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In Part Two we described considerations and procedures for selecting and defin- ing target behaviors and discussed detailed methods for measuring behavior; we also examined techniques for improving, assessing, and reporting the veracity of measurement. The product of these measurements, called data, is the medium with which the behavior analyst works. But what does the behavior analyst do with the data? The five chapters in Part Three are devoted to the presentation and interpretation of behavioral data and to the design, conduct, and evaluation of ex- periments analyzing the effects of interventions.

In Chapter 6 we describe the graphic displays used by researchers, practi- tioners, and consumers to make sense of behavioral data. We discuss considera- tions for selecting, constructing, and interpreting the major types of graphs most often used by behavior analysts. Although measurement and graphic displays can reveal whether, when, and to what extent behavior has changed, they alone can- not reveal what brought about the behavior change. Chapters 7 through 10 are devoted to the analysis in applied behavior analysis. Chapter 7 describes the req- uisite components of any experiment in behavior analysis and explains how re- searchers and practitioners apply steady-state strategy and the three elements of basic logic—prediction, verification, and replication—-to seek and verify func- tional relations between behavior and its controlling variables. In Chapters 8 and 9 we describe the logic and operation of the reversal, alternating treatments, multiple baseline, and changing criterion designs—the most commonly used experimental designs in applied behavior analysis. Chapter 10 covers a wide range of topics necessary for developing a more complete understanding of be- havioral research. Beginning with the assumption that the research methods of any science should reflect the characteristics of its subject matter, we examine the importance of analyzing behavior at the level of individual client or research par- ticipant, discuss the value of flexibility in experimental design, identify some common confounds to the internal validity of experiments, present methods for assessing the social validity of an applied behavior analysis, and describe how replication is used to determine the external validity of research. We conclude Chapter 10 and Part Three with a series of issues and questions that should be considered in evaluating the “goodness” of a published study in applied behavior analysis.

P A R T 3

Evaluating and Analyzing Behavior Change

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Constructing and Interpreting Graphic Displays of Behavioral Data

Key Terms

bar graph cumulative record cumulative recorder data data path dependent variable graph

independent variable level line graph local response rate overall response rate scatterplot semilogarithmic chart

split-middle line of progress Standard Celeration Chart trend variability visual analysis

Behavior Analyst Certification Board® BCBA® & BCABA® Behavior Analyst Task List ©, Third Edition

Content Area 7: Displaying and Interpreting Behavioral Data

7-1 Select a data display that effectively communicates quantitative relations.

7-2 Use equal-interval graphs.

7-3 Use Standard Celeration Charts (for BCBA only—excluded for BCABA).

7-4 Use a cumulative record to display data.

7-5 Use data displays that highlight patterns of behavior (e.g., scatterplot).

7-6 Interpret and base decision making on data displayed in various formats.

© 2006 The Behavior Analyst Certification Board, Inc.,® (BACB®) all rights reserved. A current version of this document may be found at www.bacb.com. Requests to reprint, copy, or distribute this document and ques- tions about this document must be submitted directly to the BACB.

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Chapter 6 Constructing and Interpreting Graphic Displays of Behavioral Data 127

Applied behavior analysts document and quan- tify behavior change by direct and repeated measurement of behavior. The product of these

measurements, called data, is the medium with which behavior analysts work. In everyday usage the word data refers to a wide variety of often imprecise and subjec- tive information offered as facts. In scientific usage the word data means “the results of measurement, usually in quantified form” (Johnston & Pennypacker, 1993a, p. 365).1

Because behavior change is a dynamic and ongoing process, the behavior analyst—the practitioner and the researcher—must maintain direct and continuous con- tact with the behavior under investigation. The data ob- tained throughout a behavior change program or a research study are the means for that contact; they form the empirical basis for every important decision: to con- tinue with the present procedure, to try a different inter- vention, or to reinstitute a previous condition. But making valid and reliable decisions from the raw data themselves (a series of numbers) is difficult, if not impossible, and in- efficient. Inspecting a long row of numbers will reveal only very large changes in performance, or no change at all, and important features of behavior change can easily be overlooked.

Consider the three sets of data that follow; each con- sists of a series of numbers representing consecutive mea- sures of some target behavior. The first data set shows the results of successive measures of the number of responses emitted under two different conditions (A and B):

Condition A Condition B

120, 125, 115, 130, 114, 110, 115, 121,

126, 130, 123, 120, 110, 116, 107, 120,

120, 127 115, 112

Here are some data showing consecutive measures of the percentage of correct responses:

80, 82, 78, 85, 80, 90, 85, 85, 90, 92

The third data set consists of measures of responses per minute of a target behavior obtained on successive school days:

65, 72, 63, 60, 55, 68, 71, 65, 65, 62, 70, 75, 79, 63, 60

What do these numbers tell you? What conclusions can you draw from each data set? How long did it take you to reach your conclusions? How sure of them are you? What if the data sets contained many more mea- sures to interpret? How likely is it that others interested

1Although often used as a singular construction (e.g., “The data shows that . . .”), data is a plural noun of Latin origin and is correctly used with plural verbs (e.g., “These data are . . .”).

in the behavior change program or research study would reach the same conclusions? How could these data be di- rectly and effectively communicated to others?

Graphs—relatively simple formats for visually dis- playing relationships among and between a series of mea- surements and relevant variables—help people “make sense” of quantitative information. Graphs are the major device with which applied behavior analysts organize, store, interpret, and communicate the results of their work. Figure 6.1 includes a graph for each of the three data sets presented previously. The top graph reveals a lower level of responding during Condition B than during Condi- tion A. The middle graph clearly shows an upward trend

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Figure 6.1 Graphic displays of three sets of hypothet- ical data illustrating changes in the level of responding across conditions (top), trend (middle), and cyclical variability (bottom).

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128 Part 3 Evaluating and Analyzing Behavior Change

over time in the response measure. A variable pattern of responding, characterized by an increasing trend during the first part of each week and a decreasing trend toward the end of each week, is evident in the bottom graph. The graphs in Figure 6.1 illustrate three fundamental proper- ties of behavior change over time—level, trend, and vari- ability—each of which will be discussed in detail later in the chapter. The graphic display of behavioral data has proven an effective means of detecting, analyzing, and communicating these aspects of behavior change.

Purpose and Benefits of Graphic Displays of Behavioral Data Numerous authors have discussed the benefits of using graphs as the primary vehicle for interpreting and com- municating the results of behavioral treatments and re- search (e.g., Baer, 1977; Johnston & Pennypacker, 1993a; Michael, 1974; Parsonson, 2003; Parsonson & Baer, 1986, 1992; Sidman, 1960). Parsonson and Baer (1978) said it best:

In essence, the function of the graph is to communicate, in a readily assimilable and attractive manner, descrip- tions and summaries of data that enable rapid and accu- rate analysis of the facts. (p. 134)

There are at least six benefits of graphic display and visual analysis of behavioral data. First, plotting each measure of behavior on a graph right after the observa- tional period provides the practitioner or researcher with immediate access to an ongoing visual record of the par- ticipant’s behavior. Instead of waiting until the investi- gation or teaching program is completed, behavior change is evaluated continually, allowing treatment and experi- mental decisions to be responsive to the participant’s per- formance. Graphs provide the “close, continual contact with relevant outcome data” that can lead to “measurably superior instruction” (Bushell & Baer, 1994, p. 9).

Second, direct and continual contact with the data in a readily analyzable format enables the researcher as well as the practitioner to explore interesting variations in be- havior as they occur. Some of the most important research findings about behavior have been made because scien- tists followed the leads suggested by their data instead of following predetermined experimental plans (Sidman, 1960, 1994; Skinner, 1956).

Third, graphs, like statistical analyses of behavior change, are judgmental aids: devices that help the prac- titioner or experimenter interpret the results of a study or treatment (Michael, 1974). In contrast to the statistical tests of inference used in group comparison research, however, visual analysis of graphed data takes less time, is relatively easy to learn, imposes no predetermined or

2A comparison of the visual analysis of graphed data and inferences based on statistical tests of significance is presented in Chapter 10. 3Graphs, like statistics, can also be manipulated to make certain interpre- tations of the data more or less likely. Unlike statistics, however, most forms of graphic displays used in behavior analysis provide direct access to the original data, which allows the inquisitive or doubtful reader to re- graph (i.e., manipulate) the data.

arbitrary level for determining the significance of be- havior change, and does not require the data to conform to certain mathematical properties or statistical assump- tions to be analyzed.

Fourth, visual analysis is a conservative method for determining the significance of behavior change. A be- havior change deemed statistically significant according to a test of mathematical probabilities may not look very impressive when the data are plotted on a graph that re- veals the range, variability, trends, and overlaps in the data within and across experimental or treatment condi- tions. Interventions that produce only weak or unstable effects are not likely to be reported as important findings in applied behavior analysis. Rather, weak or unstable effects are likely to lead to further experimentation in an effort to discover controlling variables that produce mean- ingful behavior change in a reliable and sustained man- ner. This screening out of weak variables in favor of robust interventions has enabled applied behavior ana- lysts to develop a useful technology of behavior change (Baer, 1977).2

Fifth, graphs enable and encourage independent judgments and interpretations of the meaning and sig- nificance of behavior change. Instead of having to rely on conclusions based on statistical manipulations of the data or on an author’s interpretations, readers of published re- ports of applied behavior analysis can (and should) con- duct their own visual analysis of the data to form independent conclusions.3

Sixth, in addition to their primary purpose of dis- playing relationships between behavior change (or lack thereof) and variables manipulated by the practitioner or researcher, graphs can also be effective sources of feed- back to the people whose behavior they represent (e.g., DeVries, Burnettte, & Redmon, 1991; Stack & Milan, 1993). Graphing one’s own performance has also been demonstrated to be an effective intervention for a vari- ety of academic and behavior change objectives (e.g., Fink & Carnine, 1975; Winette, Neale, & Grier, 1979).

Types of Graphs Used in Applied Behavior Analysis Visual formats for the graphic display of data most often used in applied behavior analysis are line graphs, bar graphs, cumulative records, semilogarithmic charts, and scatterplots.

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Chapter 6 Constructing and Interpreting Graphic Displays of Behavioral Data 129

Line Graphs

The simple line graph, or frequency polygon, is the most common graphic format for displaying data in applied behavior analysis. The line graph is based on a Cartesian plane, a two-dimensional area formed by the intersection of two perpendicular lines. Any point within the plane represents a specific relationship between the two di- mensions 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 be- havior (i.e., the dependent variable) in relation to a spec- ified point in time and/or environmental condition (i.e., the independent variable) in effect when the measure was taken. Comparing points on the graph reveals the presence and extent of changes in level, trend, and/or variability within and across conditions.

Parts of a Basic Line Graph

Although graphs vary considerably in their final appear- ance, 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.

1. Horizontal Axis. 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 pres- ence, 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. In Figure 6.2 succes- sive 10-minute sessions during which the number of property destruction responses (including attempts) was measured are marked on the horizontal axis. In this study, 8 to 10 sessions were conducted per day (Fisher, Lindauer, Alterson, & Thompson, 1998).

The horizontal axis on some graphs represents dif- ferent values of the independent variable instead of time. For example, Lalli, Mace, Livezey, and Kates (1998) scaled the horizontal axis on one graph in their study from less than 0.5 meters to 9.0 meters to show how the occurrence of self-injurious behavior by a girl with severe mental retardation decreased as the distance between the therapist and the girl increased.

2. Vertical Axis. 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 intersec- tion of the horizontal and vertical axes is called the origin and usually, though not necessarily, represents the zero value of the dependent variable. Each succes- sive point upward on the vertical axis represents a greater value of the dependent variable. The most com- mon practice is to mark the vertical axis with an equal- interval scale. On an equal-interval vertical axis equal distances on the axis represent equal amounts of behav- ior. The vertical axis in Figure 6.2 represents the number of property destruction responses (and attempts) per minute with a range of 0 to 4 responses per minute.

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Baseline Blocking Baseline Blocking Baseline Blocking

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Rates of property destruction (plus attempts) during baseline and the blocking condition for Milo.

Figure 6.2 The major parts of a simple line graph: (1) horizontal axis, (2) vertical axis, (3) condition change lines, (4) condi- tion labels, (5) data points, (6) data path, and (7) figure caption.

From “Assessment and Treatment of Destructive Behavior Maintained by Stereotypic Object Manipulation” by W. W. Fisher, S. E. Lindauer, C. J. Alterson, and R. H. Thompson, 1998, Journal of Applied Behavior Analysis, 31, p. 522. Copyright 1998 by the Society for the Experimental Analysis of Behavior, Inc. Used by permission.

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130 Part 3 Evaluating and Analyzing Behavior Change

3. Condition Change Lines. Condition change lines are vertical lines drawn upward from the horizontal axis to show points in time at which changes in the in- dependent variable occurred. The condition change lines in Figure 6.2 coincide with the introduction or withdrawal of an intervention the researchers called blocking. Condition change lines can be drawn as solid or dashed lines. When relatively minor changes occur within an overall condition, dashed vertical lines should be used to distinguish minor changes from major changes in conditions, which are shown by solid lines (see Figure 6.18).

4. Condition Labels. Condition labels, in the form of single words or brief descriptive phrases, are 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 inde- pendent variable) that are in effect during each phase of the study.4

5. Data Points. Each data point on a graph repre- sents 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 during Session 5, the last session of the first baseline phase, property destruction and attempted property destruction responses occurred at a rate of ap- proximately 2 responses per minute; and in Session 9, the fourth session of the first blocking phase, 0 in- stances of the target behavior were recorded.

6. Data Path. Connecting successive data points within a given condition with a straight line creates a data path. The data path represents the level and trend of behavior between successive data points, and it is a primary focus of attention in the interpretation and analysis of graphed data. Because behavior is rarely observed and recorded continuously in applied behav- ior analysis, the data path represents an estimate of the actual course taken by the behavior during the time elapsed between the two measures. The more mea- surements and resultant data points per unit of time (given an accurate observation and recording system),

4The terms condition and phase are related but not synonymous. Properly used, condition indicates the environmental arrangements in effect at any given time; phase refers to a period of time within a study or behavior- change program. For example, the study shown in Figure 6.2 consisted of two conditions (baseline and blocking) and six phases.

the more confidence one can place in the story told by the data path.

7. Figure Caption. The figure caption is a concise statement that, in combination with the axis and condi- tion labels, provides the reader with sufficient informa- tion to identify the independent and dependent variables. The figure caption should explain any symbols or ob- served but unplanned events that may have affected the dependent variable (see Figure 6.6) and point out and clarify any potentially confusing features of the graph (see Figure 6.7).

Variations of the Simple Line Graph: Multiple Data Paths

The line graph is a remarkably versatile vehicle for dis- playing behavior change. Whereas Figure 6.2 is an ex- ample of the line graph in its simplest form (one data path showing a series of successive measures of behav- ior across time and experimental conditions) by the ad- dition 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 ex- perimental conditions, (d) changes in target behavior rel- ative to the changing values of an independent variable, and (e) the behavior of two or more participants.

Two or More Dimensions of the Same Behavior. Showing multiple dimensions of the dependent variable on the same graph enables visual analysis of the ab- solute and relative effects of the independent variable on those dimensions. Figure 6.3 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 be- havior 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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Chapter 6 Constructing and Interpreting Graphic Displays of Behavioral Data 131

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