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Graphs Used by Applied Behavior Analysts
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The graphic displays most often used by applied behavior analysts are line graphs, bar graphs, cumulative records,
ratio charts, and scatterplots.
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Line Graphs
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The simple line graph D, or frequency polygon, is far and away the most common graphic format in applied
behavior analysis. Based on the Cartesian coordinate system created by René Descartes in the 17th century, the
line graph is a two-dimensional area formed by the intersection of two perpendicular reference lines, called axes.
Any point within the area enclosed by the two axes represents a specific relationship between values of the two
dimensions (or variables) described by the intersecting lines. In applied behavior analysis, each point on a line graph
shows the level of some quantifiable dimension of the target behavior (i.e., the dependent variable D) in relation to
a specified point in time and/or environmental condition (i.e., the independent variable D) in effect when the
measure was taken. Comparing points on a graph reveals the presence and extent of changes in level, trend, and/or
variability within and across conditions.
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Parts of a Basic Line Graph
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Although graphs vary considerably in their final appearance, all properly constructed line graphs share certain
elements. The basic parts of a simple line graph are shown in Figure 6.2 and described in the following sections.
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Figure 6.2
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Parts of a Basic Line Graph
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Although graphs vary considerably in their final appearance, all properly constructed line graphs share certain
elements. The basic parts of a simple line graph are shown in Figure 6.2 and described in the following sections.
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Figure 6.2
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12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44
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Figure 1. Laps walked per session for each participant. Triangles indicate days in which the
participants arrived late to the walking session.
Major parts of a simple line graph: (1) horizontal axis, (2) vertical axis, (3) axis labels, (4) condition change lines, (5)
condition labels, (6) data points, (7) data path, and (8) figure caption. (Original figure includes graphs for four
additional participants.)
Based on “Using Token Reinforcement to Increase Walking for Adults with Intellectual Disabilities” by H. Krentz, R. Miltenberger, and D. Valbuena, 2016, Journal of
Applied Behavior Analysis, 49, p. 749. Copyright 2016 by the Society for the Experimental Analysis of Behavior.
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1. Horizontal Axis
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The horizontal axis, also called the x-axis, or abscissa, is a straight horizontal line that most often represents the
passage of time and the presence, absence, and/or value of the independent variable. A defining characteristic of
applied behavior analysis is the repeated measurement of behavior across time. Time is also the unavoidable
dimension in which all manipulations of the independent variable occur. On most line graphs the passage of time is
marked in equal intervals on the horizontal axis. The horizontal axis in Figure 6.2 represents consecutive
observational sessions from 9:00 to 10:00 AM on weekdays.
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The horizontal axis on some graphs represents different values of the independent variable instead of time. For
example, Lalli, Mace, Livezey, and Kates (1998) scaled the horizontal axis of one graph in their study from less than
0.5 meter to 9.0 meters to show how the occurrence of self-injurious behavior by a girl with severe intellectual
disabilities decreased as the distance between the therapist and the girl increased.
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2. Vertical Axis
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The vertical axis, also called the y-axis, or ordinate, is a vertical line drawn upward from the left-hand end of the
horizontal axis. The vertical axis most often represents a range of values of the dependent variable, which in applied
behavior analysis is always some quantifiable dimension of behavior. The intersection of the horizontal and vertical
axes is called the origin and most often, though not necessarily, represents the zero value of the dependent variable.
Each successive point upward on the vertical axis represents a greater value of the dependent variable. The most
common practice is to mark the vertical axis with an equal-interval scale , in which equal distances on the axis
represent equal absolute amounts of behavior change. The vertical axis in Figure 6.20 represents the number of
50-meter laps walked in 1 hour.
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3. Axis Labels
Axis labels are brief descriptions of the dimension represented by and scaled along each axis; most often a
response measure on the vertical axis and experimental conditions across time on the horizontal axis.
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4. Condition Change Lines
Condition abonna linneara vartinal linne drown inward from the horizontal evie tachownainte in timant which
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4. Condition Change Lines
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Condition change lines are vertical lines drawn upward from the horizontal axis to show points in time at which
changes in the independent variable occurred. The condition change lines in Figure 6.2 coincide with the
introduction or withdrawal of an intervention the researchers called Token Reinforcement.
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5. Condition Labels
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Condition labels are single words or brief descriptive phrases printed along the top of the graph and parallel to the
horizontal axis. These labels identify the experimental conditions (i.e., the presence, absence, or some value of the
independent variable) in effect during each phase of the study.
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5The terms condition and phase are related but not synonymous. Properly used, condition indicates the environmental
arrangements in effect; phase refers to a period within a study or behavior change program.
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6. Data Points
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Each data point on a graph represents two facts: (a) a quantifiable measure of the target behavior recorded during a
given observation period and (b) the time and/or experimental conditions under which that particular measurement
was conducted. Using two data points from Figure 6.2 as examples, we can see that John walked 14 laps during
Session 6, the last session of the first baseline phase, and 21 laps in Session 7, the first session of the first phase of
the token reinforcement condition.
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7. Data Path
Connecting successive data points within a given condition with a straight line creates a data path D. The data path
represents the level and trend of behavior between successive data points and is a primary focus of attention in the
interpretation and analysis of graphed data. Because behavior is rarely observed and recorded continuously in
applied behavior analysis, the data path represents an estimate of the actual course taken by the behavior during the
time between the two consecutive measures. The more measures and resultant data points per unit of time (given an
accurate observation and recording system), the more confidence one can place in the story told by the data path.
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8. Figure Caption
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The figure caption is a concise statement that, in combination with the axis and condition labels, provides the reader
with sufficient information to identify the independent and dependent variables. The figure caption should explain any
symbols (see Figure 6.2 D) or observed but unplanned events that may have affected the dependent variable and
point out and clarify any potentially confusing features of the graph (see Figure 6.60 and Figure 6.7 9).
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Variations of the Simple Line Graph: Multiple Data Paths
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The line graph is a remarkably versatile vehicle for displaying behavior change. Whereas Figure 6.2 D is an
example of the line graph in its simplest form (one data path showing a series of successive measures of behavior
across time and experimental conditions), by the addition of multiple data paths, the line graph can display more
complex behavior-environment relations. Graphs with multiple data paths are used frequently in applied behavior
analysis to show (a) two or more dimensions of the same behavior, (b) two or more different behaviors, (c) the same
behavior under different and alternating experimental conditions, (d) changes in target behavior relative to the
changing values of an independent variable, and (e) the behavior of two or more participants.
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Two or More Dimensions of the Same Behavior
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Showing multiple dimensions of the dependent variable on the same graph enables visual analysis of the absolute
and relative effects of the independent variable on those dimensions. Figure 6.30 shows the results of a study of
the effects of training three members of a women's college basketball team proper foul shooting form (Kladopoulos
& McComas, 2001). The data path created by connecting the open triangle data points shows changes in the
percentage of foul shots executed with the proper form, whereas the data path connecting the solid data points
reveals the percentage of foul shots made. Had the experimenters recorded and graphed only the players' foul
shooting form, they would not have known whether any improvements in the target behavior on which training was
focused (correct foul shooting form) coincided with improvements in the behavior by which the social significance of
the study would ultimately be judged—foul shooting accuracy. By measuring and plotting both form and outcome on
the same graph, the experimenters were able to analyze the effects of their treatment procedures on two critical
dimensions of the dependent variable.
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