Chapter 6: Constructing and Interpreting Graphic Displays of Behavioral Data

Interpreting Graphically Displayed Behavioral Data

"It is impossible to interpret graphic data without being influenced by various characteristics of the graph itself."

ABA Line Graph

Based on the Cartesian plane • Two-dimensional area formed by intersecting lines • Points on the plane represent relationships • Level of the dependent variable when the independent variable was in effect • Comparisons of data points reveals the presence or absence of changes in level, trend, and/or variability

Labeling vertical axis

Brief label, printed, centered to the left and parallel to the vertical axis

Read the graph

Figure caption • Condition & axis labels • Location of numerical value & relative significance of scale breaks

Variability/Stability

Frequency and degree to which multiple measures of behavior yield different outcomes • High degree of variability • Little or no control over the factors influencing behavior

Types of Graphs Utilized in ABA Cumulative Record

Number of responses recorded and added to the total number of responses recorded during previous observations • Cumulative • Y-Axis (vertical axis) • Represents the total number of responses recorded since the start of data collection

Trend

Overall direction taken by the data path • Direction • Increasing, decreasing, or zero trend • Degree • Gradual or steep • Extent of variability • Trend line or line of progress • Freehand, least-squares regression equation, or split-middle line of progress

On a cumulative record...

The steeper the slope, the higher the response rate

Plural

These data are

Line Graph Variations

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

Scale Break

Use a scale break to represent discontinuities in the progression of time

Data Points & Data Paths

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

Constructing Line Graphs

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

Visually track each data path

• Are data paths properly connected? • Is the graph distorted?

ABA Bar Graph

• Based on the Cartesian plane • No distinct data points representing successive response measures through time

Direct and Repeated Measurement of Behavior

• Consecutive measures, over time • Data series vs. graphic display

• What's standard about the standard celeration chart?

• Consistent display of celeration

Standard Celeration Chart

• Developed by Ogden Lindsley • Standardized method for • Charting & analyzing how frequency of behavior changes over time

Cumulative Record

• Developed by Skinner • Primary means of data collection in EAB • Cumulative recorder • Experimental subject draws its own graph • Shows the number of responses on the ordinate against time on the abscissa

Four standard charts

• Difference in scaling on horizontal axis • Dailychart (140 calendar days) • Weekly chart • Monthly chart • Yearly chart

Function of a Bar Graph

• Displaying and comparing discrete sets of data that ARE NOT related by a common underlying dimension by which the horizontal axis can be scaled (Example) • Visual summary of participant or group performance during different experimental conditions

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

Data Paths

• 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

Parts of a Line Graph

• Horizontalaxis • Vertical axis • Condition change lines • Condition labels • Phase and condition • Data points • Data path • Figure Caption

Benefits of Graphic Display

• Immediate access to record of behavior • Variations prompt exploration • Provides judgmental aid • Relativelyeasytolearn,nopredeterminedlevelfordeterminingsignificanceofchange, no mathematical properties required • Conservative method • Encourages independent judgment & interpretation • Effective source of feedback

Precision Teaching

• Instructional decision-making system • Developed for use with standard celeration chart

Position in Precision Teaching

• Learning best measured as a change in response rate • Learning most often occurs through proportional changes in behavior • Past changes can predict future learning

Between Conditions

• Level • Mean or median level lines • Trend • Stability/Variability • Across similar conditions

Fundamental Properties of Behavior Change

• Level • Trend • Variability

Types of Graphs Utilized in ABA

• Line graph • Bar graphs • Cumulative record • Semilogarithmic charts • Standard Celeration Chart • Scatterplots

Celeration

• Linear measure of frequency change across time • A factor by which frequency multiples or divides per unit of time • Acceleration-acceleratingperformance • Deceleration-decelerating performance

• Horizontal axis

• Mark equal intervals • Left to right chronological succession of equal time periods or response opportunities • Use regularly spaced tic marks

Data

• Medium with which the behavior analyst works • Results of measurement • Empirical basis for decision making

Scaling of vertical axis

• Most significant feature of the graph • Mark the origin at zero • Mark the full range of values represented in the data set

Within Conditions of Visual Analysis

• Number of data points • Nature&extentofvariabilityinthedata • Absolute & relative level of the behavioral measure • Direction & degree of any trends in the data.

Data Points

• Place each data point in the exact coordinate of the horizontal and vertical axis • If graphing by hand - use a graph paper with appropriately spaced grid lines • Use bold, easily discernable symbols • Use a different symbol for each set of data

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) • Data were not collected, lost, etc. • It is follow-up or post-check data • Unless intersession time span same as original experiment .Data points fall beyond the values described by the vertical

Graphic Displays

• Primary function communication • Display relationships between dependent variable and independent variable • Summarization of data collected • Facilitates of accurate analyses

Figure Caption

• Printed below the graph • Concise, complete description of figure • Directviewersattentiontofeaturesofthegraphthatmaybe overlooked • E.g., scale changes • Describe the meaning of any added symbols

Semilogarithmic Charts

• Ratio or multiply-divide charts • One axis is scaled proportionally • Double response rate 4 to 8 same as 50 to 100 • All behavior changes of equal proportion are shown by equal vertical distances on the vertical axis

ABA Scatterplot

• Shows relative distribution of individual measures in a data set • Data points are unconnected • 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

• Standard chart

• Six, X 10 cycles (vertical axis) • 1 per 24hrs • 1,000 per minute • Bottom left to top right corner • Slope of 34° - celeration value X2

Relative rates of response

• The steeper the slope, the higher the response rate • Overall response rate • Local response rate

Display of a Cumulative Record

• Total number of responses at any given point in time

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;1:1.6ratioy-axistox-axis

Level

• Value on the vertical axis around which a series of data points converge • Stability • When data points fall at or near a specific level • Mean or median lines • Addedtorepresentoverallaverageortypicalperformance • Use with caution - can obscure important variability

Do's of a Cumulative Graph

• When to use cumulative graph over noncumulative graph • Progress toward a specific goal can be measured in cumulative units • E.g., Number of new words learned, quarters saved • Graph is used as personal feedback • Total progress and relativerate 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

Condition Change Labels

•Identify conditions in effect during each period of the experiment •Centered above & between condition change lines •Brief, but descriptive labels

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 (à) or other symbols to indicate small changes