDecimal totalExcessKurtosis_as_BD()
Usage:                      ekurt = aov.totalExcessKurtosis()
This method returns the excess kurtosis of the total responses as a double.

Usage:                      ekurt = aov.totalExcessKurtosis_as_BD()
This method returns the excess kurtosis of the total responses as a BigDecimal. If the data was entered as types BigDecimal or BigInteger the calculation will have been performed in arbitrary precision otherwise it will have been performed in double precision.


GAUSSIAN PROBABILITY PLOTS

GAUSSIAN PROBABILITY PLOTS:     GROUPS
Correlation coefficients
public double[] groupGPPcorrelationCoefficient()
Usage:                      corrCoeff = aov.groupGPPcorrelationCoefficient()
This method returns the correlation coefficients of the Gaussian Probability Plots of the data entered for each group against the corresponding Gaussian order statistic medians.

Gradients
public double[] groupGPPgradient()
Usage:                      gradient = aov.groupGPPgradient()
This method returns the gradients of the Gaussian Probability Plots of the data entered for each group against the corresponding Gaussian order statistic medians.

Intercepts
public double[] groupGPPintercept()
Usage:                      intercept = aov.groupGPPintercepts()
This method returns the intercepts of the Gaussian Probability Plots of the data entered for each group against the corresponding Gaussian order statistic medians.

Estimate of the means, μ
public double[] groupGPPmu()
Usage:                      mu = aov.groupGPPmu()
This method returns the estimates of the Gaussian means (μ) giving the best fits to the Gaussian Probability Plots of the data entered for each group against the corresponding Gaussian order statistic medians.

Estimate of the standard deviations, σ
public double[] groupGPPsigma()
Usage:                      sigma = aov.groupGPPsigma()
This method returns the estimates of the Gaussian standards deviations (σ) giving the best fits to the Gaussian Probability Plots of the data entered for each group against the corresponding Gaussian order statistic medians.

GAUSSIAN PROBABILITY PLOTS:     TOTAL RESPONSES
Correlation coefficient
public double totalGPPcorrelationCoefficient()
Usage:                      corrCoeff = aov.totalGPPcorrelationCoefficient()
This method returns the correlation coefficient of the Gaussian Probability Plot of the data entered for all the responses against the corresponding Gaussian order statistic medians.

Gradients
public double totalGPPgradient()
Usage:                      gradient = aov.totalGPPgradient()
This method returns the gradient of the Gaussian Probability Plot of the data entered for all the responses against the corresponding Gaussian order statistic medians.

Intercepts
public double totalGPPintercept()
Usage:                      intercept = aov.totalGPPintercept()
This method returns the intercept of the Gaussian Probability Plot of the data entered for all the responses against the corresponding Gaussian order statistic medians.

Estimate of the means, μ
public double totalGPPmu()
Usage:                      mu = aov.totalGPPmu()
This method returns the estimate of the Gaussian mean (μ) giving the best fit to the Gaussian Probability Plot of the data entered for all the responses against the corresponding Gaussian order statistic medians.

Estimate of the standard deviations, σ
public double totalGPPsigma()
Usage:                      sigma = aov.totalGPPsigma()
This method returns the estimate of the Gaussian standards deviation (σ) giving the best fit to the Gaussian Probability Plot of the data entered for all the responses against the corresponding Gaussian order statistic medians.




OTHER CLASSES USED BY THIS CLASS

This class uses the following classes in this library:

This page was prepared by Dr Michael Thomas Flanagan