A Critical Review of Line Graphs in Behavior Analytic Journals

REVIEW ARTICLE

A Critical Review of Line Graphs in Behavior

Analytic Journals

Richard M. Kubina Jr.

& Douglas E. Kostewicz

Kaitlyn M. Brennan

& Seth A. King

Published online: 3 September 2015

Springer Science+Business Media New York 2015

Abstract Visual displays such as graphs have played an instrumental role in psychology. One

discipline relies almost exclusively on graphs in both applied and basic settings, behavior

analysis. The most common graphic used in behavior analysis falls under the category of time

series. The line graph represents the most frequently used display for visual analysis and

subsequent interpretation and communication of experimental findings. Behavior analysis, like

the rest of psychology, has opted to use non-standard line graphs. Therefore, the degree to

which graphical quality occurs remains unknown. The current article surveys the essential

structure and quality features of line graphs in behavioral journals. Four thousand three

hundred and thirteen graphs from 11 journals served as the sample. Results of the survey

indicate a high degree of deviation from standards of graph construction and proper labeling. A

discussion of the problems associated with graphing errors, future directions for graphing in

the field of behavior analysis, and the need for standards adopted for line graphs follows.

Keywords Line graphs

Time series

Graphical construction guidelines

Graphing standards

Behavior analysis, a subfield of psychology, owes a great debt to the visual display of data. For

example, the cumulative recorder offered a standard visual display of an organism’sperfor-

mance data. The distinctive visual patterns of behavior led to the discoveries such as schedules

of reinforcement (Lattal 2004). As behavior analysis moved forward in time, the visual displays

shifted from cumulative recorders to line graphs. Data show that cumulative records in the

Educ Psychol Rev (2017) 29:583–598

DOI 10.1007/s10648-015-9339-x

* Richard M. Kubina, Jr.

rmk11@psu.edu

Special Education Program, The Pennsylvania State University, 209 CEDAR, Building University

Park, State College, PA 16802-3109, USA

University of Pittsburgh, Pittsburgh, PA, USA

Tennessee Technological University, Cookeville, TN, USA

Journal of the Experimental Analysis of Behavior continue to appear infrequently and in other

years not at all (Kangas and Cassidy 2010).

The shift away from cumulative records to line graphs coincided with the advent of an

emphasis on applied work. The oft-cited paper of Baer et al. (1968) laid the foundation for

discerning the facets of behavior analysis. Three of seven characteristics of applied behavior

analysis have a direct link to visual displays of data. First, Analytic refers to a convincing

demonstration of an experimental effect. The preferred medium for all analysis of data occurs

through graphs. Second, Effective conveys the requirement for the intervention to produce a

practical and meaningful magnitude of behavior change. Line graphs allow for the determi-

nation as well as the public documentation and communication of the significance of behav-

ioral improvements (Spriggs and Gast 2010). And third, Generality means that the behavior

persists across time, environments, and operant responses within a class. The line graph, part

of the family of time series graphs, directly portrays the extent to which behavior does or does

not persist.

Principles of graphic presentation for line graphs have quality standards nece ssary

for t he accurate representation of data. A number of publications have described the

standards for proper construction for line graphs (American National Standards Insti-

tute and American Society of Mechanical Engineers 1960, 1979; American Standards

Association 1938; American Statistical Association 1915; Department of the Army

2010). For example, the publication of Time series charts: a manual of design and

construction set forth ag reed upon standards for line graphs (American Standards

Association 1938). The committee provided guidance on many specific features

ranging from scale rulings and graph dimensions to the weight of lines and use of

reference symbols. Through time, many professional organizations and researchers

have continued to offer principles of design an d procedure for constructing high-

caliber line graphs (e.g., Behavior Analysis—Cooper et al. 2007; Statistics—Cleveland

1993, 1994; General Science—Scientific Illustration Committee 1988; Technical

Drawing, Drafting, and Mechanical Engineering —Giesecke et al. 2012). Table 1 lists

major quality features of line grap hs tailored toward use in the behavioral sciences.

An analysis of the following basic behavior analysis (Alberto and Troutman 2013;Catania

1998;Cooperetal.2007; Malott and Shane 2014; Mayer et al. 2014; Pierce and Cheney 2013;

Vargas 2013) and single case design books (Barlow et al. 2009;Gast2010; Johnston and

Pennypacker 2009;Kazdin2011;Kennedy2005) corresponds to the graphical standards for a

line graph previously listed. In addition to quality standards line graphs have an essential

structure consisting of two axes, the horizontal and vertical, representing a time unit and a

quantitative value, respectively. Time units can cover minutes, hours, days, weeks, and years

based on the second (National Institute of Standards and Technology 2014).

The range of

behavior on the vertical axis spans dimensionless quantities like percentages and ratios to

dimensional quantities such as repeatability and temporal extent measured with frequency and

duration, respectively (Johnston and Pennypacker 2009).

Not adhering to the essential structure may yield distorted, exaggerated, or imprecise

information. The essential structure shows change over time. Figure 1 shows three line graphs

with the same data. The first line graph made following the Bproportional construction ratio,^

discussed later, displays a series of data with a moderately increasing variable trend. The line

graph has an extended vertical axis changing the variability from moderate to low. The trend

also increases when compared to the previous graph. Stretching the horizontal axis in the third

line graph depresses the trend and decreases variability.

584 Educ Psychol Rev (2017) 29:583–598

Tabl e 1 Quality features of a line graph and measurement

Essential structure Function Measured

Vertical axis labeled with quantitative measure;

horizontal axis labeled with time unit

To show the change in the measure over time

(Harris 1999)

What label does the vertical and horizontal axes maintain?

Does the figure maintain a line for each axis?

Quality feature

Vertical axis length has a 2:3 ratio to the

horizontal axis

To properly display data variability and limit distortion

(Cooper et al. 2007; Parsonson and Baer 1978)

Is the ratio of vertical to horizontal axis 5:8 to 3:4 (63 to 75 %

difference )? Do axes line up in all multiple baseline graphs?

Are axis lengths the same for all figures with the same unit

within each article? Are all figures with the same unit scaled

to the same minimum and maximum?

Tick marks point outward To prevent or minimize data obfuscation (Cleveland 1994) Onbothaxes,aretickmarkspointing outward for the entire length

of the axes?

A minimal number of evenly spaced tick marks To decrease graph clutter emphasizing the most prominent

feature, the data (Cleveland 1994)

On both axes, are tick marks evenly spaced (i.e., at equal intervals)?

Tick marks have labels Delineates the value of the axes’ units (Robbins 2005) On both axes, are tick marks numbered? Are the scale counts

correct?

Data points clearly visible Enhances data clarity (Robbins 2005) Are data points on the figure clearly visible?

Data paths clearly visible (if used) Shows the direction of data clearly (Cooper et al. 2007) If the figure contains a data path, is it visible?

Condition change lines (if used) Visually separates data between conditions (Cooper et al. 2007) If the figure contains a condition change line, is it visible?

Condition labels Identification of experimental conditions (Cooper et al. 2007) If the figure contains a condition change line, does it have labels?

Figure caption When combined with other graphic elements, conveys meaning

(Cooper et al. 2007)

Doesthefigurecontain a caption?

Educ Psychol Rev (2017) 29:583–598 585

The Behavior of Organisms of Skinner (1938), BSome Current Dimensions of Applied

Behavior Analysis^ of Baer et al. (1968), and chapters of Cooper et al. (2007) on the

construction and interpretation of graphical displays represent examples for the use, rationale,

and creation of behavior analytic line graphs. As a result, line graphs have become the primary

visual display for presenting behavioral data in fieldwork, theses, dissertations, lectures,

conference presentations, and journal articles (Cooper et al. 2007; Mayer et al. 2014; Poling

et al. 1995;SpriggsandGast2010). How well the field of behavior analysis attends to

essential structur e and quality features of line graphs, however, remains unknown. The current

survey examines the quality of line graphs contained in behavioral journals and attempts to

answer two questions. First, how well do selected visual graphics follow the essential structure

of line graph construction? Namely, to what extent do selected line charts have time units on

the horizontal axis and quantitative units on the vertical axis? Second, how well do selected

visual graphics follow the quality features of line graphs (Table 1)?

Method

Initial selection followed criteria established in previous surveys for the identification of

prominent behavioral journals (Carr and Britton 2003; Critchfield 2002;Kubinaetal.2008).

Journals had to explicitly pertain to behavior analysis and have at least a 10-year publication

record. The survey sampled a variety of behavior analytic foci (e.g., education, cognitive

behavior modification, experimental analysis). Eleven journals met criteria.

Six journals covered technical applications, practices, and issues related to the field of

behavior analysis (Behavior Modification, Behavior Therapy, Child and Family Behavior

Fig. 1 Sample graphs containing the same scaling with variable length axes

586 Educ Psychol Rev (2017) 29:583–598

Therapy, Cognitive and Behavioral Practice, Journal of Applied Behavior Analysis, and

Journal of Behavior Therapy and Experimental Psychiatry). Five additional journals discussed

behavior analysis in relation to education (Education and Treatment of Children, Journal of

Behavioral Education), experimental behavior analysis (Journal of the Experimental Analysis

of Behavior, Learning and Behavior), and the analysis of verbal behavior (The Analysis of

Verb al B e h a vi or).

After journal identification, one random issue from every 2-year block served as the basis for

selecting graphs. The process began at each journal’s inception date and concluded in 2011. The

investigators examined all graphs that had a vertical and horizontal axis with data moving left to

right. First, the graph must have contained a maximum of one data point per data series on the

horizontal axis interval excluding scatterplot graphs (i.e., multiple data points can occur on the

same horizontal interval) and bar charts. Second, a unit of time or sessions and a quantitative

value must have occurred on the horizontal and vertical axis, respectively. Graphs scaled with

nominal or ordinal vertical axes and/or non-time based horizontal axes did not meet inclusion

criteria. Third, graphs with dually and/or logarithmically scaled vertical axes, as line graph

variants, also failed to satisfy inclusion criteria. Investigators analyzed each included graph

individually whether appearing alone or in the context of other graphs (i.e., multiple baselines).

Investigators scored each graph for components of line graph essential structure and the

presence or absence of line graph quality features (specific questions appear on Table 1).

Scorers initially determined presence or absence of axes and labels. Using rulers or straight

edges, scorers then determined the ratio of the length of the vertical to the horizontal axis and

the axes scaling and alignment to other graphs within the same figure (i.e., multiple baseline

figures) and/or article. Scorers continued to evaluate each graph according to the remaining

questions noted on Table 1 and entered all data on an accompanying Excel file. The process

repeated for each graph meeting criteria.

Scorer Calibration, Reliability, and Interobserver Agreement

Scorers received instruction on all procedures. Instruction consisted of review and guided

practice of scoring and entering data on the Excel spreadsheet for three graphs. At the

conclusion of the instructional sessions, experimenters had scorers evaluate a random, but

previously scored issue and compared results. Scorers had to meet 100 % agreement prior to

independent scoring.

Two measure ment assessment techniques evaluated scoring: reliability and interobserver

agreement. For reliability (Johnston and Pennypacker 2009), each scorer rescored 20 % of issues.

A comparison occurred between the second examination and the initial score. An exact agreement

approach (Kennedy 2005) determined the percent of agreement between individual cells of data

in Excel sheets. The average reliability totaled 95 % with a range of 94–100 %. Interobserver

agreement followed the same procedure but took place between different scorers on 20 % (28) of

issues. The average interobserver agreement equaled 91 % with a range of 89–100 %.

Results

A total of 11 behavioral journals served as the basis of the graph analysis. A random sampling

produced 191 issues, an average of 17 issues per journal with a range of 9–27. A potential

598 9 time series graphics occurred in 1622 articles. Removi ng graphs that contained

Educ Psychol Rev (2017) 29:583–598 587

logarithmically scaled (114) or dually scaled axes (203), the number of graphs came to 5672.

Graphs with nominal (60) or ordinal (227) scaled vertical axes (i.e., qualitatively scaled) or

included a label for the horizontal axis that did not fall into a unit of time (1072) failed to meet

review criteria resulting in a total of 4313 coded graphs or approximately 23 per issue.

Essential Structure

The essential structure of a simple line graph starts with two drawn axes, a vertical and

horizontal. Of the 4313 graphs meeting criteria, 98 % (4206) and 97 % (4200) of graphs

contained a drawn line on the vertical and horizontal axis, respectively. Two additional

essential structure criteria require the labeling of the two axes with a quantitative value on

the vertical axis and time along the horizontal axis. Two dot charts (Cleveland 1984b), in

Figs. 2 and 3, show the breakdown that authors used for labeling axes. On both figures, dots

represent categorical instances and appear from greatest to least.

Figure 2 shows that, of the eight vertical label categories, five contained 98 % of instances.

Authors used a percent label 27 % (1159) of the time on the vertical axes, more often than any

other classification. Count (20 % or 865), ratio (18 % or 782), no label (17 % or 753), and

frequency/rate (16 % or 677) groupings round out the initial 98 %. The remaining 2 % consist

of latency (40), duration (36), and interresponse time (1).

On Fig. 3, labels for the horizontal axes revealed less diffusion as compared to the vertical axis

breakdown. No label (1486) and sessions/trials (1469) accounted for 69 %. A total of 459 (11 %)

graphs incorporated seconds, 268 (6 %) days, and 262 (6 %) minutes along the horizontal axis. The

final 9 % include other unit of time (172), multiple units on the same axis (160), and hours (37).

Quality Features

Tables 2 and 3 show a variety of quality features coded for each graph and groupings of

graphs. Graphs meeting each instance receive a comparison to the total number of opportu-

nities resulting in a percent occurrence. Coded graphics not meeting the quality feature (except

Fig. 2 A dot chart showing the instances of vertical axis labels

588 Educ Psychol Rev (2017) 29:583–598

for data connected across condition change line) result in an error shown as a remaining

percentage in the final column. Each instance of the category data connected across condition

change line already constitutes an error; thus, the same percentage occurs in both columns.

Tick marks and scaling Considerable differences in quality occurred between tick marks

and scaling of the vertical and horizontal axes. Table 2 shows that, across the five tick mark

Fig. 3 A dot chart showing the instances of horizontal axis labels

Table 2 Quality features

Graphic quality feature Instances per opportunity Percent of

error (%)

Vertical axis tick marks Data occur on tick marks 3481/4313=81 % 19

Full or partial tick marks on

outside of graph

2460/4313=57 % 43

Tick marks occur at equal

intervals

3768/4313=87 % 13

Numbers occur on tick marks 3493/4313=81 % 19

Scale count is correct

(e.g., 10, 20, 30, etc.)

3702/4313=86 % 14

Horizontal axis tick marks Data occur on tick marks 2866/4313=66 % 34

Full or partial tick marks on

outside of graph

2115/4313=49 % 51

Tick marks occur at equal intervals 2714/4313=63 % 37

Numbers occur on tick marks 2214/4313=51 % 49

Scale count is correct

(e.g., 10, 20, 30, etc.)

2304/4313=53 % 47

Data points clearly visible 3703/4313 =86 % 14

Data connected and data path clearly visible 4193/4313=97 % 3

Figure caption 4253/4313=99 % 1

Condition change labels present 1774/2172=82 % 18

Data connected across condition change line 158/2151=7 % 7

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and scaling features, half as much average error occurred on the vertical (22 %) rather than

horizontal axis (44 %). On both axes, the highest percentages (43 and 51 %) of error related to

fully or partially placing tick marks on the outside of the figure. Instead, graphs either had no

tick marks or tick marks on the inside of the graph.

Data points and paths, condition labels, and figure captions A decrease in error

appeared when coding quality features associated with data points and paths and condition

and figure labels (Table 2). Only 1 and 3 % of the sampled graphs failed to contain a figure

caption and had connected data paths clearly visible. Although, 18 % of the time graphs

containing condition change lines failed to have a label for each condition and 7 % had data

paths connected across condition change lines.

Axes and axis comparisons Table 3 highlights quality features associated with axis com-

parisons. The first main comparison occurred between the vertical and horizontal axes with

15 % meeting a ratio of 5:8 to 3:4 or 63 to 75 % difference in length. For graphs on the same

page, both vertical and horizontal axes aligned, when possible, 79 % of instances. Expanding

the analysis to each article, graphs received coding for maintaining the same physical and

scaling structure. On both axes, approximately 70 % of instances failed to maintain similar

scaling for the same unit across the article and 40 % had variable axis length.

Discussion

Graphs have one fundamental purpose: to affect the interpretative behavior of the graph reader

(Johnston and Pennypacker 2009). Information in graphs includes documenting performance,

analyzing intervention effects, interpreting experimental and applied outcomes, and predicting

the future course of behavior. Graphs generate meaning based on physical distinctions of

Table 3 Additional quality features: comparisons of individual graph axes and of axes on multiple graphs

Graphic quality feature Instances per

opportunity

Percent

of error

(%)

Ratio of vertical to horizontal axis

length: 5:8 to 3:4 (63 to 75 % difference)

637/4313=15 % 85

For multiple graphs within the same

figure on the same page:

Vertical axes align 1016/1285=79 % 21

Horizontal axes

align

1053/1331=79 % 21

For multiple graphs

within the same

article

Vertical axes that share

the same label:

Scaled to same unit

(min and max)

262/838=31 % 69

Drawntothesame

physical length

467/838=56 % 44

Horizontal axes that

share the same

label:

Scaled to same unit

(min and max)

222/710=31 % 69

Drawntothesame

physical length

436/710=61 % 39

590 Educ Psychol Rev (2017) 29:583–598

shape, size, color, positioning, and symbols (Cleveland and McGill 1985;Tufte1990). While

all graphed data convey a message, BA graphical method is successful only if the decoding is

effective. No matter how clever and how technologically impressive the encoding, it fails if the

decoding process fails^ (Cleveland and McGill 1985,p.828).

The scien ce of behavior fundamentally relies on simple line graphs for decoding

information (Cooper et al. 2007). Not all simple line graphs, however, have equal merit.

Line graphs can vary along critical dimensions such as scaling, length of axes, and

labeling. Widely divergent construction practices distort the interpretative f unction of

graphs. The use of essential structures and quality features pro motes order and guides

graphical construction, subsequently enhancing visual clarity and a clear explanation of

the data (Cleveland 1984a). At the time of t he present review, however, no comprehensive

evaluation o f simple line graphs in behavior analysis has occurred. The specific research

questions asked how well do selected visual graphics follow the essential structure and

quality features of line graph construction.

Essential Structure

Quantity and time form a line graph’s essential structure (Few 2009; Kriglstein et al. 2014).

Behavior analysis has long valued the graphic display of quantitative rather than qualitative

representations of behavior (Baer et al. 1968; Ferster and Skinner 1957; Parsonson and Baer

1978; Poling et al. 1995). Quantification leads to precision provided by numbers. Numerical

representations of behavior, or quantitative measurement, serve as the medium through which

all analysis occurs. The data show that, out of 4313 reviewed graphs, 3560 had a quantitatively

scaled vertical axis. In other words, 83 % of the reviewed graphs prominently displayed

behavior as a quantity.

The quantitatively displayed behavior can change across time. Time series line graphs must

have a unit of time on the horizontal axis (Robbins 2005). Examples of units of time range

from seconds (e.g., Preston 1994) and minutes (e.g., Norborg et al. 1983) to hours (e.g.,

Ramirez 1997) and days (e.g., Gutentag and Hammer 2000). Twenty-eight percent of line

graphs in behavioral journals maintained a time unit label. The remaining 72 % scaled the

horizontal axis with a non-time unit (e.g., sessions, trials, no label). By labeling the horizontal

axis with sessions or trials, the line graph technically no longer qualifies as a time series

graphic and markedly influences visual analysis.

All graph readers use visual analysis to uncover functional relations and experimental

effects (Cooper et al. 2007; Kazdin 2011). In point of fact, visual analysis of line graphs serves

as the cornerstone of studies using a single case experimental design. BData are graphed for

each participant during a study with trend, level, and stability of data assessed within and

between conditions (Lane and Gast 2014, p 445).^ Trend refers to the slope or angle of a data

series; level applies to the median score of a data set, and stability captures the degree of

variability in a set of data (Gast and Spriggs 2010). Table 4 explains and Fig. 4 illustrates how

session usage produces three categories of errors affecting visual analysis: labeling error, false

equality, and non-representative data.

Labeling error involves assigning a designation other than a unit of time to the horizontal

axis.Asanexample,graph1inFig.4 shows data plotted along a horizontal axis labeled with

sessions and a vertical axis with quantified behaviors per session. Baseline data show a

gradually increasing, moderately variable trend with a level of 25 behaviors per session. Data

in intervention show the level rising to 40 behaviors per session with a slightly increasing and

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moderately variable trend. Visual analysis would suggest an experimental effect due to the

level change.

Graphs must contain all construction elements necessary to describe the data so the reader

can draw accurate conclusions (Cleveland 1994). Or, as the famous data scientist Tukey stated,

BA strongly good graph tells us everything we need to know just by looking at it^ (as cited in

Wainer 2005). Using sessions, however, fails to provide a full account of temporal information.

The graph reader does not know how long each individual session lasted, if sessions occurred

contiguously in time, or the duration of the experiment (e.g., 1 day or 1 month). Labeling

session on the horizontal axis (i.e., the absence of time), as in graph 1 (Fig. 4), inhibits a

chronologically accurate visual analysis of time series data.

Variable length sessions appearing equal on a time series graph represent false equality

shown in the contrast between graph 1 and graph 2 (Fig. 4). Individual session duration may

differ within and between experimental conditions. For instance, baseline sessions may have

lasted 3 min and intervention sessions 9 min. Graph 1 would then establish a false equality of

quantified behaviors per session. Graph 2’s time-scaled behavior per 3 min rather than per

session offers a different interpretation. Conclusions from baseline in both graph 1 and graph 2

remain the same. However, intervention data noticeably drop in level from 40 to 13.3

quantified behaviors per 3 min. In addition, trend and variability decrease. Visual analysis

on graph 2 would suggest an opposite experimental effect to graph 1.

The use of sessions promotes non-representative data by removing data from the cycle of

time (e.g., minutes, hours, days). Graph 3 appears visually distinct from graph 1, yet both

contain the same data (Fig. 4). Graph 3 presents a precise time account of the data collection.

Graph 1 compresses 80 days into 20 sessions. After properly placing the data in time, the trend

Table 4 Labeling error and visual analytic distortions

Session practice Problem when horizontal axis

has Bsessions^ as the label and

data graphed consecutively and

contiguously.

Session duration reported

as a time unit in text and…

Held consistent for the duration

of the study

Labeling error

Not held consistent (i.e., presented

as a possible range of time)

Labeling error and false

equality

Sessions graphed with respect

to time and…

Occur consecutively in time (i.e., one

session per day)

Labeling error

Occur consecutively in time (i.e., one

session per day) but do not occur

every day (i.e., sick days and/or

weekends)

Labeling error and

non-representative data

Do not occur consecutively in time

(e.g., multiple sessions 1 day and then

additional sessions later in the week)

Labeling error and

non-representative data

Session duration not reported

as a time unit and…

The experiment lasts for an unknown

duration of time

Labeling error, false equality,

and non-representative data

Time series line graph must have a unit of time depicted on the horizontal axis

Produces incorrect trend, level, and variability

Graphed data visually distorts the actual data, trend, and variability

592 Educ Psychol Rev (2017) 29:583–598

Fig. 4 Three line graphs illustrating the effects of labeling the horizontal axis with sessions

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for baseline in graph 3 becomes steeper and looks more variable. Data in the intervention

appear slightly less variable with a similar trend. Graph 1 hides important information obvious

in graph 3. The steady application of the intervention for the first five consecutive days and the

infrequent implementation across the remaining 60 days tell a revealing story. The initial five

data points show a sharp increase while the remaining six gradually decline. Graphical

integrity of time series such as the line graph necessitates respecting the passage of time.

Additional examples of session usage error appear in Table 4.

Three possible reasons exist for the proliferation of labeling the horizontal axis with

sessions: instruction, relativism, and substitution. BInstruction^ refers to the guidance provided

by behavior analytic (e.g., Cooper et al. 2007; Mayer et al. 2014) and single case design

textbooks (e.g., Gast 2010;Kazdin201 1;Kennedy2005). Both applied and basic researchers

derive a substantial part of their graphing knowledge from textbooks. The widespread usage of

sessions in journals as a labeling/graphing convention demonstrates Brelativism^ (e.g., 90 % of

reviewed graphs in the Journal of Behavioral Education used sessions). The common use of

sessions leads to the false impression of an acceptable practice. And, Bsubstitution^ occurs

when behavior analysts measure behavior temporally but switch to sessions as a time

placeholder. In other words, properly measuring behavior with time but improperly labeling

the graph with a non-time unit sessions. Regardless of the sources of control or reasons why

non-time units appear on the horizontal axis, time remains the major factor in a time series

graphic (Cleveland 1994;Tufte1983). The science of behavior should discard the practice of

using sessions in line graphs; sessions offer no advantages for visually analyzing behavior and

instead impede the accurate and efficient portrayal of behavioral data.

Quality Features

Quality features of line graphs convey representativeness and continuity of graphically

displayed, time-oriented data. Graph readers decode quantitative information based on the

visual characteristics of a graph’s construction parameters. The physical proportion of the

vertical to the horizontal axis of a graph serves as one important interpretation variable.

Published recommendations suggest a ratio of vertical to horizontal axis ranges of 5:8 to

2:3, with a maximum of 3:4 (American National Standards Institute and American Society of

Mechanical Engineers 1960, 1979;Bowen1992; Cooper et al. 2007;DepartmentoftheArmy

2010; Johnston and Pennypacker 1980; Katzenberg 1975; Parsonson and Baer 1978; Poling

et al. 1995;Schmid1992). The respective 63, 66, and 75 % size differential of height to width

presents a standardizing and protective effect. Namely, the proportional construction ratio

enhances graphical legibility (Cooper et al. 2007) and safeguards against falsely decoding

meaningful trends and variability that occur based on a stretched or compressed vertical axis

(see the bottom two graphs in Fig. 1). Only 15 % of the 4313 reviewed graphs had a

proportional construction ratio falling between 63 and 75 %. A discrepancy of the previously

mentioned magnitude may adversely affect visual analysis. As stressed by Schmid (1992), B…

grid proportions are of pronounced significance as the determinants of the visual impression

conveyed^ (p. 28).

Other factors affecting conclusions drawn from graphs include physical length and scaling

of graphs within the same article that share the same axis labels. Of the reviewed graphs, 44 %

of vertical axes and 39 % of horizontal axes had different physical lengths. Horizontal or

vertical axes with variable lengths present a false comparison. Visual analysis requires

uniformly sized data displays for proper pattern recognition.

594 Educ Psychol Rev (2017) 29:583–598

Accurate, legible, and the fine-grained detail of data further degrade when scaling differs.

Time series graphics such as the line graph must preserve the continuity of time for useful

comparisons (Robbins 2005). Differently scaled horizontal axes alter the temporal relationship

between data sets meant for comparison. Scaling of the vertical axes demands the same

drafting precision to produce visual parity. Sixty-nine percent of vertical and horizontal axes

meant for comparison contained dissimilar scaling. Improper scaling for corresponding line

graphs demonstrates poor design, violates graphic principles and standards, and makes it

difficult to distinguish between the multiple curves (Schmid 1992; Schmid and Schmid 1979).

The errors of quality features discovered in the present study may have occurred due to a

lack of standardization. Standardization refers the implementation of world-class specifications

governing the fabrication and delivery of products, systems, and services (International

Organization for Standardization 2014). Or more simply stated, standardization involves B…

an agreed-upon way of doing something^ (Spivak and Brenner 2001, p.1). The essential

structure and quality features of line graphs used as the evaluation standard in the present

article derived from a number of authoritative sources on graphic construction. The present

error rate data may reflect a general unawareness of, or misinformation about, line graph

standards. Disagreement among journal editors, reviewers, and authors as to what constitutes a

standard may also account for labeling errors and ill-formed line graphs.

Cleveland (1984a) found that 30 % of all graphs reviewed in a volume of the prestigious

journal Science contained an unacceptable amount of at least one error. In the current sample,

85 % of reviewed graphs had, at minimum, one error (i.e., violation of the proportional

construction rule). The results from the present usage survey suggest that behavior analysis

must address why so many errors occur with line graphs when compared to long-standing

accepted construction rules both within and outside of the scientific discipline (American

National Standards Institute and American Society of Mechanical Engineers 1960, 1979;

American Standards Association 1938; American Statistical Association 1915; Cleveland

1993, 1994;Cooperetal.2007; Department of the Army 2010;Gieseckeetal.2012;Harris

1999; Parsonson and Baer 1978; Poling et al. 1995; Scientific Illustration Committee 1988;

Schmid 1992; Schmid and Schmid 1979).

The present survey did not examine the conditions for the excessive errors found in graph

construction and labeling. Nevertheless, behavior analysis must determine how to remedy the

situation. Three major sources disseminate standards: education, textbooks, and journals.

Education covers colleges and universities (i.e., undergraduate and graduate programs),

continuing education courses (e.g., conferences, workshops), and coursework approved for

certification (e.g., Behavior Analysis Certification Board) and/or licensure. Textbooks provide

information ranging from foundational concepts and principles, practitioner-driven topics and

implementations, and experimental applications. And, journals distill current practices and

codify history. The entities responsible for the principles of line graph construction must work

in synchrony to publicize, regulate, and promote graphing standards. Next to measuring

behavioral data with integrity, line graphs represent the single most important factor for

analyzing, interpreting, and communicating basic and applied experimental results.

Limitations

Researchers reviewed the majority of articles through online services. The quality of the copies

varied (e.g., spacing, alignment, clarity). Copy quality may have influenced some scores such

as Number on Tick Marks and Alignment of Axes. With 49 and 21 % error, respectively, copy

Educ Psychol Rev (2017) 29:583–598 595

quality alone seems unlikely to have driven the majority of error. Another limitation involves

journal selection. The present review followed previously established guidelines for identify-

ing behavioral journals. Regardless, some may argue that the current sample excludes addi-

tional representative examples of behavior analytic journals.

Future Directions

Future researchers could expand upon the present research by examining a larger scope of

behavioral journals and move to other psychology journals. Researchers may also wish to

focus in on individual journals and determine if graphing errors changed across time. Positive

findings may indicate that certain journals provide additional information regarding graph

construction (e.g., editorial guidance).

Research spurred by the present study extends to decisions made through visual analysis.

Would graphical decisions and analyses differ if simple line graphs contained fewer errors? For

instance, sessions may have varied length in time and may not occur consecutively. The graph,

nevertheless, may improperly show sessions contiguously along the horizontal axis producing

false equality, labeling error, and non-representative data (i.e., three possible errors associated

with session usage). How would behavior analysts and practitioners of psychological disci-

plines respond to the same data regraphed in time? Scaling vertical and horizontal axes to an

equivalent minimum and maximum values for graphs meant for comparison may also produce

different decisions.

Conclusions

The present study conducted a detailed survey of the essential structure and quality features of

line graphs in behavioral journals. The data demonstrated a number of areas where errors

occurred with the construction and labeling of graphs. The results also indicate quality features

that behavior analysts can improve the visual representation of data with line graphs: following

the proportional construction ratio, when comparing data scaling the vertical and horizontal

axes to the same physical length, enhancing tick mark usage, and using time units instead of

sessions for time series data. The science of behavior may evolve more rapidly with adherence

to principles and standards of graphical excellence.

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