Visual analysis in single case experimental design studies: Brief review and guidelines

Article (PDF Available)inNeuropsychological Rehabilitation 24(3-4) · July 2013with4,015 Reads
DOI: 10.1080/09602011.2013.815636 · Source: PubMed
Visual analysis of graphic displays of data is a cornerstone of studies using a single case experimental design (SCED). Data are graphed for each participant during a study with trend, level, and stability of data assessed within and between conditions. Reliable interpretations of effects of an intervention are dependent on researchers' understanding and use of systematic procedures. The purpose of this paper is to provide readers with a rationale for visual analysis of data when using a SCED, a step-by-step guide for conducting a visual analysis of graphed data, as well as to highlight considerations for persons interested in using visual analysis to evaluate an intervention, especially the importance of collecting reliability data for dependent measures and fidelity of implementation of study procedures.



Full-text (PDF)

Available from: David L. Gast
This article was downloaded by: [Justin Lane]
On: 25 July 2013, At: 07:20
Publisher: Routledge
Informa Ltd Registered in England and Wales Registered Number: 1072954
Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,
Rehabilitation: An International
Publication details, including instructions for authors
and subscription information:
Visual analysis in single case
experimental design studies:
Brief review and guidelines
Justin D. Lane
& David L. Gast
Department of Special Education , The University of
Georgia , Athens , GA , USA
Published online: 24 Jul 2013.
To cite this article: Neuropsychological Rehabilitation (2013): Visual analysis in single
case experimental design studies: Brief review and guidelines, Neuropsychological
Rehabilitation: An International Journal
To link to this article:
Taylor & Francis makes every effort to ensure the accuracy of all the
information (the “Content”) contained in the publications on our platform.
However, Taylor & Francis, our agents, and our licensors make no
representations or warranties whatsoever as to the accuracy, completeness, or
suitability for any purpose of the Content. Any opinions and views expressed
in this publication are the opinions and views of the authors, and are not the
views of or endorsed by Taylor & Francis. The accuracy of the Content should
not be relied upon and should be independently verified with primary sources
of information. Taylor and Francis shall not be liable for any losses, actions,
claims, proceedings, demands, costs, expenses, damages, and other liabilities
whatsoever or howsoever caused arising directly or indirectly in connection
with, in relation to or arising out of the use of the Content.
This article may be used for research, teaching, and private study purposes.
Any substantial or systematic reproduction, redistribution, reselling, loan, sub-
licensing, systematic supply, or distribution in any form to anyone is expressly
forbidden. Terms & Conditions of access and use can be found at http://
Downloaded by [Justin Lane] at 07:20 25 July 2013
Visual analysis in single case experimental design
studies: Brief review and guidelines
Justin D. Lane and David L. Gast
Department of Special Education, The University of Georgia, Athens, GA, USA
Visual analysis of graphic displays of data is a cornerstone of studies using a single
case experimental design (SCED). Data are graphed for each participant during a
study with trend, level, and stability of data assessed within and between conditions.
Reliable interpretations of effects of an intervention are dependent on researchers’
understanding and use of systematic procedures. The purpose of this paper is to
provide readers with a rationale for visual analysis of data when using a SCED, a
step-by-step guide for conducting a visual analysis of graphed data, as well as to
highlight considerations for persons interested in using visual analysis to evaluate
an intervention, especially the importance of collecting reliability data for depen-
dent measures and fidelity of implementation of study procedures.
Keywords: Single case experimental design; Visu al analysis.
Visual analysis of graphic displays of data is the hallmark for interpreting
effects of an intervention during studies using a single case experimental
design (SCED; Kennedy, 2005). The independent variable is typically an
intervention designed to reduce aberrant behaviour or increase pro-social or
academic behaviours (Horner et al., 2005). The expectation is behaviours
are graphed for each participant by session for all conditions of a study.
SCED studies are based on baseline logic, meaning participants serve as
their own control for evaluating change (Gast & Hammond, 2010). The
most basic method for evaluating a behaviour-change programme is analysis
Correspondence should be addressed to Justin D. Lane, Department of Special Education,
The University of Georgia, Athens, GA 30602, USA.
Neuropsychological Rehabilitation, 2013
# 2013 Taylor & Francis
Downloaded by [Justin Lane] at 07:20 25 July 2013
of two adjacent conditions, also known as an A-B comparison. Each condition
represents a set of specific variables under which a behaviour is measured
continuously during baseline, intervention, and any subsequent conditions,
with the first condition known as baseline (A) and the second condition
known as intervention (B) (Lane, Wolery, Reichow, & Rogers, 2007). The
expectation is that data collected during baseline are stable and change in a
therapeutic direction upon introduction of the independent variable, with at
least three replications of effect across behaviours, settings, or participants
(Gast & Hammond, 2010; Kennedy, 2005; Lane et al., 2007). This is in con-
trast to traditional group design methods, which use at least one experimental
group and one control group to compare effects of treatment through appli-
cation of a statistical test (e.g., ANOVA) and a significance measure (e.g.,
p , .05; Kazdin, 2011). Traditional group design methods provide an oppor-
tunity for summative evaluation of effect for all participants. In contrast,
SCED studies allow researchers to formatively evaluate a participant’s per-
formance session to session through continuous collection of individualised
behaviour data. Researchers can modify an intervention if limited or no
change in performance is observed throughout the study (Gast, 2010; Lieber-
man, Yoder, Reichow, & Wolery, 2010; Wolery & Harris, 1982).
SCED researchers traditionally code responses for each participant in vivo
or following completion of a session using video records (Ayres & Gast,
2010). Each participant’s performance is then calculated and transferred to
a graph for purposes of visually analysing (a) trend, (b) level, and (c) stability.
Researchers select a format for graphic display which best represents the
purpose of the study based on the proposed hypotheses and research questions
(Spriggs & Gast, 2010). There are various examples of graphic formats for
presenting data, which include (a) cumulative records, (b) semi-logarithmic
charts, (c) bar graphs, and (d) line graphs. Cumulative records are rooted in
the field of experimental analysis of behaviour and originated from work
by B. F. Skinner (Cooper, Heron, & Heward, 2007; Kennedy, 2005). When
using a cumulative record, participants’ responses are recorded and added
across sessions. It is not uncommon for novice readers to report an increasing
trend across sessions since responses are added session to session. Further
inspection of a cumulative record may indicate minimal (e.g., addition of
one response from previous session) to no change (flat line from session to
session) in responding. Regardless of the magnitude of behaviour change,
one of the benefits of a cumulative record is clear depiction of total responses
within a study. Semi-logarithmic charts provide a format for presenting rela-
tive change in performance and are typically used to present rate of respond-
ing and proportional change in performance. In contrast to cumulative records
and semi-logarithmic charts, bar graphs provide a simplified format for com-
parisons of discrete data or presentation of summative performance following
completion of a study. Finally, line graphs are the most commonly used
Downloaded by [Justin Lane] at 07:20 25 July 2013
graphic format for presenting ongoing data collected during a study using a
SCED. Performance within a session is plotted as a single data point and con-
nected to subsequent data points as the study progresses (Cooper et al., 2007;
Kennedy, 2005; Spriggs & Gast, 2010). For purposes of this paper, examples
and information will focus on analysis of data using a line graph.
Researchers use A-B-C notation to differentiate conditions on a graphic
display. A major tenet of SCED is that all conditions remain constant with
exception of the introduction of one variable in the intervention condition.
Additional components of an intervention may be introduced within a con-
dition, also known as a phase change, but it is still recommended that any
additional variables be introduced systematically for purposes of controlling
threats to internal validity (Gast & Spriggs, 2010; Lane et al., 2007). If any
modifications are made in a condition the expectation is to denote this altera-
tion with a phase change line and a prime symbol (e.g., B’ for one modifi-
cation and B’’ for an additional modification and so on). Also, if any
subsequent conditions are introduced individual letters are added in alphabe-
tical order to denote a novel independent variable. When two variables are
combined in a single condition, two letters are used to denote this combi-
nation (e.g., BC to represent a combination of intervention B and C). This
contributes to the reader’s understanding of changes that occur during a
single study for each participant (Gast & Spriggs, 2010).
Cooper et al. (2007) highlight the impact of graphic displays by indicating
“an intervention that produces dramatic, replicable changes in behaviour that
last over time are readily seen in a well-designed graphic display” (p. 149).
While a “well-designed graphic display” involves multiple factors, ongoing
analysis of data contributes to a better understanding of effects of interven-
tions for researchers, as well as future readers. As stated above, visual analy-
sis involves evaluation of (a) trend, (b) level, and (c) stability of data. Wolery
and Harris (1982) define (a) trend, as “direction...the data pattern is progres-
sing”, (b) level, as the “relative value of the data pattern on the dependent
variables”, and (c) stability, as similarity “of scores in a given experimental
condition” (pp. 446447). Gast (2005) elaborates on these definitions by
defining (a) trend, as “progress over time”, (b) level, as “magnitude of the
data”, and (c) stability, as “variability or ‘bounce’ of the data” (pp. 1596
1597). Together, these three components provide the foundation for visual
analysis of behaviours within and between conditions.
Within-condition analysis refers to evaluation of data patterns within a
single condition during a study (Gast & Spriggs, 2010; Kennedy, 2005;
Wolery & Harris, 1982). Beginning with baseline, researchers look for stab-
ility of data prior to implementation of an intervention, with data collected
across a minimum of at least three to five sessions prior to introduction of
an intervention (Horner et al., 2005). If variability is observed within a con-
dition, the recommendation is to extend that condition until data are stable.
Downloaded by [Justin Lane] at 07:20 25 July 2013
This also applies to behaviours changing in a therapeutic direction during
baseline. In this instance, researchers also attend to the trend direction of
the data. Participants may improve during a baseline condition due to matu-
ration, response to specific environmental variables, or other factors outside
of the study. Regardless of cause of change in a therapeutic direction, a
researcher would be advised to wait until a clear pattern or stability is
observed (Kennedy, 2005; Wolery & Harris, 1982). One method for evaluat-
ing trend direction is the split-middle method of trend estimation, which is a
multi-step process and, as the name states, estimates trend direction within
each condition based on calculations of median values (Wolery & Harris,
1982). The split-middle method provides researchers with a systematic
process for estimating trend direction, but is less common in the literature
when compared to other evaluation methods (Gast & Spriggs, 2010; White,
1972). Within-condition analysis begins during the first condition of the
study and continues for the duration of the study, which is followed by
between-conditions analysis of data as new conditions are introduced.
Between-conditions analysis of data refers to comparisons across adjacent
conditions during a study (Gast & Spriggs, 2010; Kennedy, 2005; Wolery &
Harris, 1982). A SCED researcher would look for an immediate and abrupt
change in level and trend upon introduction of the independent variable.
With consideration of trend and level, trend is considered more important
for researchers conducting visual analysis of data (Gast & Spriggs, 2010).
The researcher would also attend to variability in the data with consideration
of overlap of data points across conditions. In the “how to” portion of this
paper, specific methods for comparing adjacent conditions are provided. Con-
sider the following example in the context of an A-B design: A participant
enrolled in a study evaluating an intervention to increase percent responsivity
to static presentation of various facial expressions by adults may display low
and stable levels of attention (zero-celerating trend) during baseline and, upon
introduction of the intervention, attending behaviours increase from 7% (final
data point in baseline) to 15% (first intervention session). While there was an
immediate level change in attention, the goal of the study was to increase
attention over time. During subsequent sessions attending behaviours
increase and stabilise at 55% across three consecutive sessions. This
pattern in the data indicates an increasing trend in a therapeutic direction,
as well as increase in level and stability of data. A replication of this effect
across at least three participants within a study would provide the researcher
data to support the likelihood of a functional relation between attending beha-
viours and the intervention for increasing attending behaviours for persons
who display similar pre-treatment behaviours (Gast & Spriggs, 2010;
Kennedy, 2005; Reichow, Volkmar, & Cicchetti, 2008).
With consideration of identifying a functional relation, measures of gener-
ality in SCED studies are evaluated through replication of effect with a single
Downloaded by [Justin Lane] at 07:20 25 July 2013
participant (intra-subject replication) and/or across participants (inter-subject
replication) within a study and across studies (Kennedy, 2005). To assist
researchers who want to replicate a study, detailed descriptions of procedures
and participants’ pre-treatment behaviours as they relate to the study are
crucial (Horner et al., 2005; Lane et al., 2007; Reichow et al., 2008). While
these general rules provide guidelines for researchers using a SCED design,
attention to patterns of data and decisions based on within and between con-
dition analyses should be the driving force behind a well-designed study
(Horner et al., 2005; Odom et al., 2005). The remainder of this paper will
provide details for visually analysing graphed data, followed by a discussion
of strengths and challenges of visual analysis of SCED studies, as well as con-
siderations and recommendations for researchers.
The purpose of this section is to apply basic principles of visual analysis using
the above hypothetical scenario (i.e., intervention to increase percent respon-
sivity to static presentation of various facial expressions by adults). Gast and
Spriggs (2010) provide a detailed description for visual analysis of graphed
data using a SCED, which is the basis for the “how to” section of this
paper. Each step is numbered and designed as an assistive tool for novice
researchers who will visually analyse data when using a SCED. Steps are
based on graphic display (see Figure 1 for hypothetical data for purposes of
exemplifying visual analysis) and divided into (a) within-condition and (b)
between-conditions analysis of data (see Figure 2). Figures 3 9 provide
detailed guidelines for conducting each step of the visual analysis process.
Figure 1. Graphic display using hypothetical data.
Downloaded by [Justin Lane] at 07:20 25 July 2013
Within-condition analysis
Step 1 is assigning a letter to each condition (i.e., A-B-C notation) and Step 2
is counting the number of sessions for each condition.
Step 3 is calculating the mean, median, range, and stability envelope of
data for each condition.
Step 4a is calculating level change within each condition and 4b is calcu-
lating the difference between the first and last value within each condition.
Step 5 is calculating trend using the split-middle method of trend estimation.
Step 6 is calculating percent of data points within the stability envelope for
each condition and Step 7 is using the “freehand method” to evaluate data
Between-condition analysis
Step 1 is determining the number of variables that changed between con-
ditions. It should be noted that the ideal is only one change across conditions.
Step 2 is identifying trend direction across adjacent conditions as accelerat-
ing, decelerating, or zero-celerating in a therapeutic or contra-therapeutic
Figure 2. Steps of visual analysis.
Figure 3. Within-condition analysis: Steps 1 and 2.
Downloaded by [Justin Lane] at 07:20 25 July 2013
direction. Step 3 is comparing the decision from Step 6 of from the
within-condition analysis section to Step 2 of the between-condition analysis
Steps 4ad are evaluating (a) relative, (b) absolute, (c) median, and
(d) mean level change.
Steps 5a b are calculating percent of non-overlapping data (PND) and
percent of overlapping data (POD; Scruggs, Mastropieri, & Casto, 1987).
Summary of sample visual analysis
Within-condition analysis. Evaluation of each condition indicated data
were variable during baseline and intervention (Step 3). Evaluation of level
Figure 4. Within-condition analysis: Step 3.
Downloaded by [Justin Lane] at 07:20 25 July 2013
change within conditions indicated performance was deteriorating during
baseline and improving during intervention (Steps 4ab). Split-middle
method of trend estimation was conducted and indicated there was decreasing
contra-therapeutic trend during baseline and increasing trend in a therapeutic
direction during intervention (Step 5), but data were considered variable fol-
lowing application of a stability envelope to trend lines (Step 6).
Between-condition analysis. Evaluation of behaviour change across con-
ditions indicated only one variable was introduced across both conditions
(Step 1). With consideration of within-condition analysis of trend, a change
in performance across conditions went from a decelerating, deteriorating
trend to an accelerating, improving trend (Steps 2 and 3). All level change
measures indicated a positive (improving) change across conditions (Steps
4a d). The limitations of calculating change in level across adjacent con-
ditions should be considered. First, relative level change provides information
regarding proportional change from the last half of baseline to the first half of
the intervention condition using median values, but does not provide infor-
mation regarding immediacy of change. Second, absolute level change only
provides information regarding the immediacy of change from the last
session of baseline to the first session during intervention without consider-
ation of other data points. Third, mean level change may be influenced by out-
liers within either condition and thus would skew the mean value for the
Figure 5. Within-condition analysis: Steps 4a-b.
Downloaded by [Justin Lane] at 07:20 25 July 2013
corresponding condition. Finally, due to the limitations of calculating the
mean value for each condition, calculating the median level change is rec-
ommended since median values are less likely to be influenced by outliers
in the data. Based on this information, it is the recommendation of the
Figure 6. Within-condition analysis: Step 5.
Downloaded by [Justin Lane] at 07:20 25 July 2013
authors that none of these methods be used in isolation since there are poten-
tial limitations across all. Finally, calculations of PND and POD indicated
there were 100% non-overlap and 0% overlap of behaviours observed
during baseline and intervention (Step 5). If the results were replicated
across participants, behaviours, or settings, investigators could report obser-
vation of a functional relation (Gast & Spriggs, 2010; Kennedy, 2005;
Reichow et al., 2008).
Considerations of visual analysis of SCED studies
Visual analysis of graphic displays of data collected during SCED studies is a
tradition in fields interested in ongoing evaluation of behaviour-change pro-
grammes for individuals or groups of individuals (Wolery & Harris, 1982).
This individualised approach to evaluation of behaviours allows opportunity
to systematically adapt or modify a programme based on characteristics
observed during sessions (Gast, 2005). As with any approach to evaluation
of data, limitations and recommendations which maximise understanding of
results must be addressed. First, researchers using a SCED should evaluate
data using multiple methods to better understand and improve confidence
in findings (Gast, 2005). For example, PND provides a metric for measuring
Figure 7. Within-condition analysis: Steps 6 and 7.
Downloaded by [Justin Lane] at 07:20 25 July 2013
improvement in target behaviours when compared to performance during
baseline condition. The general idea of PND is higher percentages constitute
a larger magnitude of change in a therapeutic direction, but PND is not
without limitations. A participant may display change in a therapeutic direc-
tion during baseline, and upon introduction of an intervention this change
continues. Using PND as the only metric would incorrectly identify a
change in a therapeutic direction when in reality improvement across con-
ditions was not influenced by the introduction of an intervention (Gast &
Spriggs, 2010). For this reason, researchers should use multiple measures
of evaluation, recognising the limitations of single approaches for interpret-
ation. Second, each step listed in the “how to” section is not necessary for
Figure 8. Between-condition analysis: Steps 1 4b.
Downloaded by [Justin Lane] at 07:20 25 July 2013
every study. For example, the split-middle method of trend estimation is typi-
cally conducted at the end of a study and is less common in the literature. In
regard to trend estimation, the split-method is recommended over another
trend method, such as ordinary-least squares regression due to issues
related to auto-correlation of data and outliers. Ordinary-least squares
regression is based on the assumption that data are independent and may
also be influenced by outliers. In contrast, the split-middle method of trend
Figure 9. Between-condition analysis: Steps 4c 5b.
Downloaded by [Justin Lane] at 07:20 25 July 2013
estimation does not require independence of data and relies on median values,
which are less sensitive to outliers than mean values (Good & Shinn, 1990).
Measures included in the visual analysis process should be included for pur-
poses of strengthening an unbiased interpretation of effects of an intervention
(Gast & Spriggs, 2010).
A third consideration when using visual analysis with SCED data is the
understanding all possible threats to the internal validity of a study. Internal
validity refers to control and recognition of confounds during a study that
could possibly provide an “alternative explanation of findings” (Gast, 2010,
p. 4). Some of these threats have been addressed or will be addressed in
more detail, but are listed here for readers consideration: (a) history, (b) matu-
ration, (c) testing, (d) instrumentation (or reliability of measurement of the
dependent variable), (e) fidelity of implementation, (f) attrition, (g) multi-
treatment interference, (h) variability or instability in data, (i) adaptation,
and (j) the Hawthorne effect (Cooper et al., 2007; Gast, 2010; Kennedy,
2005). Finally, researchers should recognise and adhere to quality indicators
when conducting SCED studies. Horner et al. (2005) and Kratochwill et al.
(2010) provide guidelines for researchers conducting SCED studies. It is rec-
ommended that guidelines by Horner et al. (2005) and Kratochwill et al.
(2010) be reviewed prior to conducting a SCED study. Some of the key
issues to consider are as follows: (a) report fidelity of implementation and
reliability of measurement of the dependent variable, (b) with the goal of at
least 80% agreement or higher. In addition, (c) collect a minimum of three
to five data points for each condition, and (d) demonstrate at least three repli-
cations of effect before reporting a functional relation.
Reliability of findings and fidelity of implementation
Confidence in results is mediated by reliability of measurement of the depen-
dent variable and fidelity of implementation of procedures during pre-inter-
vention and intervention conditions, as well as any subsequent or
intermediate conditions (e.g., maintenance, generalisation probe) that may
occur during the study (Kennedy, 2005; Wolery, 2011). While there is not
a rule regarding number or percent of sessions during which reliability and
fidelity data should be collected, the general expectation and recommendation
is at least 20% of conditions for each participant by at least one independent
observer (i.e., person who is not implementing the intervention; Kazdin,
2011; Kennedy, 2005). The general idea regarding collection of reliability
and fidelity data is “more is better”. Baer, Wolf, and Risley (1968) emphasise
the importance of detailed behavioural definitions and technological descrip-
tions of behaviour-change programmes. In their seminal work on applied be-
haviour analysis (ABA), Baer et al. (1968) indicate well-written procedures
are written as such a “[novice] reader could replicate. . .procedure[s] well
Downloaded by [Justin Lane] at 07:20 25 July 2013
enough to produce the same results” (p. 95). They continue, “explicit
measurement of the reliability of human observers...becomes not merely
good technique, but a prime criterion of whether the study was appropriately
behavioural” (p. 93).
Lack of agreement regarding measurement of the dependent variable
negates the results of visual analysis since disagreements exist about occur-
rence and/or non-occurrence of the target behaviour (Gast, 2005). For
example, a researcher interested in decreasing perseverative speech of an ado-
lescent with traumatic brain injury implements an intervention across
environments (i.e., home, school, vocational training site), replicating
effects of decreasing the target behaviour to a rate of 1 occurrence per two-
hour observation for the final five intervention sessions. Another researcher
collects data 20% of sessions across the study across environments and
agrees with primary researchers’ observations of the target behaviour on
the average of 12% (e.g., both observers agreed that the behaviour occurred
or did not occur only 12/100 times). This lack of agreement reduces the like-
lihood of replication since it is unclear what, if any, behaviour changed during
the study. This uncertainty lessens trust that a proposed intervention is an
appropriate choice for persons with similar pre-intervention behaviours.
Human error is expected during observation, and while exact agreement is
ideal, it is not a “rule” that observers agree 100% across all observations. It
should be stressed that researchers strive for agreement between 80 and
100%. While an arbitrary figure, agreement below 80% is considered a
“red flag” when interpreting results of a study (Kennedy, 2005). Multiple
factors may be responsible for low-levels of agreement and require consider-
ation during design and implementation of a study. Prior to beginning a study,
(a) detailed descriptions of target behaviours should be provided to all persons
who will collect data and (b) training should occur until agreement is con-
sidered acceptable for purposes of the study. Complexity of behavioural
descriptions may require researchers to further examine the purpose of the
study and potentially create multiple target behaviours or remove unnecessary
components of a behaviour-change programme. If, at any point during the
study, there is low-level agreement between observers the study should
cease until issues are identified and addressed (Ayres & Gast, 2010). Tra-
ditionally, agreement is reported as a percentage (and range) across a study
by participants or across all participants (Artman, Wolery, & Yoder, 2012).
In an effort to address limitations of reporting agreement data as a summative
measure, some researchers advocate for graphing these data as a means for
visually analysing agreement (or disagreement) between independent obser-
vers (Ledford & Wolery [in press]; Ledford, Wolery, Meeker, & Wehby,
Fidelity of implementation of procedures across conditions is another key
factor to consider when interpreting results of a study. In a commentary on the
Downloaded by [Justin Lane] at 07:20 25 July 2013
importance of fidelity of measurement, Wolery (2011) describes the “essence
of experimental work” as confidence that a behaviour-change programme was
responsible for prosocial “shifts” in socially valued behaviours for purposes
of improving experiences of participants’ across their lifespan (p. 156).
Adherence to specific procedural descriptions, in conjunction with data to
support appropriate implementation of procedures, gives credence to
interpretations of data using visual analysis and allows readers an opportunity
to replicate these effects with participants with similar pre-treatment beha-
viours. It is the responsibility of researchers to report fidelity of implemen-
tation of each step of a behaviour-change programme by condition (Gast,
2010). This is especially important for researchers and practitioners attempt-
ing to replicate effects of an intervention. For example, a researcher attempts
to replicate an intervention designed to improve recall for persons with
dementia. In their report they indicate inability to replicate the magnitude
of effect of a previous study, but only report percent and range of correct
implementation collapsed across all steps. In this example, it is unknown if
a step or multiple steps were excluded, thus impacting the magnitude of the
behaviour-change programme. Even if the purpose of a study is evaluation
of necessity of steps (i.e., addition or omission of steps) in a behaviour-
change programme, researchers are urged to report adherence to procedures
as written across each proposed component of an intervention. As with
reliability of measurement of the dependent variable, detailed descriptions
of procedures should be provided to all persons who will implement a
study and collect data (Wolery, 1994). Specific criteria (e.g., 100% correct
implementation of procedures across three consecutive opportunities)
should be used as a guideline for mastery of procedures before beginning a
study, and evaluated during a study (Ayres & Gast, 2010).
Statistics and SCED
Application of statistical methods to SCED data has received increased atten-
tion in the literature, especially as it relates to calculation of an effect size for
interventions (Wolery, Busick, Reichow, & Barton, 2008). Campbell and
Herzinger (2010) propose considerations regarding statistical analysis and
SCED studies in that statistical tests may (a) add to the confidence of
results of visual analysis of data, (b) “quantify strengths of outcomes”, and
(c) increase objectivity of analysis (pp. 421 422). The first author conducted
an informal search of on-line databases (i.e., ERIC, PsycInfo, Education
Research Complete, and Medline) for articles on visual analysis (i.e., key-
words were visual analysis, special education, psychology, education,
single subject research, single subject research design, single case, single
case experimental design, single subject, single subject experimental
design, in peer reviewed journals) and found 42 articles related to visual
Downloaded by [Justin Lane] at 07:20 25 July 2013
analysis and SCED. Of the 42 articles, 22 related to application of statistical
methods to data from SCED studies with emphasis on calculations of effect
size. The purpose of this informal search was to highlight the relatively
large number of articles on various methods for calculating effect size, as
well as to highlight that an optimal method for calculating effect size is not
currently available, which corresponds with Campbell and Herzinger
(2010) report that “little consensus exists regarding the appropriate calcu-
lation of effect sizes for single case designs” (p. 440). Campbell (2004) high-
lights the issues of application of statistical methods to SCED, specifically,
observations are “usually not independent” (i.e., auto-correlated) and trend
of data may “confound” results of effect size calculations (p. 235). Analysis
of SCED data using statistical methods is a controversial topic that currently
lacks a clear answer for researchers, but efforts are ongoing to identify appro-
priate procedures that summarise effects of multiple articles (Campbell, 2004;
Wolery et al., 2008).
As highlighted by Cooper et al. (2007), visual analysis of SCED data answers
two questions: “(1) Did behaviour change in a meaningful way, and (2) if so,
to what extent can that change in behaviour be attributed to the independent
variable” (p. 149). Baer et al. (1968) emphasise the importance and meaning
of “applied” research when designing behaviour-change programmes in that
an intervention should attempt to change behaviours which benefit individual
participants. The primary goal of visual analysis is to identify if a functional
relation exists between the introduction of an intervention and change in a
socially desirable behaviour, as well as replicate effects across multiple par-
ticipants. Visual analysis is sensitive to changes in behaviour and allows
researchers to analyse each participant’s behaviour through repeated
measurement and evaluation, allowing observation of abrupt, as well as
subtle changes over time. Challenges of visual analysis should also be con-
sidered when conducting a study. First, as seen through multiple attempts
to apply statistical methods to SCED data, it can be difficult to summarise
the effects of interventions across participants since various behaviours are
measured, and individual modifications to an intervention may be made
during a study. A second consideration is generality of findings to participants
outside of studies. The issue of generality relies on researchers providing
detailed descriptions of participant’s pre-intervention behaviours to increase
the likelihood of understanding for whom and under what conditions inter-
ventions may be effective. Third, researchers should evaluate agreement for
results of visual analysis conducted by independent observers. Previous
studies have found agreement can vary across persons for various reasons
(Ottenbacher, 1993), but adherence to detailed procedures, as presented in
Downloaded by [Justin Lane] at 07:20 25 July 2013
this article, and familiarity of methods for increasing agreement (e.g., train-
ing) address possible variability that may arise during visual analysis of iden-
tical graphs across persons (Ledford et al., 2012). Finally, researchers using a
comparison design (e.g., alternating treatments design) should be aware of
specific considerations for conducting visual analysis of graphs. For more
detail on comparison designs and visual analysis review Wolery, Gast, and
Hammond (2010).
The purpose of this paper is to introduce readers to visual analysis of
graphic displays of data collected during SCED studies. Visual analysis
involves evaluation of performance within and across conditions using sys-
tematic procedures. Training using the above procedures should occur with
multiple graphical displays prior to conducting visual analysis of data for pub-
lication. Agreement data should also be collected across persons training to
use visual analysis. The guidelines and considerations presented should
assist researchers in objectively evaluating behaviour-change programmes
for individual participants or groups of participants across settings, beha-
viours, and participants. Confidence in findings is furthered by replication
of effect using detailed procedures and understanding of results in regard to
agreement of occurrence and non-occurrence of behaviours, as well as under-
standing implementation of procedures as designed. Visual analysis of data
within a SCED framework offers researchers alternatives to understanding
effect of behaviour-change programmes outside of special education and
related fields.
Artman, K., Wolery, M., & Yoder, P. (2012). Embracing our visual inspection and analysis tra-
dition: Graphing interobserver agreement data. Remedial and Special Education, 33, 71–77.
Ayres, K., & Gast, D. L. (2010). Dependent measures and measurement procedures. In D. L.
Gast (Ed.), Single subject research methodology in behavioral sciences (pp. 129–165).
New York, NY: Routledge.
Baer, D. M., Wolf, M. M., & Risley, T. R. (1968). Some current dimensions of applied behavior
analysis. Journal of Applied Behavior Analysis, 1, 91–97.
Campbell, J. M. (2004). Statistical comparison of four effect sizes for single-subject designs.
Behavior Modification, 28, 234–246.
Campbell, J. M., & Herzinger, C. V. (2010). Statistics and single subject research methodology.
In D. L. Gast (Ed.), Single subject research methodology in behavioral sciences
(pp. 91–109). New York, NY: Routledge.
Cooper, J. O., Heron, T. E., & Heward, W. L. (2007). Applied behavior analysis (2nd ed.).
Columbus, OH: Pearson.
Gast, D. L. (2005). Visual analysis of graphic data. In G. Sugai & R. Horner (Eds.), Encyclo-
pedia of behavior modification and cognitive behavior therapy: Educational applications
(Vol. 3, pp. 1595–1599). Thousand Oaks, CA: Sage.
Gast, D. L. (Ed.). (2010). General factors in measurement and evaluation. Single subject
research methodology in behavioral sciences (pp. 91–109). New York, NY: Routledge.
Downloaded by [Justin Lane] at 07:20 25 July 2013
Gast, D. L., & Hammond, D. (2010). Withdrawal and reversal designs. In D. L. Gast (Ed.),
Single subject research methodology in behavioral sciences (pp. 234–275). New York,
NY: Routledge.
Gast, D. L., & Spriggs, A. D. (2010). Visual analysis of graphic data. In D. L. Gast (Ed.), Single
subject research methodology in behavioral sciences (pp. 199–233). New York, NY:
Good, R. H., & Shinn, M. R. (1990). Forecasting accuracy of slope estimates for reading curri-
culum-based measurement: Empirical evidence. Behavioral Assessment, 12, 179–193.
Horner, R. H., Carr, E. G., Halle, J., McGee, G., Odom, S., & Wolery, M. (2005). The use of
single-subject research to identify evidence-based practice in special education. Exceptional
Children, 71, 165–179.
Kazdin, A. E. (2011). Single-case research designs: Methods for clinical and applied settings
(2nd ed.). New York, NY: Oxford University Press.
Kennedy, C. H. (2005). Single-case designs for educational research. Boston, MA: Allyn &
Kratochwill, T. R., Hitchcock, J., Horner, R. H., Levin, J. R., Odom, S. L., Rindskopf, D. M., &
Shadish, W. R. (2010). Single-case designs. Technical documentation. Retrieved from What
Works Clearinghouse website:
Lane, K., Wolery, M., Reichow, B., & Rogers, L. (2007). Describing baseline conditions: Sug-
gestions for study reports. Journal of Behavioral Education, 16, 224–234.
Ledford, J. R., & Wolery, M. (in press). Effects of plotting a second observer’s data on A-B-A-B
graphs when observer disagreement is present. Journal of Behavioral Education.
Ledford, J. R., Wolery, M., Meeker, K. A., & Wehby, J. H. (2012). The effects of graphing a
second observer’s data on judgments of functional relations in A-B-A-B graphs. Journal
of Behavioral Education, 21, 350–364.
Lieberman, R. G., Yoder, P. J., Reichow, B., & Wolery, M. (2010). Visual analysis of multiple
baseline across participants’ graphs when change is delayed. School Psychology Quarterly,
25, 28–44.
Odom, S. L., Brantlinger, E., Gersten, R., Horner, R. H., Thompson, B., & Harris, K. R. (2005).
Research in special education: Scientific methods and evidence-based practices. Exceptional
Children, 71, 137–148.
Ottenbacher, K. J. (1993). Interrater agreement of visual analysis in single-subject decisions:
Quantitative review and analysis. American Journal of Mental Retardation, 98, 135–142.
Reichow, B., Volkmar, F. R., & Cicchetti, D. V. (2008). Development of the evaluative method
for evaluating and determining evidence-based practices in autism. Journal of Autism and
Developmental Disorders, 38, 1311–1319.
Scruggs, T. E., Mastropieri, M. A., & Casto, G. (1987). The quantitative synthesis of single-
subject research: Methodology and validation. Remedial and Special Education, 8, 24–33.
Spriggs, A. D., & Gast, D. L. (2010). Visual representation of data. In D. L. Gast (Ed.), Single
subject research methodology in behavioral sciences (pp. 166–198). New York, NY:
White, O. R. (1972). The split-middle: A quickie method of trend analysis. Eugene, OR:
Regional Center for Handicapped Children.
Wolery, M. (1994). Procedural fidelity: A reminder of its functions. Journal of Behavioral Edu-
cation, 4, 381–386.
Wolery, M. (2011). Intervention research: The importance of fidelity measurement. Topics in
Early Childhood Special Education
, 31, 155–157.
Wolery, M., Busick, M., Reichow, B., & Barton, E. E. (2008). Comparison of overlap methods
for quantitatively synthesizing single-subject data. Journal of Special Education, 44, 18–28.
Downloaded by [Justin Lane] at 07:20 25 July 2013
Wolery, M., Gast, D. L., & Hammond, D. (2010). Comparative intervention designs. In D. L.
Gast (Ed.), Single subject research methodology in behavioral sciences (pp. 329–381).
New York, NY: Routledge.
Wolery, M., & Harris, S. R. (1982). Interpreting results of single-subject research designs. Phys-
ical Therapy, 62, 445–452.
Manuscript received May 2013
Revised manuscript received June 2013
First published online July 2013
Downloaded by [Justin Lane] at 07:20 25 July 2013
    • "Visual aids for systematic assessment (Kratochwill et al., 2010; Lane & Gast, 2014) Establish effectiveness Formal decision rules If you want to have an overall quantification of the effect that summarizes withinsubject or across subjects replications Figure 2shows a replication of Winkens et al. (2014) Randomization test: choose intervention start point at random for an AB design Possibility to use a meaningful effect size as a test statistic random when to change conditions Sil et al. (2013) Randomization test: restricted randomization for alternating treatments design If you want to obtain statistical significance + you cannot choose at random when to change conditions Tunnard & Wilson (2014) used Tau quantifying the difference between pairs of conditions and for its p value Multilevel models: modeling different data aspects Tau: controlling for trend Simulation modeling analysis: taking autocorrelation into account p values for effects and variances p values for nonoverlap p value for pointbiserial correlation If you want to carry out a statistically sound metaanalysis (incl. weighted average, confidence intervals, heterogeneity tests) Graves, Roberts, Rapoff, & Boyer (2010) use Cohen's d and its standard error for confidence intervals and its inverse variance for weighting Multilevel models: consider nested structure of the data (measurements within participants within studies) HPS d-statistic: for designs as multiplebaseline or (AB) k PHS d-statistic: after multilevel analysis "
    [Show abstract] [Hide abstract] ABSTRACT: The current paper responds to the need to provide guidance to applied single-case researchers regarding the possibilities of data analysis. The amount of available single-case data analytical techniques has been growing during recent years and a general overview, comparing the possibilities of these techniques, is missing. Such an overview is provided here referring to techniques that yield results in terms of a raw or standardized difference, procedures related to regression analysis, as well as nonoverlap and percentage change indices. The comparison is provided in terms of the type of quantification provided, the data features taken into account, the conditions in which the techniques are appropriate, the possibilities for meta-analysis, and the evidence available on their performance. Moreover, we provide a set of recommendations for choosing appropriate analysis techniques, pointing at specific situations (aims, types of data, researchers’ resources) and the data analytical techniques that are most appropriate in these situations. The recommendations are contextualized using a variety of published single-case datasets in order to illustrate a range of realistic situations that researchers have faced and may face in their investigations.
    Full-text · Article · May 2016 · Behavior Research Methods
    • "It has been the traditionally preferred and most frequently used approach (Busk & Marascuilo, 1992), but has significant limitations (for discussion, see Lane & Gast, 2014; Smith, 2012 ). Authorities have proposed guidelines for systematizing visual analysis (e.g., Lane & Gast, 2014 ), but there is not yet complete agreement about decisionmaking criteria to guide the process. Statistical analyses have advantages in that they (a) use an explicit set of operational rules and replicable methods, (b) provide a direct test of the null hypothesis, (c) utilize precisely defined criteria for significance, (d) are useful when there is instability in the baseline or treatment effects are not well understood, and (e) can help to control for extraneous factors (e.g., Kazdin, 1982aKazdin, , 1982b). "
    [Show abstract] [Hide abstract] ABSTRACT: Single-case experimental design (SCED) studies in the behavioral sciences literature are not only common, but their proportion has also increased over past decades. Moreover, methodological complexity of SCEDs and sophistication in the techniques used to analyze SCED data has increased apace. Yet recent reviews of the behavioral sciences literature have shown that reporting of SCED research is highly variable and often incomplete. Explicit, precise and transparent reporting is crucial not only for critical evaluation of the study methodology and conclusions, but also to facilitate exact replication of investigations, and ascertain applicability and possible generality of results. Accordingly, we developed the SCRIBE 2016 (Single-Case Reporting guideline In BEhavioural interventions) by a consensus process by experts in SCED methodology and research in the behavioral sciences, as well as experts in reporting guideline development. The SCRIBE 2016 Explanation and Elaboration article describes a set of 26 items to guide and structure the reporting of SCED research. A rationale and minimum reporting standards that stipulate what needs to be reported are provided for each item. In addition, examples of adequate and clear reporting drawn from the literature are included for each item. It is recommended that the SCRIBE 2016 Explanation and Elaboration article is used in conjunction with the complementary SCRIBE 2016 Statement (Tate et al., 2016) by authors preparing manuscripts for publication and journal reviewers and editors considering manuscripts for publication.
    Full-text · Article · Apr 2016
    • "In the hypothetical research examples, we will use the unstandardized and standardized mean difference as ES measures for the alternation designs and we will use the immediate treatment effect index (which is also a mean difference type test statistic) for the phase designs. However, we should point out that there is currently little consensus in the SCE community regarding which type of ESs are optimal for use with single-case data (e.g., Campbell & Herzinger, 2010; Lane & Gast, 2014). Ideally, different types of effects require different types of ESs which are optimally capable of capturing a specific type of effect. "
    [Show abstract] [Hide abstract] ABSTRACT: In the current paper, we present a method to construct nonparametric confidence intervals (CIs) for single-case effect size measures in the context of various single-case designs. We use the relationship between a two-sided statistical hypothesis test at significance level α and a 100 (1 - α) % two-sided CI to construct CIs for any effect size measure θ that contain all point null hypothesis θ values that cannot be rejected by the hypothesis test at significance level α. This method of hypothesis test inversion (HTI) can be employed using a randomization test as the statistical hypothesis test in order to construct a nonparametric CI for θ. We will refer to this procedure as randomization test inversion (RTI). We illustrate RTI in a situation in which θ is the unstandardized and the standardized difference in means between two treatments in a completely randomized single-case design. Additionally, we demonstrate how RTI can be extended to other types of single-case designs. Finally, we discuss a few challenges for RTI as well as possibilities when using the method with other effect size measures, such as rank-based nonoverlap indices. Supplementary to this paper, we provide easy-to-use R code, which allows the user to construct nonparametric CIs according to the proposed method.
    Full-text · Article · Feb 2016
Show more