Class WilcoxonSignedRankGUI

java.lang.Object

java.awt.Component

java.awt.Container

java.awt.Window

java.awt.Frame

javax.swing.JFrame

WilcoxonSignedRankGUI

All Implemented Interfaces:

java.awt.event.ActionListener, java.awt.event.FocusListener, java.awt.event.ItemListener, java.awt.image.ImageObserver, java.awt.MenuContainer, java.io.Serializable, java.util.EventListener, javax.accessibility.Accessible, javax.swing.RootPaneContainer, javax.swing.WindowConstants

public class WilcoxonSignedRankGUI
extends javax.swing.JFrame
implements java.awt.event.ActionListener, java.awt.event.FocusListener, java.awt.event.ItemListener

WilcoxonSignedRank - GUI Version

• A Java utility to perform a Wilcoxon Signed-Rank test on a table of data

The Wilcoxon Signed-Rank test is a non-parametric statistical procedure to assess the difference between two correlated samples, which is to say, between two conditions assigned within-subjects. The relationship with other non-parametric tests is illustrated below:

Design	Conditions (samples)
	2	3 or more
Between-subjects (independent samples)	Mann-Whitney U	Kruskal Wallis
Within-subjects (correlated samples)	Wilcoxon Signed-Rank	Friedman

The test is also called the Wilcoxon Matched-Pairs Signed-Rank Test. Without "Matched-Pairs" the test assumes one of the samples is a default or assumed score against which variations in the other sample are compared. Either way, the computations are identical.

The procedure involves first building an array of difference scores (the difference between pairs of values for each participant). Differences equal to zero are ignored (i.e., no difference). An array of ranks is then built from the array of difference scores. The ranks are tested to determine if there is a significant difference between the two conditions. More formally, the hypothesis evaluated is "whether or not in the underlying populations represented by the samples/experimental conditions, the median of the difference scores equals zero. If a significant difference is obtained it indicates there is a high likelihood the two samples/conditions represent two different populations" (D. J. Sheskin, Handbook of Parametric and Non-parametric Statistical Procedures, 5th ed., CRC Press, 2011, p. 809).

The test is intended for ordinal data, such as rankings, assessments, or questionnaire responses (where the responses are non-linear). Using the Wilcoxon Signed-Rank test (or other non-parametric tests) for interval or ratio data might be preferred over a parametric ANOVA if there is a concern over the underlying assumptions in the distribution of the data. The researcher must bear in mind, however, that the data transformation bears a cost: Information is sacrificed. For example, interval or ratio scores of 80, 79, and 49 are converted to ranks 1, 2, and 3. Yes, information is sacrificed.

Launch WilcoxonSignedRankGUI from GoStats as follows:

Example. Consider an experiment seeking to evaluate the "cool appeal" for two new designs of media players. Young tech-savvy individuals are of particular interest. Ten young tech enthusiasts are recruited and then given a demo of, and allowed to play with, each media player. At the end, they are asked to rate the media players on a 10-point scale (1 = not cool at all, 10 = really cool) with the assessments stored in a text file as a table, one row per participant, one column per media player (see wilcoxonsignedranks-ex1.txt ):

      3   3
      6   6
      4   3    
     10   3
      6   5
      5   6
      9   2
      7   4
      6   2
      8   3
 

The mean responses (not shown) were 6.4 for media player #1 (left) and 3.7 for media player #2 (right). Evidently, the participants preferred media player #1 over media player #2. But, was the difference in responses statistically significant or was it just a chance outcome? To determine this, the Wilcoxon Signed-Rank test is used as follows:

The test statistic is a z-score. Since the customary threshold for statistical significance is exceeded ( p < .05), we conclude there is indeed a difference between the two media players in their "cool appeal".

The test also provides z' which is corrected for ties. The difference is minor. NOTE: Correcting for ties is with reference to the difference scores, not to the raw scores. For example, the 3rd and 5th rows have difference scores of 1 (4 - 3 = 1, 6 - 5 = 1), thus generating a tie in the ranks.

StatView provides the following output using the above data set:

Author:

Scott MacKenzie, 2012-2018

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class java.awt.Window

java.awt.Window.Type

Nested classes/interfaces inherited from class java.awt.Component

java.awt.Component.BaselineResizeBehavior

Field Summary

Fields inherited from class javax.swing.JFrame

EXIT_ON_CLOSE

Fields inherited from class java.awt.Frame

CROSSHAIR_CURSOR, DEFAULT_CURSOR, E_RESIZE_CURSOR, HAND_CURSOR, ICONIFIED, MAXIMIZED_BOTH, MAXIMIZED_HORIZ, MAXIMIZED_VERT, MOVE_CURSOR, N_RESIZE_CURSOR, NE_RESIZE_CURSOR, NORMAL, NW_RESIZE_CURSOR, S_RESIZE_CURSOR, SE_RESIZE_CURSOR, SW_RESIZE_CURSOR, TEXT_CURSOR, W_RESIZE_CURSOR, WAIT_CURSOR

Fields inherited from class java.awt.Component

BOTTOM_ALIGNMENT, CENTER_ALIGNMENT, LEFT_ALIGNMENT, RIGHT_ALIGNMENT, TOP_ALIGNMENT

Fields inherited from interface javax.swing.WindowConstants

DISPOSE_ON_CLOSE, DO_NOTHING_ON_CLOSE, HIDE_ON_CLOSE

Fields inherited from interface java.awt.image.ImageObserver

ABORT, ALLBITS, ERROR, FRAMEBITS, HEIGHT, PROPERTIES, SOMEBITS, WIDTH

Method Summary

Modifier and Type	Method and Description
void	actionPerformed(java.awt.event.ActionEvent ae)
void	focusGained(java.awt.event.FocusEvent fe)
void	focusLost(java.awt.event.FocusEvent fe)
double	getP1() Return the p statistic (probability) for this WilcoxonSignedRank object.
double	getP2() Return the p statistic (probability) for this WilcoxonSignedRank object.
double[]	getRanks(double[] d) Given an array of data, return an array of ranks (handles ties).
double	getZ1() Return the z statistic for this WilcoxonSignedRank object.
double	getZ2() Return the z statistic for this WilcoxonSignedRank object.
void	itemStateChanged(java.awt.event.ItemEvent ie)
double	mean(double[] n) Calculate the mean of the values in a double array.

Methods inherited from class javax.swing.JFrame

getAccessibleContext, getContentPane, getDefaultCloseOperation, getGlassPane, getGraphics, getJMenuBar, getLayeredPane, getRootPane, getTransferHandler, isDefaultLookAndFeelDecorated, remove, repaint, setContentPane, setDefaultCloseOperation, setDefaultLookAndFeelDecorated, setGlassPane, setIconImage, setJMenuBar, setLayeredPane, setLayout, setTransferHandler, update

Methods inherited from class java.awt.Frame

addNotify, getCursorType, getExtendedState, getFrames, getIconImage, getMaximizedBounds, getMenuBar, getState, getTitle, isResizable, isUndecorated, remove, removeNotify, setBackground, setCursor, setExtendedState, setMaximizedBounds, setMenuBar, setOpacity, setResizable, setShape, setState, setTitle, setUndecorated

Methods inherited from class java.awt.Window

addPropertyChangeListener, addPropertyChangeListener, addWindowFocusListener, addWindowListener, addWindowStateListener, applyResourceBundle, applyResourceBundle, createBufferStrategy, createBufferStrategy, dispose, getBackground, getBufferStrategy, getFocusableWindowState, getFocusCycleRootAncestor, getFocusOwner, getFocusTraversalKeys, getIconImages, getInputContext, getListeners, getLocale, getModalExclusionType, getMostRecentFocusOwner, getOpacity, getOwnedWindows, getOwner, getOwnerlessWindows, getShape, getToolkit, getType, getWarningString, getWindowFocusListeners, getWindowListeners, getWindows, getWindowStateListeners, hide, isActive, isAlwaysOnTop, isAlwaysOnTopSupported, isAutoRequestFocus, isFocusableWindow, isFocusCycleRoot, isFocused, isLocationByPlatform, isOpaque, isShowing, isValidateRoot, pack, paint, postEvent, removeWindowFocusListener, removeWindowListener, removeWindowStateListener, reshape, setAlwaysOnTop, setAutoRequestFocus, setBounds, setBounds, setCursor, setFocusableWindowState, setFocusCycleRoot, setIconImages, setLocation, setLocation, setLocationByPlatform, setLocationRelativeTo, setMinimumSize, setModalExclusionType, setSize, setSize, setType, setVisible, show, toBack, toFront

Methods inherited from class java.awt.Container

add, add, add, add, add, addContainerListener, applyComponentOrientation, areFocusTraversalKeysSet, countComponents, deliverEvent, doLayout, findComponentAt, findComponentAt, getAlignmentX, getAlignmentY, getComponent, getComponentAt, getComponentAt, getComponentCount, getComponents, getComponentZOrder, getContainerListeners, getFocusTraversalPolicy, getInsets, getLayout, getMaximumSize, getMinimumSize, getMousePosition, getPreferredSize, insets, invalidate, isAncestorOf, isFocusCycleRoot, isFocusTraversalPolicyProvider, isFocusTraversalPolicySet, layout, list, list, locate, minimumSize, paintComponents, preferredSize, print, printComponents, remove, removeAll, removeContainerListener, setComponentZOrder, setFocusTraversalKeys, setFocusTraversalPolicy, setFocusTraversalPolicyProvider, setFont, transferFocusDownCycle, validate

Methods inherited from class java.awt.Component

action, add, addComponentListener, addFocusListener, addHierarchyBoundsListener, addHierarchyListener, addInputMethodListener, addKeyListener, addMouseListener, addMouseMotionListener, addMouseWheelListener, bounds, checkImage, checkImage, contains, contains, createImage, createImage, createVolatileImage, createVolatileImage, disable, dispatchEvent, enable, enable, enableInputMethods, firePropertyChange, firePropertyChange, firePropertyChange, firePropertyChange, firePropertyChange, firePropertyChange, getBaseline, getBaselineResizeBehavior, getBounds, getBounds, getColorModel, getComponentListeners, getComponentOrientation, getCursor, getDropTarget, getFocusListeners, getFocusTraversalKeysEnabled, getFont, getFontMetrics, getForeground, getGraphicsConfiguration, getHeight, getHierarchyBoundsListeners, getHierarchyListeners, getIgnoreRepaint, getInputMethodListeners, getInputMethodRequests, getKeyListeners, getLocation, getLocation, getLocationOnScreen, getMouseListeners, getMouseMotionListeners, getMousePosition, getMouseWheelListeners, getName, getParent, getPeer, getPropertyChangeListeners, getPropertyChangeListeners, getSize, getSize, getTreeLock, getWidth, getX, getY, gotFocus, handleEvent, hasFocus, imageUpdate, inside, isBackgroundSet, isCursorSet, isDisplayable, isDoubleBuffered, isEnabled, isFocusable, isFocusOwner, isFocusTraversable, isFontSet, isForegroundSet, isLightweight, isMaximumSizeSet, isMinimumSizeSet, isPreferredSizeSet, isValid, isVisible, keyDown, keyUp, list, list, list, location, lostFocus, mouseDown, mouseDrag, mouseEnter, mouseExit, mouseMove, mouseUp, move, nextFocus, paintAll, prepareImage, prepareImage, printAll, removeComponentListener, removeFocusListener, removeHierarchyBoundsListener, removeHierarchyListener, removeInputMethodListener, removeKeyListener, removeMouseListener, removeMouseMotionListener, removeMouseWheelListener, removePropertyChangeListener, removePropertyChangeListener, repaint, repaint, repaint, requestFocus, requestFocusInWindow, resize, resize, revalidate, setComponentOrientation, setDropTarget, setEnabled, setFocusable, setFocusTraversalKeysEnabled, setForeground, setIgnoreRepaint, setLocale, setMaximumSize, setName, setPreferredSize, show, size, toString, transferFocus, transferFocusBackward, transferFocusUpCycle

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.awt.MenuContainer

getFont, postEvent

Method Detail

actionPerformed

public void actionPerformed(java.awt.event.ActionEvent ae)

Specified by:

actionPerformed in interface java.awt.event.ActionListener

focusGained

public void focusGained(java.awt.event.FocusEvent fe)

Specified by:

focusGained in interface java.awt.event.FocusListener

focusLost

public void focusLost(java.awt.event.FocusEvent fe)

Specified by:

focusLost in interface java.awt.event.FocusListener

itemStateChanged

public void itemStateChanged(java.awt.event.ItemEvent ie)

Specified by:

itemStateChanged in interface java.awt.event.ItemListener

getZ1

public double getZ1()

Return the z statistic for this WilcoxonSignedRank object.

Returns:

the z statistic

getZ2

public double getZ2()

Return the z statistic for this WilcoxonSignedRank object. The statistic is corrected for ties.

Returns:

the z statistic (correct for ties).

getP1

public double getP1()

Return the p statistic (probability) for this WilcoxonSignedRank object.

Returns:

the p statistic

getP2

public double getP2()

Return the p statistic (probability) for this WilcoxonSignedRank object. The statistic is corrected for ties.

Returns:

the p statistic (corrected for ties)

getRanks

public double[] getRanks(double[] d)

Given an array of data, return an array of ranks (handles ties). The order of the original data is preserved. As an example, if the passed array contains

      25, 75, 80, 81, 75
 

the returned array contains

      1.0, 2.5, 4.0, 5.0, 2.5
 

Parameters:

d - a double array

Returns:

an array of ranks

mean

public double mean(double[] n)

Calculate the mean of the values in a double array.

Parameters:

n - a double array

Returns:

a double equal to the mean of the values in the array.