- java.lang.Object
-
- java.awt.Component
-
- java.awt.Container
-
- java.awt.Window
-
- java.awt.Frame
-
- javax.swing.JFrame
-
- ChiSquareGUI
-
- 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 ChiSquareGUI extends javax.swing.JFrame implements java.awt.event.ActionListener, java.awt.event.FocusListener, java.awt.event.ItemListener
ChiSquare - GUI Version
Summary
- A utility to perform a chi-square test on a table of data
Background
The chi-square test, also known as the Pearson chi-square test, and sometimes using "squared" instead of "square," investigates whether there is a significant difference between the observed and expected frequencies across one or more categories of interest. The categories are the levels of nominal-scale variables representing attributes of people, systems, interaction techniques, etc. Examples of nominal-scale variables with categories or levels in parentheses are- Gender (male, female)
- Handedness (left, right)
- Age (<20, 20-30, 30-40, >40)
- E-mails sent per day (<10, 10-30, 30-100, >100)
- Voting attitude (for, against)
- Preferred OS (Mac OS, Windows, linux, other)
- Vision correction (none, glasses, contact lenses)
- Roll of a die (1, 2, 3, 4, 5, 6)
In the examples above, "age" and "e-mails sent per day" are nominal-scale variables only insofar as the indicated categories are relevant to the research. These variables are normally considered on a ratio-scale.
The frequencies are counts of the number of occurrences or observations in the category. The chi-square test investigates whether the observed frequencies and the expected frequencies are the same in each category. The null hypothesis is "no difference."
The chi-square test is commonly used for two types of comparisons:
- The chi-square test of association
- The chi-square test for goodness-of-fit
The chi-square test of association examines the relationship between the observed frequencies over the levels of two variables. The chi-square test for goodness-of-fit examines the observed frequencies over the levels of a single variable. Both uses are supported in this utility.
Launch ChiSquareGUI from GoStats as follows:
Example 1
Do males and females differ in the way they perform scrolling operations on desktop computer systems? To investigate this, a large number of computer users are observed. For each, it is noted whether they are male or female and how they perform scrolling tasks. The scrolling methods are categorized as mouse wheel (MW), scrollbar by clicking and dragging (CD), or keyboard (KB). The variables — with categories or levels in parentheses — are gender (male, female) and scrolling method (MW, CD, KB). One hundred and one users were observed, including 56 males and 45 females. Counts for usage of the scrolling methods were 49 (MW), 24 (CD), and 28 (KB). The data are conveniently organized in a contingency table:Gender Scrolling Method Totals MW CD KB Males 28 15 13 56 Females 21 9 15 45 Totals 49 24 28 101 The data above are in the GoStatsExamples folder in the file chisquare-ex1.txt. The chi-square test for significant differences across categories is performed by selecting the data file and clicking "Analyse": (click to enlarge)
StatView (now JMP) provides the following output for the data set above:
The test statistic is χ2 = 1.462, which follows the chi-square distribution with df = 2. Since the p-value is above .05, the customary threshold for significance is not achieved. The conclusion is that there is no difference in the scrolling methods used by males or females.
The ChiSquareGUI utility also includes a verbose option to output additional information:
Let's work through another example, where the outcome is statistically significant and where post hoc comparisons are used to determine which conditions differ significantly from one another.
Example 2
A researcher wishes to investigate whether students, teachers, and parents hold the same opinion on the issue of mobile phone usage in the classroom. To study this, a large number of students, teachers, and parents are randomly sampled and asked if they agree that students should be allowed to use mobile phones in the classroom. The variables and levels are opinion (agree, disagree) and group (student, teacher, parent). In all, 300 people were sampled, including 40 students, 60 teachers, and 200 parents. The responses were 120 agree and 180 disagree. A contingency table shows the data organized by opinion and group:Opinion Group Totals Student Teacher Parent Agree 10 12 98 120 Disagree 30 48 102 180 Totals 40 60 200 300 The 2 × 3 contingency table for the data above are stored in chisquare-ex2.txt. To test whether there is a difference in opinion by group, ChiSquareGUI is used as follows:
StatView (now JMP) provides the following output for the data set above:
The test statistic is χ2 = 20.5, which follows the chi-square distribution with df = 2. Since p < .05, the customary threshold for statistical significance is exceeded. The null hypothesis is rejected. The conclusion is that there is a difference between students, teachers, and parents in their response to the question about mobile phone usage in the classroom.
The data in this example are from a chi-square test described by Glass and Hopkins (Statistical Methods in Education and Psychology, 2nd ed., Prentice Hall, 1984, p. 286). Glass and Hopkins' example pertained to the attitude of school superintendents, teachers, and principals toward collective bargaining.
Post Hoc Comparisons
If a variable has more than two levels, as in the example above, a significant result can be followed with post hoc comparisons to determine which levels differ significantly from one another. ChiSquareGUI supports this using the output option "Post hoc tests". To use this option, ensure the data table is organized as two rows by n columns. The comparisons are among the proportions in each column. An example follows:
The calculations are detailed in the Glass and Hopkins' reference on page 392. For paired comparisons, the null hypothesis of no difference is rejected if p < .05. As seen above, this occurred for pairs 1:3 and 2:3. This implies that the responses to the question were different between the students and the parents and between the teachers and the parents. However, the null hypothesis remains tenable for the 1:2 comparison; thus, the students and teachers are not deemed to have responded differently to the question. Note that a majority in each group disagreed with the assertion that mobile phone usage should be allowed in the classroom.
Degrees of Freedom
A contingency table is organized in m rows and n columns. The degrees of freedom for the chi-square statistic is df = (m - 1) × (n - 1).Example 3
This example is from Ayyavu and Jensen's paper, "Integrating user feedback with heuristic security and privacy management systems" in the CHI '11 proceedings. Their research concerned tools to assist users in determining if web sites are trustworthy; that is, free of spam, predators, etc. In particular, are there differences in the ratings provided by community-based tools vs. heuristics-based tools. The tools are Web Of Trust (WOT) as a community-based tool and McAfee's Site Advisor (MSA) as a heuristics-based tool. After assessing 18,650 web sites, the results were as follows (as stored in chisquare-ex3.txt):16968 1722
The first row are the assessments generated by WOT, the second row are the assessments generated by MSA. The first column is the number of sites considered "good", the second column is the number of sites considered "bad". Thankfully, most of the sites were deemed good, or safe. WOT rated 9.21% of the sites bad, or not trustworthy. The figure was 3.36% for MSA. That seems like a substantial difference. The research question is this: Do the results for good vs. bad differ between the two tools? A chi-square test is used to answer the question. The analysis using GoStats is shown below.
18062 628
The result was χ2 = 543.5, df = 1, p < .0001. The answer is "yes". The tools differ in their assessments of web sites as trustworthy.
If df = 1, the calculation of the chi-square statistic may include a "correction for continuity" (see D. J. Sheskin, Handbook of Parametric and Nonparametric Statistical Procedures, 5th ed., CRC Press, 2011, pp. 285-286). The correction is based on the premise that if a continuous distribution, such as the chi-square distribution, is used to estimate a discrete distribution (counts), the Type-I error rate is inflated. The problem is more pronounced for df = 1. The correction downgrades the chi-square statistic slightly to bring it more in line with the desired alpha.
Since df = 1 in this example, a second set of statistics is provided that includes a correction for continuity. The test is a bit more conservative with the correction for continuity; however, the outcome is the same: There was a statistically significant difference between the assessments provided by the two tools (χ2 = 542.5, df = 1, p < .0001).
Single-sample Chi-square
A chi-square test can also be done on a single sample of k mutually exclusive categories. In this case, the degrees of freedom is one less than the number of categories: df = k - 1.Example 4
A researcher heard a claim that half the attendees at the annual ACM SIGCHI conference ("CHI") own mobile phones running the Android operating system. To test this claim the researcher randomly sampled 112 attendees at the conference. Fifty-two were found to own a mobile phone running the Android operating system and 60 were found to not own such a phone (see chisquare-ex4.txt). The null hypothesis is that the probability of CHI attendees owning an Android mobile phone is .5 (50%). Is the null hypothesis tenable, given the observations? To investigate this, a chi-square test is used:
Again, since df = 1, a second set of statistics is provided that includes the correction for continuity. The test is a bit more conservative; however, the outcome is the same. The null hypothesis remains tenable (χ2 = 0.438, df = 1, p > .05).
The data in this example are from a chi-square test described by Wetherill (Elementary Statistical Methods, London: Methuen, 1969, p. 204). Wetherill's example — from 1969! — was not about mobile phones. The example pertained to the occurrence of a certain disease in a random sample of 112 children.
Example 5
A help-desk employee at a university's data centre wishes to determine if the number of e-mails requesting technical assistance is the same each day of the week (Monday to Saturday). The employee records the number of such e-mails during one week and obtains the following frequencies: Monday, 20; Tuesday, 14; Wednesday, 18; Thursday, 17; Friday, 22; Saturday, 29 (see chisquare-ex5.txt). Do the data indicate there is a difference in the number of e-mails received on different days of the week? To investigate, ChiSquareGUI is used as follows:
The null hypothesis is that the number of e-mails received each day is the same. Since p = .2439, the null hypothesis remains tenable (χ2 = 6.7, df = 5, p > .05).
The data for this example are from a chi-square test described by Sheskin (Handbook of Parametric and Nonparametric Statistical Procedures, 5th ed., CRC Press, 2011, p. 279). The data in Sheskin's example pertain to the number of books signed out of a library each day of the week.
Since the two examples above use a single variable, they are examples of the chi-square test for goodness-of-fit. The distribution against which the observed values are compared is the set of expected values. The expected values are computed under the assumption that the categories are equally probable.
- Author:
- Scott MacKenzie, 2012-2023
- See Also:
- Serialized Form
-
-
Field Summary
-
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
-
-
Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method and Description voidactionPerformed(java.awt.event.ActionEvent ae)voidfocusGained(java.awt.event.FocusEvent fe)voidfocusLost(java.awt.event.FocusEvent fe)voiditemStateChanged(java.awt.event.ItemEvent ie)-
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
-
-
-
-
Method Detail
-
actionPerformed
public void actionPerformed(java.awt.event.ActionEvent ae)
- Specified by:
actionPerformedin interfacejava.awt.event.ActionListener
-
focusGained
public void focusGained(java.awt.event.FocusEvent fe)
- Specified by:
focusGainedin interfacejava.awt.event.FocusListener
-
focusLost
public void focusLost(java.awt.event.FocusEvent fe)
- Specified by:
focusLostin interfacejava.awt.event.FocusListener
-
itemStateChanged
public void itemStateChanged(java.awt.event.ItemEvent ie)
- Specified by:
itemStateChangedin interfacejava.awt.event.ItemListener
-
-