# SPED 8013 | Chapter 6: Constructing and Interpreting Graphic Displays of Behavioral Data

## Chapter Focus Questions

• What are the benefits of graphic display and visual analysis of behavioral data?
• What are the fundamental properties of behavior change over time?
• What are the different visual formats for the graphic display of behavioral data? what are the relative strengths and limitations of each visual format?
• What are the basic parts of a properly constructed line graph?
• What is the purpose of visual analysis?
• How is a visual analysis of behavioral data conducted?

## Direct and Repeated Measurement of Behavior

• Data
• Medium with which the behavior analyst works
• “Results of measurement, usually in quantitative form”
• Empirical basis for decision making
• Plural (Data is the plural form of datum and as such we should actually say, “These data are..”
• These data are

Data can be displayed in table format as indicated to the left in the Number Correct table, or it can be displayed in a list as indicated in the Percent of Correct Responses Panel to the left and bottom. However, as you can see the data here is not easily accessible in that at a glance you do not know what it is telling you

Alternately, data can be
displayed in a graphic display as indicated to the right and here the data (which is the same data displayed in the number correct table) and the the bottom left (which is the same data displayed in the Percent correct of responses panel) is quite accessible and immediately tells the viewer what they are looking at.

## Purposes & Benefits of Graphic Display

• Purpose
• Primary function communication
• Display relationships between dependent variable and independent variable
• Summarization of data collected
• Facilitates accurate analyses
• Benefits
• Real-time information regarding variations prompts exploration
• Provides judgmental aid
• Relatively easy to learn, no predetermined level for determining significance of change, no mathematical properties required
• Conservative method
• Encourages independent judgment & interpretation
• Effective source of feedback

## Types of Graphs Utilized in ABA

• Line Graph: The line graph is based on the Cartesian plane. (See left for basic line graph example) Two-dimensional area formed by intersecting lines. Points on the plane represent relationships (Level of the dependent variable when specific environmental conditions were in effect.) Comparisons of data points reveals the presence or absence of changes in level, trend, and/or variability

Parts of a Line Graph: Horizontal (X) axis, Vertical (Y) axis, Condition change lines, Condition labels (Phase and condition), Data points, Data path, Figure Caption (See below for line graph with condition lines, condition labels, etc.)

Line Graph Variations:

• Two or more dimensions of the same behavior
• Two or more different behaviors
• Measure of the same behavior under different conditions
• Change values of the independent variable
• Same behavior of two or more participants

• Bar Graph: The bar graph is based on the Cartesian plane. (See right for basic bar graph example). There are no distinct data points representing successive response measures through time. The function of a bar graph in ABA is for displaying and comparing discrete sets of data that ARE NOT related by a common underlying dimension by which the horizontal axis can be scaled. (An example is the visual summary of a participant or group performance during different experimental conditions). The bar graph provides an efficient summary of data, but DOES NOT allow for analysis of variability and trends in behavior.
• Cumulative Record: The Cumulative Record (See below left for example) was developed by Skinner, and is the primary means of data collection in EAB (experimental analysis of behavior). A cumulative record is used, and here the experimental subject draws its own graph (via its response rate). The cumulative record shows the number of responses on the ordinate (Vertical, Y-axis) against the time on the abscissa (Horizontal, X-axis). Display, or visually it is the total number of responses at any given point in time. Relative rates in response, the steeper the slope, the higher the response rate. (Overall response rate /Local response rate) Cumulative Number Correct. Sessions. The thing to keep in mind is that the difference say between a recorder of seismic activity and a cumulative recorder is that in cumulative recording the response never goes down. Only up.

When to use a cumulative graph over noncumulative graph?

• Progress towards a specific goal can be measured in cumulative units (e.g., Number of new words learned, quarter saved)
• Graph is used as personal feedback (Total progress and relative rate of performance easily detected)
• Target behavior can only occur once per observation period (yes/no)
• Intricate details between behavior & environmental variables are of interest (e.g., within session analyses)

***All of the Previous Graphs are Equal-Interval Graphs***
Distance between any two consecutive points on each axis is always the same
Increase/decrease in performance expressed by equal distances on the y-axis
Distance between sessions, days, etc. expressed by equal distance on the x-axis

• Semilogarthimic charts (Standard Celeration Chart): Also called a ratio or multiply-divide chart. One axis is scaled proportionally, the Y-axis, or the behavior axis. (One remains at equal interval, which is why the chart is semi-logarithmic and not logarithmic which would indicate proportional scaling on both axis). The proportion double response rate, or 4 to 8 is the same as 10 to 20, and 50 to 100 and so on. In other words, all behavior changes of equal proportions are shown by equal vertical distances on the vertical axis.
• Standard Celeration Chart:
• Developed by Ogden Lindsley
• Standardized method for
• Charting and analyzing how frequency of behavior changes over time
• Not typically used in most settings, but it can be a very precise, robust, and sensitive way to measure progress over time.
• (Example below from the Journal of Precision Teaching and Celebration, 19(1), p.. 54. Copyright 2002 by The Standard Celeration Society. from Cooper, Heron, and Heward. (2007). Applied Behavior Analysis.

• Standard Celeration Chart & Precision Teaching
• Precision Teaching
• Instructional decision-making system
• Developed for use with standard celeration chart
• Position
• Learning best measured as a change in response rate
• Learning most often occurs through proportional changes in behavior
• Past changes can predict future learning
• Chart uses estimations for most frequency values
• Scatterplots: Scatterplot charts show relative distribution of individual measures in a data set. Data points are unconnected. It depicts changes in value on one axis correlated with changes in value on the other axis. Patterns suggest certain relationships (Sometimes used to discover the temporal distribution of the target behavior)

## Constructing Line Graphs

• An effective graph presents data
• Accurately
• Completely
• Clearly
• Makes visual analysis as easy as possible
• Does not create distortion or biased interpretation

Drawing, Scaling & Labeling Axes

• Use a balanced ratio between the height and width of the axes
• Relative length of the vertical axis to horizontal axis
• Suggestions:
• 5:8, 3:4, 1:1.6 ration y-axis to x-axis
• Horizontal axis
• Mark equal intervals
• Left to right chronological succession of equal time periods or response opportunities
• Use regularly spaced tic marks (i.e., 10, 15, 10 or 20, 30, 40, etc.)
• Use a scale break to represent discontinuities in the progression of time (two |  | vertical lines on the X-axis)
• Vertical axis
• Most significant feature of the graph
• Mark the origin at zero
• Mark the full range of values represented in the data set

**Good practice: Plot the data set against several different vertical axis scales–watch for distortion that may lead to inaccurate interpretations**

• If relatively small changes in performance are socially significant
• Y-axis should reflect a smaller range of values
• Brief label, printed, centered to the left and parallel to the vertical axis
• Condition Change Lines
• Vertical lines
• Extend upward
• Indicate change in treatment or experimental condition
• Solid or dashed lines
• Major changes – solid
• Minor changes – dashed
• Asterisks (*), arrows (–>) or other symbols to indicate small changes
• Condition Change Labels
• Identify conditions in effect during each period of the experiment or intervention
• Centered above & between condition change lines
• Brief but descriptive labels
• Data Points and Data Paths
• Place each data point in the exact coordinate of the horizontal and vertical axis
• If graphing by hand-use graph paper with appropriately spaced grid lines
• Use bold, easily discernible symbols
• Use a different symbol for each set of data
• Draw data paths using a straight line
• The center of each data point in a given data set to the center of the next data point in the same set
• DO NOT CONNECT DATA POINTS IF
• Points fall on either side of a condition change line
• A significant span of time passed and behavior was not measured
• There was a discontinuity in time in the horizontal axis (e.g., school vacation)
• It is follow-up or post-check data
• Data points fall beyond the valued describe by the vertical axis

• Use Different styles of lines for multiple data paths on the same graph
• Clearly identify what each data path represents
• Use arrows or a legend
• Figure caption
• Printed below the graph
• Concise, complete description of figure
• Direct viewers attention to features of the graph that may be overlooked
• Eg. scale changes
• Describe the meaning of any added symbols
• Print graphs in one color – black

## Constructing Graphs – Using Computer Software

• Use with caution
• Check the range of scales available
• Check the accuracy of the data point plotting
• Check the precision of the data paths
• Further information
• Carr & Burkholder (1998)
• Silvestri (2003)
• www.prenhall.com/cooper

## Interpreting Graphically Displayed Behavioral Data

• Visual analysis
• Did behavior change in a meaningful way?
• If so, to what extent can that change in behavior be attributed to the independent variable?
• Identification of
• Variability
• Level
• Trend

“It is impossible to interpret graphic data without being influenced by various characteristics of the graph itself” -Johnson & Pennypacker, 1993b, p. 230

• Figure caption
• Condition & axis labels
• Location of numerical values & relative significance of scale breaks
• Visually track each data path
• Are data paths properly connected?
• Is the graph distorted?
• Visual analysis
• Within Conditions
• Number of data points (minimum of 3 point required to indicate trend, more is  better)
• Nature and extent of variability in the data
• Absolute and relative level of the behavioral measure
• Direction and degree of any trends in the data
• Visual analysis
• Between Conditions
• Level
• mean or median level lines
• Trend
• Stability/Variability
• across similar conditions
• Level
• Value on the vertical axis around which a series of data point converge
• Stability
• When data points fall at or near a specific level
• Median or median lines
• Added to represent overall average or typical performance
• Use with caution-can obscure important variability
• Trend
• Overall direction taken by the data path
• Direction
• Increasing, decreasing or zero trend
• Degree