Copyright 2008 by the American Psychological Association
2008, Vol. 53, No. 3, 357–369
Advanced Regression Methods for Single-Case Designs: Studying
Propranolol in the Treatment for Agitation Associated With Traumatic
Daniel F. Brossart
Texas A&M University
Wayne State University
Richard I. Parker, James McNamara, and Timothy R. Elliott
Texas A&M University
The use of single-case designs in intervention research is discussed. Regression methods for
analyzing data from these designs are considered, and an innovative use of logistic regression to analyze
data from a double-blind, randomized clinical trial of propranolol for agitation among persons with
traumatic brain injury (TBI) is used. Method:
Double-blind, randomized clinical trial performed in an
outpatient rehabilitation setting. Participants:
Nine men and 4 women with TBI. Results:
models indicated that propranolol was not associated with less agitation for most participants (⌽ ⫽ .135;
90% exact confidence interval was ⫺.03 ⬍ .135 ⬍ .29). Four participants displayed a significant
response to propanolol. Two participants demonstrated significant improvement, and the other 2 expe-
rienced significantly more agitation in the treatment phase. Summary:
Advanced regression methods can
be used to analyze data from single-case designs to obtain information of clinical and statistical
significance from a variety of psychological and medical treatments.
single-case design, logistic regression, propranolol, brain injury, agitation
In a thoughtful commentary, Aeschleman (1991) observed a
informs otherwise: Many of the influential research programs in
decreasing interest in single-case research (SCR) designs in the
rehabilitation psychology first appeared in the literature in single-
rehabilitation psychology literature: Between 1985 and 1989, Ae-
case designs. Behavioral approaches— championed in the classic
schleman found only 6 out of 402 empirical papers published in
Behavioral Methods in Chronic Pain and Illness
, Archives of Physical Medicine and
1976)—were based on earlier single-case studies. The potential of
, and Rehabilitation Counseling Bulletin
used a sin-
supported employment— arguably one of the few evidence-based
gle-subject design (⬍1.5% of the total; Aeschleman, 1991, p. 43).
practices in rehabilitation psychology with considerable support
A brief examination of the past 15 years of Rehabilitation Psy-
from many randomized clinical trials (RCTs; Dunn & Elliott, in
reveals one article that offered an innovative way to
press)— appeared in a study using a single-case case design
analyze single-case data (Callahan & Barisa, 2005) and another
published in the Journal of Applied Behavior Analysis
that was a true single-case study (Pijnenborg, Withaar, Evans, van
al., 1989). And the ground-breaking extensions of Neal Miller's
den Bosch, & Brouwer, 2007).
operant learning models to visceral, reflex, and motor responses
We disagree with Aeschleman's bleak conclusion that SCR
were achieved in single-case designs (Brucker & Ince, 1977; Ince,
designs ". . have not made a methodological impact on research
Brucker, & Alba, 1978). Clearly, SCR designs have played a
in rehabilitation psychology" (Aeschleman, 1991, p. 47). History
pivotal role in the rehabilitation psychology research base.
Unfortunately, SCR and case studies are often misconstrued as
one in the same. An uncontrolled case study is a study of a singleclient, dyad, or group in which observations are made under
Daniel F. Brossart, Richard I. Parker, James McNamara, and Timothy R.
Elliott, Department of Educational Psychology, Texas A&M University;
uncontrolled and unsystematic conditions. The lack of experimen-
Jay M. Meythaler, Department of Physical Medicine and Rehabilitation,
tal control in such a study may have contributed to an overall
Wayne State University and Rehabilitation Institute of Michigan, Detroit,
suspicion or distrust of results based on a single subject in general.
Designs that add more experimental control include systematic,
This study was funded in part by National Institute of Disability Re-
repeated observations of a single client, dyad, or group and are
search and Rehabilitation Grant H 133G000072 awarded to Jay M.
often called intensive single-case designs
. For even more experi-
Meythaler. Appreciation is expressed to Michael E. Dunn for sharing
mental rigor, one could use a single-case experimental design,
information and opinions about the history of single-case designs in reha-
which is typically viewed as having greater control than intensive
bilitation psychology research. Graphs of participant data not presented in
single-case designs. These designs usually have behavioral goals or
this article are available upon request from Daniel F. Brossart.
target behaviors that are the main focus of interest and function as the
Correspondence concerning this study should be addressed to Daniel F.
Brossart, Department of Educational Psychology, 4225 TAMU, College
dependent variable. They also have repeated measurements over time
Station, TX, 77845. E-mail: email@example.com
and at least two treatment phases (baseline and treatment). Some have
BROSSART, MEYTHALER, PARKER, MCNAMARA, AND ELLIOTT
stated that the core essence of single-case research is that "all
(if not impossible) to attain due to the lack of services that negate
dependent measures are collected repeatedly over the course of the
a "usual treatment" scenario for a controlled, comparison group
experiment, and these data are not combined with those from other
(such that any attention to control participants would be above and
participants to produce group averages for purposes of data anal-
beyond the typical experience or "treatment-as-usual"; Elliott,
ysis" (Morgan & Morgan, 2001, p. 122). Nevertheless, there are
also instances in which evaluating single-case data across partic-
The use of single-case designs also helps address the overuse of
ipants is helpful because it can increase the internal validity of the
cross-sectional methods so common in rehabilitation psychology.
Just as many introductory research design texts talk about the
In this article, we begin by briefly discussing some present
monomethod bias for a single research study, overuse of a single
issues, past practice, and some misunderstandings regarding sin-
design within a field creates a lopsided literature base that lacks the
gle-case research. We then show how the application of single-
advantages of triangulation with multiple research methodologies.
case research can be helpful in answering substantive questions.
Researchers across the health care fields have called for an ex-
To illustrate this, we use data collected from a double-blind,
panded evidence base, reflected in a broadened focus and a plu-
crossover RCT to examine the effectiveness of drug therapy in
rality of methodologies to answer questions regarding informed
reducing agitation in individuals with a traumatic brain injury
practice (Concato, Shah, & Horwitz, 2000; Spring et al., 2005).
(TBI). Furthermore, we introduce a new methodology for analyz-
Single-case designs seem a ready way to add methodological
ing single-case data and compare it with a more traditional regres-
diversity to the literature base.
SCR Compared With Traditional Cross-Sectional
Why Consider SCR Now?
Although others have urged for an increased use of single-case
The more commonly applied cross-sectional research designs
research, such calls for the use of single-case research appear to
are, in general, nomothetic approaches: They "aim to establish
have had little effect in changing the behavior of researchers
lawful relations that apply across individuals" (Nesselroade, 1991,
(Blampied, 2000; Goldfried & Wolfe, 1996; Hilliard, 1993; Mor-
p. 96). Thus, two key characteristics of cross-sectional designs are
gan & Morgan, 2001). SCR continues to be an underused research
"static observations and multiple behavioral categories" (Baltes &
Nesselroade, 1979, pp. 11–12). In contrast, SCR designs may be
Several forces, however, do appear to be making an impact. One
seen as a hybrid form of the longitudinal approach. Longitudinal
is the present-day focus on effect sizes. Many journals now require
designs have the ability to identify not only the processes and
investigators to report effect size with contextual information for
causes of intraindividual change but also the processes and causes
their interpretation (Fidler, 2002). A similar trend toward account-
of interindividual patterns of intraindividual change in behavioral
ability, objectively measured outcomes, and greater scientific rigor
development. Although single-case designs may be used to explore
can be seen in policy statements by influential groups such as the
patterns and processes, they typically focus on evaluating the
National Research Council (Shavelson & Towne, 2002). The med-
impact of a treatment on a client, student, or patient. Because
ical profession's accountability reform has also played a part in the
attention is given to collecting data before treatment begins, after
movement for the broader use of effect sizes (Oakley, 2002).
treatment starts, and sometimes even after treatment ends, each
Funding agencies, public and private, are increasingly requiring
research participant may serve as their own control. Thus, SCR can
empirical results and effect sizes. In addition, the call for greater
be viewed as an alternative methodology for answering many of
accountability and objective, defensible results (Shavelson &
the same research questions as cross-sectional group research and
Towne, 2002) in psychological and educational research has been
as a methodology that is uniquely capable of answering different
an important factor leading to greater scrutiny of how SCR is
and new research questions.
When Should One Use SCR Designs?
Recognizing the Limitations of RCTs
SCR should be considered as a top candidate research design
There appears to be an increasing recognition that RCTs are
to use in several circumstances. It is ideally suited for studying
ideal for answering some research questions but that the design
low-incidence problems and conditions. Many behavioral issues
itself is not able to answer all important questions and that its
that accompany conditions such as TBI and spinal cord injury
implementation has certain limitations. This has led some to con-
(SCI) are difficult to study in designs that rely on large, repre-
tinue to call for both efficacy and effectiveness studies (Tucker &
sentative samples for randomization and treatment. For exam-
Roth, 2006). Important questions about how any given single RCT
ple, SCR has been used to study treatments to promote wheel-
is conducted and the validity of the results gained have prompted
chair pushups among men with SCIs (White, Mathews, &
guidelines for registering RCTs for public scrutiny (Elliott, 2007).
Fawcett, 1989) and other attempts to prevent pressure sores
The intention is that this requirement will address deficiencies in
(Malament, Dunn, & Davis, 1975). These are significant clini-
the quality control of RCTs. However, the validity of RCTs are
cal issues that often challenge and confound clinicians; how-
often compromised in many applications relevant to rehabilitation
ever, they are not manifested in a sufficient number of individ-
psychology by a low number of available participants (with low-
uals required to attract the necessary attention and financial
incidence disabilities) and because true control groups are difficult
support for a large-scale (or multisite) RCT.
SPECIAL ISSUE: SINGLE-CASE RESEARCH
For low-incidence problems, SCR designs are probably one of
Our own experience highlights the importance of using both
the few designs that researchers could use to expand the knowl-
visual and statistical analysis. For example, in previous studies,
edge base productively in a time-efficient manner. Cross-sectional
we noticed large differences between visual analysis and the
designs can take a considerable amount of time to obtain a sample
output from ITSACORR (Crosbie, 1993, 1995). Further inves-
of sufficient size for data analysis. SCR designs are also indicated
tigation showed that ITSACORR was unrelated to other statis-
for studies in which few participants are able to meet the inclusion
tical techniques as well as to visual analysis of single-case data
criteria for a study. In addition, SCR would be beneficial in any
(Brossart & Parker, 2001; Parker & Brossart, 2003), which
study in which participants are required to participate over an
raised serious concerns about its viability as a useful technique.
extended period of time. Such studies often experience a fair
Additional empirical studies have also highlighted its weak-
amount of attrition. If an SCR design was used, for the data that
nesses (Huitema, 2004). It is time for single-case researchers to
was complete, although possibly much smaller than the number of
abandon the sole use of visual analysis; the dogged refusal to
participants the study began with, this would still allow important
incorporate statistical analysis of single-case data will simply
research questions to be answered. Because each participant serves
result in various fields or lines of research being ignored as
as their own control, the existing data would still allow one to
irrelevant, archaic, and unsophisticated.
make important inferences (this is not to diminish the import of
Some of the underuse of statistical methods has been due to the
considerations one must make when interpreting results with high
cautiousness of researchers in applying univariate parametric anal-
levels of attrition). Multiple scenarios are presented in Appendix A
yses because of well-placed concerns that the data fail to meet
as examples of when SCR should be considered.
assumptions of homogeneity of variance, normality, and serialindependence. In fact, these assumptions are commonly violated
Problems With Data Analyses
by short, interrupted data series. Even greater concerns have beenvoiced about the use of more complex parametric analyses, such as
In spite of the fact that SCR has played an important historical role
repeated measures analysis of variance (ANOVA), as it makes
in psychology and that there have been a number of replicable
even stronger assumptions of the data (sphericity; Stevens, 2007).
empirical findings in differing domains, Morgan and Morgan (2001)
Because of these stringent assumptions, multivariate analysis of
stated that SCR "remains relatively obscure because of its disavowal
variance (MANOVA) has sometimes been used to replace re-
of the statistical machinery that defines psychological research in the
peated measures ANOVA (RM-ANOVA). However, MANOVA
21st century" (p. 120). Furthermore, those involved in SCR have
still has strict assumptions (homogeneity of variance-covariance
historically relied on visual analysis (Busk & Marascuilo, 1992;
matrices, absence of multicollinearity and singularity) and does not
Kratochwill & Brody, 1978), which Kazdin (1982) defined as the
provide output as useful as RM-ANOVA's partial effect sizes.
procedure (largely informal) for reaching a judgment about reliable or
For simpler parametric analyses, concerns about unequal variance
consistent intervention effects by examining graphed data visually.
and nonnormal distributions are reasonably well addressed by boot-
Indeed, one of the most recent review articles on single-subject
strapping, a resampling technique that sidesteps data assumptions by
research in rehabilitation failed to acknowledge any of the available
relying on an empirical sampling distribution (Davison & Hinkley,
statistical procedures for analyzing data from these designs (Back-
1997; Good, 2001; Lunneborg, 2000; Simon, 1999). The bootstrap is
man, Harris, Chisholm, & Monette, 1997).
attractive and is just beginning to be applied to SCR (Parker, 2006).
There is a continued and legitimate need for visual analysis. As
Violation of the assumption of serial independence can be addressed
recently noted by Parker, Cryer, and Byrns (2006), visual analysis
through autoregressive integrated moving average backcasting
plays at least seven important roles in SCR:
(Parker et al., 2006). We take a different approach in the presentarticle; however, the use of nonparametric analyses is burdened by
(a) to simultaneously consider multiple data attributes in complex
only the minimal assumptions of nominal-level data.
graphs; (b) to identify cycles and other patterns embedded within and
Advantages of nominal-level data analysis include its applica-
across phases; (c) to distinguish between improvement and deterioration
bility to any SCR data set, regardless of parametric assumptions,
in effect sizes, and to interpret effect size magnitudes; (d) to validate
and its greater ease of use, as remedial data transformations are not
whether results (with predictions lines) are meaningful, by being withinscore-scale limits; (e) to select the best statistical analysis techniques
needed. The main assumption made by nominal-level data analy-
from multiple options; (f) to validate the procedures and results from
ses is an adequate sample size for a 2 ⫻ 2 table of about five
newer SCR analytic techniques, which lack a track record of successful
expected data points per cell (total N
of at least 20 –25). All
published applications; (g) to judge whether SCR datasets meet para-
nominal-level analyses based on the 2 ⫻ 2 table can produce two
metric data assumptions (p. 420).
effect sizes: (a) Phi (⌽), which is Pearson's R
for a 2 ⫻ 2 table, and
Nevertheless, results on the basis of visual analysis have been
(b) the clinical outcome index, the "risk difference" (medical
shown to have low reliability even when judges are experienced
terminology), here more appropriately named "improvement rate
professionals, editors of single-case journals, or others provided
difference" (IRD). Given a 2 ⫻ 2 table with balanced marginal
with fully contextualized graphs with other design and measure-
values, these two values are equal (⌽ ⫽ IRD). Standard output for
ment improvements (Brossart, Parker, Olson, & Mahadevan, 2006;
both indices includes confidence intervals around the obtained
DeProspero & Cohen, 1979; Harbst, Ottenbacher, & Harris, 1991;
values. For more complex single-case designs, these nominal-level
Ottenbacher, 1990; Park, Marascuilo, & Gaylord-Ross, 1990).
indices can be obtained through logistic regression (LR).
Neither technique—visual analysis or statistical analysis—should
Other concerns with using statistical analyses on SCR data are
be used in isolation: "In single-case research it seems especially
related to the lack of relevance of effect sizes to the traditional
important to investigate how these two methods inform and sup-
standard of visual analysis (Parsonson & Baer, 1992). An R
2 (or R
port each other" (Brossart et al., 2006, p. 558).
effect size derived from ordinary least squares regression and
BROSSART, MEYTHALER, PARKER, MCNAMARA, AND ELLIOTT
interpreted as "percent of variance accounted for" does not re-
produced. In addition, because Phase A-predicted values are gen-
sound with more traditional SCR practitioners. A further advan-
erated for Phase B, the technique may infrequently produce values
tage of nominal-level 2 ⫻ 2 table-based analyses is that they are
that extend beyond the range of the dependent variable (on the y
based on nonoverlapping data between phases, a keystone of visual
-axis). Such values should be constrained to fit within the limits of
analysis. Depending on the particular method, the approach to
-axis variable. An additional limitation of the regression
measuring nonoverlapping data varies, but in all cases, the data
model promoted by Allison is that one cannot graph the output for
overlap can be confirmed visually.
visual analysis. The semipartialing performed by this methodchanges the data so much that visual analysis is difficult. Althoughtrend is removed, graphing the final output does not lend itself
Comparison Method: Simple Mean Shift
toward a straightforward interpretation. In an effort to improve the
Allison technique, Parker et al. (2006) renamed the techniquemean and slope adjustment (MASAJ) and modified it so that it was
Regression models have been used by single-case researchers
visually interpretable and the question it addressed was slightly
since at least 1983 (Gorsuch, 1983). Since that time, many differ-
adjusted. The MASAJ technique now answers the question, "What
ent models for analyzing single-case data have been proposed
if phase A trend influence were eliminated or controlled in phase
(e.g., Allison & Gorman, 1993; Center, Skiba, & Casey, 1985–
B?" (Parker et al., 2006, p. 426). In contrast, the Allison technique
1986; Faith, Allison, & Gorman, 1996). One of the advantages of
answers a similar but different question: "What phase differences
regression models is that they are familiar to many because they
would have been obtained if there had been no phase A trend in the
are often covered in doctoral training programs in the behavioral
entire dataset?" (p. 426).
sciences. They also produce a common effect size, R
2, which can
We used a regression model that looks at an SMS between the
be converted to other effect sizes such as Cohen's d
baseline and treatment phase for the present study to provide a
1991). Results from individual studies may also be summarized in
comparison to the LR technique. Although it is one of the simplest
meta-analytic studies. Additional advantages include the relative
models and does not control for baseline trend, we felt it was
ease of evaluating power and creating confidence intervals around
important to provide a familiar comparison technique because it is
the effect size. It is also fairly easy to bootstrap regression models,
very different from the LR technique in terms of conceptual
especially those models that entail a single step (as opposed to
framework and output. This technique was also chosen because a
those that involve multiple steps; e.g., Allison & Gorman, 1993).
few data sets contained the treatment drug in the first phase with
Every statistical method has limitations, and one disadvantage
the "baseline" or placebo phase following. We deemed it inappro-
of the regression models is that the effect size, R
2, is not easily
priate to use a regression method that controlled for baseline trend
interpreted in terms of treatment effectiveness. Another disadvan-
when the treatment phase came prior to the "baseline" phase.
tage is that there are numerous regression models a single-caseresearcher may choose from. Some models try to control for trend
in various ways, some across the entire data series similar to acovariate in analysis of covariance (e.g., Gorsuch, 1983), others
In cases in which the investigator chooses to use a regression
attempt to control for trend in the baseline phase only (Allison &
technique, it is important to be aware that autocorrelation has been
Gorman, 1993; Faith et al., 1996). The choice of model depends on
an enduring problem. Data sets with levels of autocorrelation ⱖ ⫾
the question the investigator wants to answer. Furthermore, the
.20 may be considered problematic regardless of statistical signif-
effect sizes produced by these regression methods are not directly
icance (Matyas & Greenwood, 1996). The presence of autocorre-
comparable to those found in typical cross-sectional regression
lation violates the assumption of data independence. To remove
studies in terms of the characteristic range and magnitude seen in
autocorrelation, one may use an autoregressive integrated moving
SCR. Thus, the interpretive guidelines found in texts by Cohen
average model with a lag-1 parameter for backcasting rather than
(Cohen, 1988), for instance, are of little help in SCR. Investigators
forecasting, as is typically done. The traditional cautions against
have made some progress in trying to provide tentative interpretive
using time series analysis for this application do not apply (see
guidance, but guidelines per se are not available yet (see Brossart
Parker et al., 2006).
et al., 2006; Parker & Brossart, 2003; Parker et al., 2005). Thus,the effect size coefficient does not directly communicate the de-gree of intervention effectiveness.
Addressing Threats to Validity
Among the regression methods available, the one discussed by
Allison and colleagues appears to be one of the more conceptually
Among the strongest (in internal validity) and most flexible
and empirically sound options (Allison & Gorman, 1994; Brossart
SCR designs is the multiple baseline design (MBD) across
et al., 2006; Parker & Brossart, 2003). This method involves
subjects (Kazdin, 1982). The MBD permits an overall judgment
multiple steps and effectively controls baseline trend, but it is not
of intervention effectiveness from multiple (typically 3 or 4)
without limitations. Because it controls for baseline trend, the data
data series. Each data series represents one client. The most simple
series needs to have enough data points to assess trend accurately.
data series is AB, that is, a baseline phase followed by an inter-
Although one may draw a trend line through three data points, any
vention phase. The strength of the MBD is in implementing the
baseline based on only three data points should only be analyzed
intervention at different times for the clients, thus reducing the
by a regression method in which mean shift is examined, and even
likelihood that the performance change is due to some event other
then such analysis should be considered tentative. More data in
than the intervention. Increasing the number of clients, each with
each phase serves to increase the accuracy of any trend line
staggered intervention onset, improves the control of "history" as
SPECIAL ISSUE: SINGLE-CASE RESEARCH
an alternative explanation for behavior change (Kazdin, 1982). For
with a placebo control among patients who were more than 1 year
history to be present, the external event would need to impact the
postbrain injury (BI).
participants concurrently. Any history effect should be seen across
Agitated behavior after BI can be very disruptive during acute
all individuals at approximately the same time. Without such
medical care, inpatient rehabilitation, and in the community. Pre-
evidence, the threat of history can usually be ruled out. Maturation
vious studies have reported agitated behavior in 11%–34% of
is only a problem in special circumstances in which the length of
patients with BI in the acute phase (Brooke, Questad, Patterson, &
the study and the variables measured may, in fact, reflect devel-
Bashak, 1992; Levin & Grossman, 1978; Reyes, Bhattacharyya, &
opmental changes in the participants.
Heller, 1981). Although prevalence rates of agitation in the post-
With MBD, each data series and client are viewed as an inde-
acute phase are lacking, many patients seen in long-term follow-up
pendent replication, contributing evidence to the omnibus judg-
after severe BI demonstrate significant behavioral dyscontrol and
ment. That judgment is easy to make when improvement is uni-
agitation. Such sequelae have a devastating impact on family
formly strong across clients, but when results vary, the overall
relationships and overall functioning, considerably hampering
judgment of intervention effectiveness is more difficult to make.
community reintegration of persons with BI.
That problem situation can be handled by calculating effect sizes.
Agitation is generally regarded as a disturbed behavioral pattern
often accompanied by overactivity and an "explosive" (i.e., lack-ing goal direction), impulsive aggression among persons with BI
Statistical Methods Have Improved
who have regained cognitive awareness (Corrigan & Mysiw, 1988;Silver & Yudofsky, 1994). Historically, clinicians have relied on
Recent innovations in SCR include the ability to calculate
pharmacological treatments of agitated behavior (Cardenas &
effects sizes, in most cases with confidence intervals (Parker et al.,
McLean, 1992; Rowland & DePalma, 1995). A recent Cochrane
2005; Parker & Hagan-Burke, 2007b), the use of phase contrasts
review of these agents observed that beta-blockers (particularly
(Parker & Brossart, 2006), controlling autoregression, controlling
propanolol) appear to have the best evidence of effectiveness
preexisting baseline trend (Parker et al., 2006), and the use of the
(Fleminger, Greenwood, & Oliver, 2006). In spite of such reviews
bootstrap (Parker, 2006). In the past 20 years, the number of
supporting the use of beta-blockers, a recent survey indicates that
analytic techniques available for short data series has easily tripled
specialists seem to prefer anti-epileptics and atypical antipsychot-
since the early 1980s (Barlow & Hersen, 1984; Kazdin, 1982). The
ics (Francisco, Walker, Zasler, & Bouffard, 2007). The mechanism
difficulty has been that few studies compared the statistical tech-
of action for the anti-aggressive properties of propanolol is essen-
niques with each other and with visual analysis. Thus, those who
tially unknown, although it is unlikely to be due to propranolol's
wanted to use these statistical techniques had little information in
peripheral beta-blocking activity because the doses required to
terms of how to interpret the output. Increasingly, researchers have
manage agitated behavior often well exceed the doses required to
recognized this deficiency in the literature base and have made
saturate fully peripheral beta-adrenergic receptors (Coltart &
some progress in addressing this need (e.g., Brossart et al., 2006;
Shand, 1970; Yudofsky, Williams, & Gorman, 1981). Propranolol
Parker & Brossart, 2003). Presently, it appears that effect sizes
may likely exert its anti-aggressive properties via central antago-
vary, depending on the statistical technique used to produce them,
nism of noradrenergic and serotonergic neurotransmission at sev-
and that the effect size magnitudes produced from cross-sectional
eral subsets of receptors.
research are very different than those produced from SCR (e.g.,
For example, both the noradrenergic and serotonergic sys-
Parker et al., 2005).
tems have been implicated as neurophysiologic substrates ofaggressive behavior in animal studies, though these systems
probably subserve different types of aggressive behavior andseem to interact in a complex fashion (Cassidy, 1990; Eichel-
To summarize, SCR designs should be used because they are
man, 1987; Miczek, Weerts, Haney, & Tidey, 1994). The loca-
ideally suited to address questions unanswerable by cross-sectional
tions of noradrenergic and serotonergic cell bodies (the locus
designs, they address the overuse of cross-sectional designs in the
ceruleus and dorsal raphe nuclei, respectively), as well as their
literature base, and it is no longer the case that there are few
neuronal (white matter) projections, are particularly vulnerable
statistical methods to analyze single-case data. In addition, the
to injury within the brain as a result of acceleration/deceleration
MBD is a powerful design that competes well against other de-
injuries, the most common mechanism of BI (Morrison, Millier,
signs in terms of internal validity. In the remainder of the present
& Grzanna, 1979; Whyte & Rosenthal, 1993). Because propran-
article, we present a small RCT that can be conceptualized as a
olol has effects on both beta-adrenergic receptors as well as
hybrid multiple baseline study. We then analyze these data using
serotonin 5-HT1A and 5-HT1B receptors, its apparent effec-
a statistical technique burdened by few assumptions, which is well
tiveness in managing agitation may be related to modulation of
suited for SCR.
neurotransmission in these damaged pathways.
However, the Cochrane review noted several problems that
undermine our confidence in the evidence base that merit a closer
scrutiny of propanolol as preferred intervention for agitation. Thereviewers found very few RCTs to evaluate (only six were iden-
To illustrate the usefulness of SCR and advanced regression
tified, generally, in the pharmacological literature), a reliance on
methods for analyzing data from these designs, we examined data
small sample sizes and lack of a systematic reporting of all treated
collected from a funded project (awarded to Jay Meythaler) to
participants, and no replication studies and a lack of a global
conduct a randomized, double-blind, crossover trial of propanolol
outcome measure to assess the complexity of agitated behavior in
BROSSART, MEYTHALER, PARKER, MCNAMARA, AND ELLIOTT
this population (Fleminger et al., 2006). Although the reviewers
ethnicity consisted of 12 Caucasians and 1 African American. The
cited the need for further RCTs of the effectiveness of pharmaco-
average age of the participants was 34 (SD
logical agents, researchers and clinicians were strongly advised torevisit the use of "N of 1 research methods" to analyze the
effectiveness of the intervention in research projects and in clinicalcase management (Fleminger et al., 2006).
The ABS (Corrigan, 1989) was used to assess agitation. The
As we observed earlier, these clinical realities and methodolog-
ABS is a 14-item scale designed to assess agitation objectively
ical issues often vex intervention research in rehabilitation. And as
among persons with TBI. At the end of each observation period,
we demonstrate, SCR designs and advanced regression techniques
raters assign a number ranging from 1 (absent
) to 4 (present to an
can be used efficiently to examine the effectiveness of clinical
) for each item, representing the frequency of the
interventions for grouped data (necessary for RCTs) and for clin-
agitated behavior and/or the severity of a given incident. Total
ical case management (to monitor individual response to treat-
scores range from 14 (no agitation
) to 56 (extremely severe agi-
ment). In the remainder of this article, we demonstrate the use and
). In previous studies, the ABS has demonstrated adequate
implications of SCR and regression techniques in a randomized,
reliability and validity (Corrigan, 1989). Factor analysis of the
double-blind crossover trial of propanolol in the treatment of
ABS yielded a three-factor solution: Aggression, Disinhibition,
agitation among persons with postacute BI.
and Lability (Corrigan & Bogner, 1994).
The initial ABS was completed by a family member in an
interview conducted by Timothy R. Elliott. This was used to
determine sufficient level of agitation to qualify for the study. Atthe introductory evaluation prior to randomization, family mem-
Twenty individuals with BI who were sequentially enrolled in
bers met with Timothy R. Elliott to learn how they were to assess
an outpatient brain injury clinic were invited to participate in the
agitation each week of participation with the ABS. During this
present study. Each potential participant and his or her family
session, family members were instructed in the use of the ABS. An
members were given a thorough explanation of the study together
instructional videotape (depicting various agitated behaviors) was
with a detailed informed consent document. Every effort was made
played for the family members to rate the depictions of agitation
to explain the purpose of the study and the risks and benefits of
on the ABS. These ratings were reviewed and critiqued by the staff
participation to the potential participant, and to obtain assent or
member. Family members were given copies of the ABS and
refusal. For individuals unable to provide informed consent, deci-
instructed to rate the participant's agitation each week. Completed
sions regarding participation fell to family members or the per-
scales were mailed to the research team or returned in subsequent
son's designated surrogate decision maker.
The inclusion criteria were as follows: (a) BI due to closed or
penetrating head trauma and/or hypoxia greater than 1 year prior toentry into the study; (b) 14 years of age or older; and (c) a
clinically significant level of agitated behavior, defined as that
The study was designed to be a randomized, double-blinded,
which interferes with activities of daily living or independent
crossover trial. Upon enrollment in the study, each participant had
living skills. In order to more carefully operationalize the level of
a 2-week observation period during which placebo was adminis-
agitated behavior necessary for inclusion, this study relied on the
tered in a single-blind fashion. ABS observations began during this
behavioral ratings by family members on the Agitated Behavior
period. Pharmacy personnel used a double-blind randomization
Scale (ABS; Corrigan, 1989) obtained by the staff member. Pro-
procedure to assign participants to receive either the active agent
spective individuals qualified for entry into the study if they obtain
(propranolol) or placebo for the first arm of the study. The study
at least two scores on the ABS (described in the Measures
drug (propranolol or placebo) was prepared by the pharmacy and
of 25 or greater in a 2-week period.
delivered to the clinic. A 2-week supply of study drug contained in
The exclusion criteria were as follows: (a1) medical contrain-
a blister pack and labeled with the dosage increment was provided
dications to initiation of a beta-adrenergic blocker, including a
at each clinic visit.
recent history of congestive heart failure, cardiac arrhythmia, atrio-
Participants had pulse and blood pressure checked at each clinic
ventricular conduction defect (2nd degree or higher), or asthma
visit. Dose of the study drug was adjusted to a tolerated dosage
requiring pharmacologic intervention; (b) clear medical indica-
increment for supine blood pressures less than 55 diastolic or 95
tions for prescription of a beta-adrenergic blocker for reasons other
systolic in patients under 50 years of age; less than 70 diastolic or
than agitation; (c) demonstrated inability to tolerate propranolol
110 systolic in patients 50 years of age and over. Eight participants
due to hypotension or bradycardia; (d) suspected development of
were started at an initial dose of 60 mg of long-acting propranolol
increased intracranial pressure requiring neurosurgical interven-
(Inderal-LA) per day; 2 participants were started at an initial dose
tion (e.g., placement or revision of ventricular-peritoneal shunt).
of 80 mg of propranolol (Participants 4 and 7). Dosages wereincreased for participants who demonstrated tolerance for thepreceding dosage. From this protocol, 1 participant received a
maximum dosage of 180 mg (Participant 1), 1 received a maxi-
The sample available for study consisted of 13 persons with TBI
mum dosage of 120 mg (Participant 8), 6 participants received a
(4 women, 9 men). Participants who had only two data points in
maximum dosage of 80 mg (Participants 3, 4, 5, 6, 7, 10), and 2
either the baseline or treatment phase were excluded. The final
were maintained at a dosage of 60 mg (Participants 2 and 9).
sample that was analyzed consisted of 10 participants. Sample
Ratings of agitation for each individual were conducted weekly
SPECIAL ISSUE: SINGLE-CASE RESEARCH
from 6 to 14 weeks (average 10 weeks). Of the 10 clients, 7 were
ANOVA or OLS regression. The dependent variable, PhaseAB, is
assessed over 10 or more weeks. The design for each of 9 clients
dichotomous (Levels A, B). A one-way (noninteraction) model is
was a simple AB (baseline period of no treatment, followed by a
specified. The output needed for the present study is only the 2 ⫻ 2
treatment period). For 1 participant, the treatment preceded the
prediction accuracy table, which is ordinarily used for prediction
baseline period, forming a BA design. Baseline phases ranged
specificity and sensitivity (involving false negatives and false
from 3 to 8 data points (mean 5.3 data points), and treatment
positives). Through LR, an attempt is made to predict the phase to
phases had the same range (mean 5.1 data points).
which a score belongs (baseline vs. treatment), based on its size.
The prediction is made on the basis of all participants' data, but the
classification results also can be disaggregated by individualparticipant.
For many research designs, logistic regression (LR) is a close
contender to ANOVA in power and sensitivity, while being bur-
dened with fewer data assumptions (Fox, 2000; Menard, 2002;Pampel, 2000; Tabachnick & Fidell, 1996). LR is similar to
Analysis of the propranolol data set results in a classification
ordinary least squares (OLS) multiple regression but uses iterative
table presented in Table 1. Table 1 indicates that the classification
maximum likelihood estimation (MLE) rather than OLS. Like
accuracy for these data is only about chance level, 50%. Any given
multiple regression, LR can use any combination of categorical or
data point has an equal chance of belonging to the baseline versus
continuous predictors, but the dependent variable must be categor-
treatment condition. These results represent an unsuccessful inter-
ical. LR performs similarly to discriminant function analysis
vention. From a total of 104 data points, only 57% were classified
(DFA), but it is increasingly favored over the latter because of its
correctly for phase membership, which is close to chance level.
fewer data assumptions (Press & Wilson, 1978). Unlike OLS
Submitting this table (only the interior four scores) to a chi-square
regression, LR does not assume (a) a linear relationship between
analysis yields, 2 ⫽ 1.9. Phi is output directly as .135 or can be
the independent variables and the dependent variable, (b) normally
calculated as, ⌽ ⫽ 冑2/N
⫽ 冑1.9/104 ⫽ .135. Phi can be inter-
distributed variables, or (c) equal variance per cell. LR is offered
preted approximately as "prediction accuracy beyond chance."
by most statistics packages, including NCSS (Hintze, 2007), SPSS,
From the 2 ⫻ 2 table, we also can calculate phi from the
Stata, S-Plus, SYSTAT, and SAS.
difference between two ratios: d/f ⫺ b/e ⫽ 30/51 ⫺ 24/53 ⫽
Although LR is burdened by few data assumptions, ideally it
.5882 ⫺ .4528 ⫽ .135. A two proportions statistical module
needs at least 10 observations for each predictor variable level
provides a 90% exact confidence interval as: ⫺.03 ⬍ .135 ⬍ .29,
(e.g., the smaller Phase A or B; Peduzzi, Concato, Kemper, Hol-
and because it spans zero, we note that it could have been obtained
fold, & Feinstein, 1996). In addition, all predictor cells should
by chance alone. On the basis of all 10 participants, this phi effect
have frequencies of at least 1, and no more than 20% of cells
size of approximately .14 indicates the magnitude of change from
should have less than 5 per cell.
baseline to intervention phases for this particular intervention.
LR does not yield a true effect size but rather one or more
Guidelines for interpreting phi magnitudes were recently derived
2 approximations (e.g., Cox & Snell, 1989; Nagelkerke,
from 165 analyses of published SCR data (Parker & Hagan-Burke,
1991). These quasi effect sizes must be interpreted cautiously (e.g.,
2007a). LR results correlated .83 with visual judgments, and
they do not represent "percent of variance explained" as do true
studies judged to show small or negligible results had effect sizes
2s). A second LR output, and the one most important to this
(interquartile range [IQR]) of .09 –.43. Studies judged as showing
article, is a summary of LR prediction accuracy in a 2 ⫻ 2 table.
medium-size results had effect sizes (IQR) of .53–.72. And studies
LR predicts membership of each data point in either baseline or
judged as showing large results had effect sizes (IQR) of .82–1.0.
intervention phase, based on its relative magnitude. Chance level is
This effect size does not indicate whether this change (or lack of
50% accuracy. The 2 ⫻ 2 agreement table, when analyzed by
change) can be attributed to the intervention. Attributing change to
using chi-square, yields the Pearson's phi index of association, a
the intervention depends on strength of the design. The design of
bona fide effect size. Pearson's ⌽ and ⌽2 are R
2 family members,
this example is a multiple-baseline design with 10 independent
and familiar to many researchers (Cohen, 1988). Phi also can be
client AB data series, and with treatment initiated at 10 different
calculated from chi-square: ⌽ ⫽ 冑2/N
is the total
times. Most single-case researchers would consider this a strong
number of frequency counts in the 2 ⫻ 2 table).
design. Thus, our hypothesis that participants with agitation would
In a balanced 2 ⫻ 2 table (from LR), phi also can be obtained
have a significant reduction in ABS scores on propranolol as
by submitting four internal scores to analysis in a "two propor-
compared with placebo was not supported.
tions" statistical module. Phi approximates the difference betweenthe two proportions and is exactly the same in a balanced table. Anadvantage of using a "two proportions" module for analysis is that
it commonly outputs confidence intervals.
Classification Accuracy Table
In a single-case design, LR analysis requires two predictor
variables, participant and scores, and the dependent measure,
PhaseAB. Though not essential, a fourth serial sequence variable,time, should be added. Participant is a categorical predictor vari-
able whose number of levels equals the number of clients (data
series) (Levels I, II, III, etc.). Scores serve as a predictor ratherthan as a dependent or criterion variable, as is the case with
Percent correctly classified ⫽ 56.7%.
BROSSART, MEYTHALER, PARKER, MCNAMARA, AND ELLIOTT
Analyses by Participant
tistical output needs to include visual analysis. These results showthat large effect sizes do not inform one as to the directionality of
Besides obtaining an index of overall intervention effect, diag-
the results. This study produced some high-correct classification
nostic understanding can be gained from effect sizes for individual
rates; however, half those participants did better on propranolol,
participants. This is accomplished in LR by dropping the partici-
and the other half did worse on propranolol.
pant predictor variable and entering the data only one participant ata time. Table 2 includes the 10 effect sizes for the individual
participants, which is compoised of roughly two groups: a largergroup of "little or no effect" (⌽ ⫽ .04, .00, .00, .07, .33, .00) and
Our main objective in this article was to present a discussion of
a smaller group of "moderate to strong effect" (⌽ ⫽ .52, 1.0, .63,
advanced regression methods for the analysis of data produced by
.87). We include these effect sizes and confidence intervals for the
SCR. We presented two very different methods, LR and OLS
individual participants because clinicians involved in monitoring
regression. This is the first attempt that we are aware of in which
patient progress would focus on each unique client's progress,
investigators have used LR to analyze SCR. The application to a
whereas researchers would probably want to distill the results
RCT with multiple-baseline data from a drug study of the effec-
across multiple baselines in order to determine whether the treat-
tiveness of propranolol to treat agitation among individuals with
ment was effective. Generally, these results indicate that propran-
BI was ideal for this demonstration because of the high internal
olol was not effective in lowering agitation for the majority of
validity and the multiple data sets available for analysis. Factors
participants. The level of analysis one uses depends on the ques-
suggesting a high degree of internal validity include multiple-
tion one needs answered.
baseline design, double-blind features, and random assignment tothe ordering of treatment condition. Thus, although the overall
Comparison to Regression
sample size was small, the degree of experimental control for thepresent study appears to be rather high.
The results from the SMS regression model conducted on each
Our analysis of the multiple-baseline data suggests that overall
participant are included in Table 2. In general, there were three
propranolol was not an effective treatment for agitation. The effect
groups of participants. The largest group contained those partici-
size based on these data was .14. This is a small and nonsignificant
pants that demonstrated no effect while taking propranolol. These
effect size and could have been obtained by chance alone. Yet,
participants obtained R
2 values of .02, .07, .04, .05, .22, and .02
when we analyzed participants separately, we found that there
and classification rates of 54.5%, 50%, 50%, 54.5%, 66.7%, and
were interesting differences among the participants. Six individu-
62.5%, respectively. A graphic depiction of the lack of effects
als experienced little or no effect on propanolol. Four others
observed for one participant in this group is presented in Figure 1.
evidenced a moderate to strong effect in response to propranolol:
Two participants exhibited significantly elevated agitation dur-
2 of these participants improved, and the other 2 did worse. The
ing the propranolol phase (a 33-year-old Caucasian woman and a
individual variations in treatment response, which any analysis of
37-year-old Caucasian man). We obtained R
2 values of .23 and .70
overall group performance cannot address, suggest that agitation
with classification rates of 80% and 83.3%. The small R
2 value for
may be influenced by several factors that have yet to be isolated or
the first participant seems to reflect the nonstatistically significant
understood. The results of our demonstration, then, have implica-
phi. Figure 2 depicts the ratings obtained for the 37-year-old man
tions for clinical case management and for isolating other variables
who exhibited significantly greater agitation on propranolol com-
in future studies of propanolol in the treatment of agitation.
pared with placebo.
Clinical scientists are typically interested in their patient's re-
Two other participants displayed significantly less agitation on
sponse to treatment. The analysis of each participant's data sepa-
propranolol than on placebo (a 51-year-old African American man
rately is in line with the clinician's interest in patient progress. We
and a 23-yearold Caucasian man). We obtained R
2 values of .70
can see in these profiles that any particular client's response may
and .73 and classification rates of 100% and 92.9%. Figure 3
vary markedly from the overall analysis (which suggested no
depicts the significant improvement exhibited by the 51-year-old
effect for the group). As seen in these results, a few participants
man during the propanolol phase.
had notable results with propranolol. In the absence of contrain-
There were 2 participants who obtained results with R
dications and troublesome side effects, some clinicians may
of .23 and .22. Their classification rates and phi values were
choose to prescribe propranolol for agitation because it was effec-
80%, .52 (p
⫽ .10) and 66.7%, .33 (p
⫽ .41), respectively. The
tive for some clients. Such a choice would seem to require ade-
case with the 80% classification rate is rather high, but the phi
quate monitoring to determine whether continued administration
value and examination of the confidence interval for the boot-
was beneficial, worthwhile, and cost-effective. These observations
2 value, which contains zero, suggest that such a high
are consistent with other expert opinions concerning the use of
classification rate should be interpreted with caution. Interpretabil-
propanolol in the treatment of agitation (Fleminger et al., 2006).
ity would likely be increased if this case had one or two more data
There are limitations with the techniques we have demon-
points in the baseline phase, beyond the minimum of three. The
strated in this study. One does not evaluate trends or curves
2 value of .22 was not associated with a high classification
with LR. In some cases, trend lines or curves may be of primary
rate. This data series also obtained a non-significant phi, and the
interest. In such cases, LR would not be an ideal analytic tool.
confidence interval from the bootstrapped R
2 also contained zero.
LR also has a ceiling limitation. If a treatment obtains a 100%
One can more confidently conclude that there is no treatment effect
correct classification rate (a ⌽ of 1), then there is no way in which
in these cases.
to evaluate any magnitude of difference with the technique beyond
It is important to emphasize that the interpretation of any sta-
the minimum required to obtain the 100% classification rate.
SPECIAL ISSUE: SINGLE-CASE RESEARCH
Table 2Classification Tables for Each Individual Participant
% correctly classified ⫽ 80.0
% correctly classified ⫽ 100.0
2 ⫽ 2.74, ⌽ ⫽ .52, p
2 ⫽ 12, ⌽ ⫽ 1.0, p
90% exact C.I. around difference between 2 proportions: ⫺.04 ⬍ .52 ⬍ .86
90% exact C.I. around difference between 2 proportions: .56 ⬍ 1.00 ⬍ 1.00
2 ⫽ .23, bootstrapped Mean SMS R
2 ⫽ .28, 90% C.I. ⫽ 0, .45
2 ⫽ .70, bootstrapped Mean SMS R
2 ⫽ .70, 90% C.I. ⫽ .48, .88
% correctly classified ⫽ 54.5
% correctly classified ⫽ 83.3
2 ⫽ .02, ⌽ ⫽ .04, p
2 ⫽ 4.68, ⌽ ⫽ .625, p
90% exact C.I. around difference between 2 proportions: ⫺.38 ⬍ .03 ⬍ .46
90% exact C.I. around difference between 2 proportions: .09 ⬍ .63 ⬍ .88
2 ⫽ .02, bootstrapped Mean SMS R
2 ⫽ .11, 90% C.I. ⫽ 0, .39
2 ⫽ .70, bootstrapped Mean SMS R
2 ⫽ .70, 90% C.I. ⫽ .45, .89
% correctly classified ⫽ 92.9
% correctly classified ⫽ 50.0
2 ⫽ 10.5, ⌽ ⫽ .87, p
2 ⫽ 0, ⌽ ⫽ 0, p
90% exact C.I. around difference between 2 proportions: .44 ⬍ .88 ⬍ .99
90% exact C.I. around difference between 2 proportions: ⫺.40 ⬍ .00 ⬍ .40
2 ⫽ .73, bootstrapped Mean SMS R
2 ⫽ .75, 90% C.I. ⫽ 47, .93
2 ⫽ .07, bootstrapped Mean SMS R
2 ⫽ .26, 90% C.I. ⫽ 0, .15
% correctly classified ⫽ 50.0
% correctly classified ⫽ 54.5
2 ⫽ 0, ⌽ ⫽ 0, p
2 ⫽ .05, ⌽ ⫽ .07, p
90% exact C.I. around difference between 2 proportions: ⫺.40 ⬍ .00 ⬍ .40
90% exact C.I. around difference between 2 proportions: ⫺.40 ⬍ .07 ⬍ .53
2 ⫽ .04, bootstrapped Mean SMS R
2 ⫽ .17, 90% C.I. ⫽ 0, .56
2 ⫽ .05, bootstrapped Mean SMS R
2 ⫽ .14, 90% C.I. ⫽ 0, .47
% correctly classified ⫽ 66.7
% correctly classified ⫽ 62.5
2 ⫽ .67, ⌽ ⫽ .33, p
2 ⫽ .00, ⌽ ⫽ .00, p
90% exact C.I. around difference between 2 proportions: ⫺.33 ⬍ .33 ⬍ .81
90% exact C.I. around difference between 2 proportions: ⫺.40 ⬍ .00 ⬍ .54
2 ⫽ .22, bootstrapped Mean SMS R
2 ⫽ .32, 90% C.I. ⫽ 0, .81
2 ⫽ .02, bootstrapped Mean SMS R
2 ⫽ .16, 90% C.I. ⫽ 0, .49
Prt ⫽ Participant; C.I. ⫽ confidence interval; SMS ⫽ simple mean shift.
Furthermore, additional work remains to determine how this LR
tant to note that the ratings we obtained in this study were not
procedure performs with a wide variety of single-case data sets.
complicated by patient self-report. The participants were rated by
Although we have focused on the statistical results, it is impor-
their family member. Thus, for any participant who improved on
BROSSART, MEYTHALER, PARKER, MCNAMARA, AND ELLIOTT
Example data set of noneffective treatment of agitation with
propranolol. ABS ⫽ Agitated Behavior Scale. Solid circles represent datacollected in the baseline phase; solid triangles represent data from the
Example data set of participant improvement while on pro-
pranolol for the treatment of agitation. ABS ⫽ Agitated Behavior Scale.
Solid circles represent data collected in the baseline phase; solid trianglesrepresent data from the treatment phase.
propranolol, it may not be necessary for statistical significance tobe achieved. Improved quality of life for the family may be a moreimportant consideration in some clinical scenarios.
Beyond the findings of this particular study, it should be noted
key elements in place, any reluctance to publish such a study
that with an appropriate measure of outcome and the implemen-
probably reflects editorial bias more than a scholarly critique.
tation of a multiple-baseline design, we presented in this article a
In many respects, the present controversies and needs in our
statistical procedure that should be appreciated by peer reviewers
research make for an exciting time for single-case researchers.
and peer-reviewed outlets. There is no longer an acceptable ratio-
New statistical methods continue to be developed and refined. No
nale for conducting SCR without statistical analysis. Single-case
longer must the single-case researcher rely solely on visual anal-
studies that feature a strong rationale, a multiple-baseline design,
ysis: Regression methods such as those presented here provide two
and appropriate statistical analyses deserve a place in the eviden-
powerful yet very different methods for analyzing single-case data.
tiary foundation of rehabilitation psychology research. With all the
In conjunction with visual analysis, it is hoped that those who mayhave previously avoided SCR will now see new avenues forproductive inquiry that can improve clinical practice, enrich theliterature base, and improve the quality of life for consumers of
Aeschleman, S. R. (1991). Single-subject research designs: Some miscon-
ceptions. Rehabilitation Psychology, 36,
Allison, D. B., & Gorman, B. S. (1993). Calculating effect sizes for
meta-analysis: The case of the single case. Behaviour Research and
Allison, D. B., & Gorman, B. S. (1994). "Make things as simple as
possible, but no simpler." A rejoinder to Scruggs and Mastropieri.Behaviour Research and Therapy, 32,
Backman, C. L., Harris, S. R., Chisholm, J. M., & Monette, A. (1997).
Single-subject research in rehabilitation: A review of studies using AB,withdrawal, multiple baseline, and alternating treatments designs. Ar-
chives of Physical Medicine and Rehabilitation, 78,
Baltes, P. B., & Nesselroade, J. R. (1979). History and rationale of
longitudinal research. In J. R. Nesselroade & P. B. Baltes (Eds.),Longitudinal research in the study of behavior and development
Example data set of participant deterioration while on propran-
1–39). London: Academic Press.
olol for the treatment of agitation. ABS ⫽ Agitated Behavior Scale. Solid
Barlow, D. H., & Hersen, M. (Eds.). (1984). Single case experimental
circles represent data collected in the baseline phase; solid triangles rep-
designs: Strategies for studying behavior change
(2nd ed.). Oxford,
resent data from the treatment phase.
England: Pergamon Press.
SPECIAL ISSUE: SINGLE-CASE RESEARCH
Blampied, N. M. (2000). Single-case research designs: A neglected alter-
Eichelman, B. (1987). Neurochemical and psychopharmacologic aspects
native. American Psychologist, 55,
for aggressive behavior. In H. Y. Meltzer (Ed.), Psychopharmacology:
Brooke, M. M., Questad, K. K., Patterson, D. R., & Bashak, K. J. (1992).
The third generation of progress.
New York: Raven Press.
Agitation and restlessness after closed head injury: A prospective study
Elliott, T. R. (2007). Registering randomized clinical trials and the case
of 100 consecutive admissions. Archives of Physical Medicine and
for CONSORT. Experimental and Clinical Psychopharmacology, 15,
Brossart, D. F., & Parker, R. I. (2001, March). Evaluating client improve-
Faith, M. S., Allison, D. B., & Gorman, B. S. (1996). Meta-analysis of
ment: Interrupted time series methods.
Poster session presented at the
single-case research. In R. D. Franklin, D. B. Allison, & B. S. Gorman
Houston 2001 National Counseling Psychology Conference, Houston,
(Eds.), Design and analysis of single-case research
Mahwah, NJ: Erlbaum.
Brossart, D. F., Parker, R. I., Olson, E. A., & Mahadevan, L. (2006). The
Fidler, F. (2002). The fifth edition of the APA Publication Manual: Why its
relationship between visual analysis and five statistical analyses in a
statistics recommendations are controversial. Educational and Psycho-
simple AB single-case research design. Behavior Modification, 30,
logical Measurement, 62,
Fleminger, S., Greenwood, R. J., & Oliver, D. L. (2006). Pharmacological
Brucker, B. S., & Ince, L. P. (1977). Biofeedback as an experimental
management for agitation and aggression in people with acquired brain
treatment for postural hypotension in a patient with a spinal cord lesion.
injury. Cochrane Database of Systematic Reviews,
(4), CD003299. DOI:
Archives of Physical Medicine and Rehabilitation, 58,
Busk, P. L., & Marascuilo, L. A. (1992). Statistical analysis in single-case
Fordyce, W. E. (1976). Behavioral methods in chronic pain and illness.
research: Issues, procedures, and recommendations, with applications to
Louis, MO: Mosby, Inc.
multiple behaviors. In T. R. Kratochwill & J. R. Levin (Eds.), Single-
Fox, J. (2000). Multiple and generalized nonparametric regression.
case research design and analysis: New directions for psychology and
sand Oaks, CA: Sage.
(pp. 159 –185). Hillsdale, NJ: Erlbaum.
Francisco, G. E., Walker, W. C., Zasler, N. D., & Bouffard, M. H. (2007).
Callahan, C. D., & Barisa, M. T. (2005). Statistical process control and
Pharmacological management of neurobehavioral sequelae of traumatic
rehabilitation outcome: The single-subject design reconsidered. Reha-
brain injury: A survey of current physiatric practice. Brain Injury, 21,
bilitation Psychology, 50,
Cardenas, D. D., & McLean, A. (1992). Psychopharmacologic manage-
Goldfried, M. R., & Wolfe, B. E. (1996). Psychotherapy practice and
ment of tramatic brain injury. Physical Medicine and Rehabilitaion
research: Repairing a strained alliance. American Psychologist, 51,
Clinics of North America, 3,
Cassidy, J. W. (1990). Neurochemical substrates of aggression: Toward a
Good, P. I. (2001). Resampling methods: A practical guide to data anal-
model for improved intervention, part 1. Journal of Head Trauma
Boston: Birkha¨user Boston.
Gorsuch, R. L. (1983). Three methods for analyzing time-series (N of 1)
Center, B. A., Skiba, R. J., & Casey, A. (1985–1986). A methodology for
data. Behavioral Assessment, 5,
the quantitative synthesis of intra-subject design research. Journal of
Harbst, K. B., Ottenbacher, K. J., & Harris, S. R. (1991). Interrater
Special Education, 19,
reliability of therapists' judgments of graphed data. Physical Therapy,
Cohen, J. (1988). Statistical power analysis for the behavioral sciences
(2nd ed.). Hillsdale, NJ: Erlbaum.
Hilliard, R. B. (1993). Single-case methodology in psychotherapy process
Coltart, D. J., & Shand, D. G. (1970). Plasma propranolol levels in the
and outcome research. Journal of Consulting and Clinical Psychology,
quantitative assessment of beta-adrenergic blockade in man. British
Medical Journal, 3,
Hintze, J. (2007). NCSS, PASS, and GESS
[Computer software]. Kaysville,
Concato, J., Shah, N., & Horwitz, R. I. (2000). Randomized, controlled
trials, observational studies, and the hierarchy of research designs. NewEngland Journal of Medicine, 342,
Huitema, B. E. (2004). Analysis of interrupted time-series experiments
Corrigan, J. D. (1989). Development of a scale for assessment of agitation
using ITSE: A critique. Understanding Statistics: Statistical Issues in
following traumatic brain injury. Journal of Clinical and Experimental
Psychology, Education, and the Social Sciences, 3,
Ince, L. P., Brucker, B. S., & Alba, A. (1978). Reflex conditioning in a
Corrigan, J. D., & Bogner, J. A. (1994). Factor structure of the Agitated
spinal man. Journal of Comparative and Physiological Psychology, 92,
Behavior Scale. Journal of Clinical and Experimental Neuropsychology,
796 – 802.
Kazdin, A. E. (1982). Single-case research designs: Methods for clinical
Corrigan, J. D., & Mysiw, W. J. (1988). Agitation following traumatic
and applied settings.
New York: Oxford University Press.
brain injury: Equivocal evidence for a discrete stage of cognitive recov-
Kratochwill, T. R., & Brody, G. H. (1978). Single subject designs: A
ery. Archives of Physical Medicine and Rehabilitation, 69,
perspective on the controversy over employing statistical inference and
Cox, D. R., & Snell, E. J. (1989). Analysis of binary data
implications for research and training in behavior modification. Behavior
London: Chapman & Hall.
Crosbie, J. (1993). Interrupted time-series analysis with brief single-subject
Levin, H. S., & Grossman, R. G. (1978). Behavioral sequelae of closed
data. Journal of Consulting and Clinical Psychology, 61,
head injury: A quantitative study. Archives of Neurology, 35,
Crosbie, J. (1995). Interrupted time-series analysis with short series: Why
Lunneborg, C. E. (2000). Data analysis by resampling: Concepts and
it is problematic; how it can be improved. In J. M. Gottman (Ed.), The
Pacific Grove, CA: Brooks/Cole.
analysis of change
(pp. 361–395). Mahwah, NJ: Erlbaum.
Malament, I. B., Dunn, M. E., & Davis, R. (1975). Pressure sores: An
Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their
operant conditioning approach to prevention. Archives of Physical Med-
Cambridge, England: Cambridge University Press.
icine and Rehabilitation, 56,
DeProspero, A., & Cohen, S. (1979). Inconsistent visual analyses of
Matyas, T. A., & Greenwood, K. M. (1996). Serial dependency in single-
intrasubject data. Journal of Applied Behavior Analysis, 12,
case time series. In R. D. Franklin, D. B. Allison, & B. S. Gorman (Eds.),
Dunn, D., & Elliott, T. (in press). The place and promise of theory in
Design and analysis of single-case research
(pp. 215–243). Mahwah,
rehabilitation psychology. Rehabilitation Psychology.
BROSSART, MEYTHALER, PARKER, MCNAMARA, AND ELLIOTT
Menard, S. (2002). Applied logistic regression analysis
(2nd ed.). Thou-
Pijnenborg, G. H. M., Withaar, F. K., Evans, J. J., van den Bosch, R. J., &
sand Oaks, CA: Sage.
Brouwer, W. H. (2007). SMS text messages as a prosthetic aid in the
Miczek, K. A., Weerts, E., Haney, M., & Tidey, J. (1994). Neurobiological
cognitive rehabilitation of schizophrenia. Rehabilitation Psychology, 52,
mechanisms controlling aggression: Preclinical developments for
pharmacotherapeutic interventions. Neuroscience & Biobehavioral
Press, S. J., & Wilson, S. (1978). Chosing between logistic regresssion and
discriminant analysis. Journal of the American Statistical Association,
Morgan, D. L., & Morgan, R. K. (2001). Single-participant research
design: Bringing science to managed care. American Psychologist, 56,
Reyes, R. L., Bhattacharyya, A. K., & Heller, D. (1981). Traumatic head
injury: Restlessness and agitation as prognosticators of physical and
Morrison, J. H., Millier, M. E., & Grzanna, R. (1979, July 20). Noradren-
psychologic improvement in patients. Archives of Physical Medicine
ergic innervation of cerebral cortex: Widespread effects of local cortical
and Rehabilitation, 62,
lesions. Science, 205,
Rosenthal, R. (1991). Meta-analytic procedures for social research
Nagelkerke, N. J. D. (1991). A note on a general definition of the
ed.). Newbury Park, CA: Sage.
coefficient of determination. Biometrika, 78,
Rowland, T., & DePalma, L. (1995). Current neuropharmacologic inter-
Nesselroade, J. R. (1991). Interindividual differences in intraindividual
ventions for the management of brain injury agitation. Neuro Rehabili-
change. In L. M. Collins & J. L. Horn (Eds.), Best methods for the
analysis of change: Recent advances, unanswered questions, futuredirections
(pp. 92–105). Washington, DC: American Psychological
Shavelson, R., & Towne, L. (Eds.). (2002). Scientific research in educa-
Washington, DC: Committee on Scientific Principles for Educa-
Oakley, A. (2002). Social science and evidence-based everything: The case
tional Research, National Research Council, National Academy Press.
of education. Educational Review, 54,
Silver, J. M., & Yudofsky, S. C. (1994). Aggressive disorders. In J. M.
Ottenbacher, K. J. (1990). Visual inspection of single-subject data: An
Silver, S. C. Yudofsky, & R. E. Hales (Eds.), Neuropsychiatry of
empirical analysis. Mental Retardation, 28,
traumatic brain injury
(pp. 313–356). Washington, DC: American Psy-
Pampel, F. C. (2000). Logistic regression: A primer.
Thousand Oaks, CA:
Simon, J. L. (1999). Resampling: The new statistics.
Arlington, VA: Rita
Park, H., Marascuilo, L., & Gaylord-Ross, R. (1990). Visual inspection and
statistical analysis of single-case designs. Journal of Experimental Ed-
Spring, B., Pagoto, S., Kaufmann, P. G., Whitlock, E. P., Glasgow, R. E.,
Smith, T. W., et al. (2005). Invitation to a dialogue between researchers
Parker, R. I. (2006). Increased reliability for single-case research results: Is
and clinicians about evidence-based behavioral medicine. Annals of
the bootstrap the answer? Behavior Therapy, 37,
Behavioral Medicine, 30,
Parker, R. I., & Brossart, D. F. (2003). Evaluating single-case research
Stevens, J. (2007). Repeated measures analysis. In Intermediate statistics:
data: A comparison of seven statistical methods. Behavior Therapy, 34,
A modern approach
(3rd ed.). Mahwah, NJ: Erlbaum.
Tabachnick, B. G., & Fidell, L. S. (1996). Using multivariate statistics
Parker, R. I., & Brossart, D. F. (2006). Phase contrasts for multiphase single
ed.). New York: Harper Collins.
case intervention designs. School Psychology Quarterly, 21,
46 – 61.
Tucker, J. A., & Roth, D. L. (2006). Extending the evidence hierarchy to
Parker, R. I., Brossart, D. F., Vannest, K. J., Long, J. R., De-Alba, R. G.,
enhance evidence-based practice for substance use disorders. Addiction,
Baugh, F. G., et al. (2005). Effect sizes in single case research: How
large is large? School Psychology Review, 34,
Wehman, P., West, M., Fry, R., Sherron, P., Groah, C., Kreutzer, J., et al.
Parker, R. I., Cryer, J., & Byrns, G. (2006). Controlling baseline trend in
(1989). Effect of supported employment on the vocational outcomes of
single-case research. School Psychology Quarterly, 21,
418 – 443.
persons with traumatic brain injury. Journal of Applied Behavior Anal-
Parker, R. I., & Hagan-Burke, S. (2007a). Median-based overlap analysis for
single case data: A second study. Behavior Modification, 31,
Parker, R. I., & Hagan-Burke, S. (2007b). Useful effect size interpretations
White, G. W., Mathews, R. M., & Fawcett, S. B. (1989). Reducing risk of
for single-case research. Behavior Therapy, 38,
pressure sores: Effects of watch prompts and alarm avoidance on wheel-
Parsonson, B. S., & Baer, D. M. (1992). The visual analysis of data, and
chair push-ups. Journal of Applied Behavior Analysis, 22,
current research into the stimuli controlling it. In T. R. Kratochwill &
Whyte, J., & Rosenthal, M. (1993). Rehabilitation of the patient with traumatic
J. R. Levin (Eds.), Single-case research design and analysis
brain injury. In J. A. DeLisa (Ed.), Rehabilitation medicine: Principles and
40). Hillsdale, NJ: Erlbaum.
(2nd ed., pp. 825– 611). Philadelphia: Lippincott.
Peduzzi, P., Concato, E., Kemper, T. R., Holfold, T. R., & Feinstein, A. R.
Yudofsky, S., Williams, D., & Gorman, J. (1981). Propranolol in the
(1996). A simulation of the number of events per variable in logistic
treatment of rage and violent behavior in patients with chronic brain
regression analysis. Journal of Clinical Epidemiology, 49,
syndromes. American Journal of Psychiatry, 138,
SPECIAL ISSUE: SINGLE-CASE RESEARCH
Scenarios In Which Single-Case Research Designs are Useful
Sample or Client Characteristics
1. When participants are few and/or uniquely different, so pooling together may obscure important differences.
2. When clients are atypical, so are not well represented in normative samples of standardized assessments.
3. When clients have limited response repertoires or low attention abilities, so standardized assessment procedures are of questionable validity.
Clinical or Research Issue
1. When one extensive assessment may have doubtful validity, and periodic, shorter probes would be more credible.
2. When participant performance shows considerable variability over time, from day-to-day or week-to-week.
3. When short-term and medium-term client improvements are of interest and expected.
4. When the concern is about the process of learning or development, styles, etc., rather than outcomes alone.
5. When formative evaluation data are needed to inform further development of an intervention or program.
6. When the amount, intensity, or type of intervention can be varied to an optimum level to better meet individual client needs.
7. When participants are likely to respond to an intervention at different rates, or with different trajectories, curves, profiles, etc.
8. When the focus is on typical daily performance rather than on capacity or aptitude, e.g., habits, addictions, tolerances, social interactions,
9. When the "ecological validity" of measurement is very important.
10. When events or behaviors over the recent past are important, and yet their recall retrospectively would be inaccurate.
11. When the interest is in the relationship between two behavioral measures over time (cross-correlation).
12. When the interest is in the sequence of behavioral measures over time (lag-sequential conditional probability analysis).
13. When the interest is in contingent relationships between events and behaviors over time (ordinal contingency analysis).
14. When atypical results (e.g., amount of improvement or qualitative pattern of improvement) from individual subjects could be washed out in group
dence Intervals box. The output will list the Phi
under the columntitled Estimated Value, and the confidence intervals will be listed
Within NCSS 2007, select Analysis, Regression/Correlation,
next to it. Using the Confidence Intervals tab, one may set the
Logistic Regression. Enter phase variable as dependent variable
range of the confidence intervals the program produces. One may
and the variable for treatment score as Numeric Independent
also use the Chi-square Effect Size Estimator found under Anal-
Variable (assuming it is continuous). Under the Response Analysis
ysis, Descriptive Statistics, Contingency Tables. When the classi-
Section in the output, you will find the % Correctly Classified, look
fication table is entered in the cell boxes, the program produces the
in the row titled Total, for the overall % of correctly classified data
chi-square, effect size (Phi
), and the probability level. Following
points. In the output under the section titled Classification Table
these directions should give one all the necessary output to report
are the values you will enter into the Proportions –Two Indepen-
dent analysis, which is listed under Analysis, Proportions. Makesure you enter the values from the classification table correctly into
Received December 31, 2007
the cells for the proportions test. Select Difference in the Statistics
Revision received June 3, 2008
box and Exact (although a Bootstrap is available) in the Confi-
Accepted June 5, 2008 䡲
Berichte Silmaril 2009 4. Bericht: 19. August bis 25. November 2009 von Svolvær 68° 14.4'N, 14°34.4'E bis Litlebergen 60 32.3'N, 5°14.2'E mit Unterbruch von zwei Reisen in die Schweiz Am 11. August starb Alexs Mutter, Hanny. Wir haben für sie eine sehr familiäre und schöne Abschiedsfeier in der Kirche in Interlaken erleben dürfen. Die ganze Familie und viele Freunde und Bekannte von Hanny sind angereist. Wir hatten ein gutes Gefühl, bald nach der Beerdigung wieder abzureisen. Am Mittwoch, 19. August reisten wir zusammen mit Renzo in aller Herrgottsfrühe wieder nach Svolvær ab. Tagwacht um 04:20, Fahrt per Auto zum Flughafen Zürich, Abflug nach Stockholm, nach Stunden Weiterflug nach Oslo, dann recht zügig Oslo-Bodø und schlussendlich Bodø-Svolvær. Die Flugzeuge wurden immer kleiner, ab Oslo waren wir mit Propellerflugzeugen unterwegs. Die letzte Strecke war sagenhaft eindrücklich, das Wetter perfekt und die Flughöhe so tief, dass jedes Schaf (Grössenangabe!) auf den vielen kleinen Inseln im blauen Wasser zu sehen gewesen wäre. Gesehen haben wir allerdings keine. Todmüde nach 16 Stunden Reise kamen wir bei Silmaril an, machten aber trotzdem noch klar Schiff, damit wir am nächsten Tag früh aufbrechen konnten. Wir waren von Anfang an unter Zeitdruck, da wir die Rückreise in die Schweiz mit Renzo schon vor unserer überstürzten Rückkehr in die Schweiz am 12. August gebucht hatten. Wir wurden in der Schweiz auch erwartet. Ein Treffen mit Freunden und eine Klassenzusammenkunft waren seit Monaten geplant. Wir mussten die Strecke nach Ålesund bis zum 28. August schaffen. Am 29. sollten wir fliegen.
UNIVERSITY OF MAIDUGURI Maiduguri, Nigeria CENTRE FOR DISTANCE LEARNING HED 207 DRUG AND ALCOHOL EDUCATION UNIT: 2 DRUG AND ALCOHOL EDUCATION Published 2010© Al rights reserved. No part of this work may be reproduced in any form, by mimeograph or any other means without prior permission in writing from the University of Maiduguri. This text forms part of the learning package for the academic programme of the Centre for Distance Learning, University of Maiduguri. Further enquiries should be directed to the: Coordinator Centre for Distance Learning University of Maiduguri P. M. B. 1069 Maiduguri, Nigeria. This text is being published by the authority of the Senate, University of Maiduguri, Maiduguri – Nigeria. ISBN: