what is single case study methodology

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Single-Case Design, Analysis, and Quality Assessment for Intervention Research

Michele a. lobo.

1 Biomechanics & Movement Science Program, Department of Physical Therapy, University of Delaware, Newark, DE, USA

Mariola Moeyaert

2 Division of Educational Psychology & Methodology, State University of New York at Albany, Albany, NY, USA

Andrea Baraldi Cunha

Iryna babik, background and purpose.

The purpose of this article is to describe single-case studies, and contrast them with case studies and randomized clinical trials. We will highlight current research designs, analysis techniques, and quality appraisal tools relevant for single-case rehabilitation research.

Summary of Key Points

Single-case studies can provide a viable alternative to large group studies such as randomized clinical trials. Single case studies involve repeated measures, and manipulation of and independent variable. They can be designed to have strong internal validity for assessing causal relationships between interventions and outcomes, and external validity for generalizability of results, particularly when the study designs incorporate replication, randomization, and multiple participants. Single case studies should not be confused with case studies/series (ie, case reports), which are reports of clinical management of one patient or a small series of patients.

Recommendations for Clinical Practice

When rigorously designed, single-case studies can be particularly useful experimental designs in a variety of situations, even when researcher resources are limited, studied conditions have low incidences, or when examining effects of novel or expensive interventions. Readers will be directed to examples from the published literature in which these techniques have been discussed, evaluated for quality, and implemented.

Introduction

The purpose of this article is to present current tools and techniques relevant for single-case rehabilitation research. Single-case (SC) studies have been identified by a variety of names, including “n of 1 studies” and “single-subject” studies. The term “single-case study” is preferred over the previously mentioned terms because previous terms suggest these studies include only one participant. In fact, as will be discussed below, for purposes of replication and improved generalizability, the strongest SC studies commonly include more than one participant.

A SC study should not be confused with a “case study/series “ (also called “case report”. In a typical case study/series, a single patient or small series of patients is involved, but there is not a purposeful manipulation of an independent variable, nor are there necessarily repeated measures. Most case studies/series are reported in a narrative way while results of SC studies are presented numerically or graphically. 1 , 2 This article defines SC studies, contrasts them with randomized clinical trials, discusses how they can be used to scientifically test hypotheses, and highlights current research designs, analysis techniques, and quality appraisal tools that may be useful for rehabilitation researchers.

In SC studies, measurements of outcome (dependent variables) are recorded repeatedly for individual participants across time and varying levels of an intervention (independent variables). 1 – 5 These varying levels of intervention are referred to as “phases” with one phase serving as a baseline or comparison, so each participant serves as his/her own control. 2 In contrast to case studies and case series in which participants are observed across time without experimental manipulation of the independent variable, SC studies employ systematic manipulation of the independent variable to allow for hypothesis testing. 1 , 6 As a result, SC studies allow for rigorous experimental evaluation of intervention effects and provide a strong basis for establishing causal inferences. Advances in design and analysis techniques for SC studies observed in recent decades have made SC studies increasingly popular in educational and psychological research. Yet, the authors believe SC studies have been undervalued in rehabilitation research, where randomized clinical trials (RCTs) are typically recommended as the optimal research design to answer questions related to interventions. 7 In reality, there are advantages and disadvantages to both SC studies and RCTs that should be carefully considered in order to select the best design to answer individual research questions. While there are a variety of other research designs that could be utilized in rehabilitation research, only SC studies and RCTs are discussed here because SC studies are the focus of this article and RCTs are the most highly recommended design for intervention studies. 7

When designed and conducted properly, RCTs offer strong evidence that changes in outcomes may be related to provision of an intervention. However, RCTs require monetary, time, and personnel resources that many researchers, especially those in clinical settings, may not have available. 8 RCTs also require access to large numbers of consenting participants that meet strict inclusion and exclusion criteria that can limit variability of the sample and generalizability of results. 9 The requirement for large participant numbers may make RCTs difficult to perform in many settings, such as rural and suburban settings, and for many populations, such as those with diagnoses marked by lower prevalence. 8 To rely exclusively on RCTs has the potential to result in bodies of research that are skewed to address the needs of some individuals while neglecting the needs of others. RCTs aim to include a large number of participants and to use random group assignment to create study groups that are similar to one another in terms of all potential confounding variables, but it is challenging to identify all confounding variables. Finally, the results of RCTs are typically presented in terms of group means and standard deviations that may not represent true performance of any one participant. 10 This can present as a challenge for clinicians aiming to translate and implement these group findings at the level of the individual.

SC studies can provide a scientifically rigorous alternative to RCTs for experimentally determining the effectiveness of interventions. 1 , 2 SC studies can assess a variety of research questions, settings, cases, independent variables, and outcomes. 11 There are many benefits to SC studies that make them appealing for intervention research. SC studies may require fewer resources than RCTs and can be performed in settings and with populations that do not allow for large numbers of participants. 1 , 2 In SC studies, each participant serves as his/her own comparison, thus controlling for many confounding variables that can impact outcome in rehabilitation research, such as gender, age, socioeconomic level, cognition, home environment, and concurrent interventions. 2 , 11 Results can be analyzed and presented to determine whether interventions resulted in changes at the level of the individual, the level at which rehabilitation professionals intervene. 2 , 12 When properly designed and executed, SC studies can demonstrate strong internal validity to determine the likelihood of a causal relationship between the intervention and outcomes and external validity to generalize the findings to broader settings and populations. 2 , 12 , 13

Single Case Research Designs for Intervention Research

There are a variety of SC designs that can be used to study the effectiveness of interventions. Here we discuss: 1) AB designs, 2) reversal designs, 3) multiple baseline designs, and 4) alternating treatment designs, as well as ways replication and randomization techniques can be used to improve internal validity of all of these designs. 1 – 3 , 12 – 14

The simplest of these designs is the AB Design 15 ( Figure 1 ). This design involves repeated measurement of outcome variables throughout a baseline control/comparison phase (A ) and then throughout an intervention phase (B). When possible, it is recommended that a stable level and/or rate of change in performance be observed within the baseline phase before transitioning into the intervention phase. 2 As with all SC designs, it is also recommended that there be a minimum of five data points in each phase. 1 , 2 There is no randomization or replication of the baseline or intervention phases in the basic AB design. 2 Therefore, AB designs have problems with internal validity and generalizability of results. 12 They are weak in establishing causality because changes in outcome variables could be related to a variety of other factors, including maturation, experience, learning, and practice effects. 2 , 12 Sample data from a single case AB study performed to assess the impact of Floor Play intervention on social interaction and communication skills for a child with autism 15 are shown in Figure 1 .

An example of results from a single-case AB study conducted on one participant with autism; two weeks of observation (baseline phase A) were followed by seven weeks of Floor Time Play (intervention phase B). The outcome measure Circles of Communications (reciprocal communication with two participants responding to each other verbally or nonverbally) served as a behavioral indicator of the child’s social interaction and communication skills (higher scores indicating better performance). A statistically significant improvement in Circles of Communication was found during the intervention phase as compared to the baseline. Note that although a stable baseline is recommended for SC studies, it is not always possible to satisfy this requirement, as you will see in Figures 1 – 4 . Data were extracted from Dionne and Martini (2011) 15 utilizing Rohatgi’s WebPlotDigitizer software. 78

If an intervention does not have carry-over effects, it is recommended to use a Reversal Design . 2 For example, a reversal A 1 BA 2 design 16 ( Figure 2 ) includes alternation of the baseline and intervention phases, whereas a reversal A 1 B 1 A 2 B 2 design 17 ( Figure 3 ) consists of alternation of two baseline (A 1 , A 2 ) and two intervention (B 1 , B 2 ) phases. Incorporating at least four phases in the reversal design (i.e., A 1 B 1 A 2 B 2 or A 1 B 1 A 2 B 2 A 3 B 3 …) allows for a stronger determination of a causal relationship between the intervention and outcome variables, because the relationship can be demonstrated across at least three different points in time – change in outcome from A 1 to B 1 , from B 1 to A 2 , and from A 2 to B 2 . 18 Before using this design, however, researchers must determine that it is safe and ethical to withdraw the intervention, especially in cases where the intervention is effective and necessary. 12

An example of results from a single-case A 1 BA 2 study conducted on eight participants with stable multiple sclerosis (data on three participants were used for this example). Four weeks of observation (baseline phase A 1 ) were followed by eight weeks of core stability training (intervention phase B), then another four weeks of observation (baseline phase A 2 ). Forward functional reach test (the maximal distance the participant can reach forward or lateral beyond arm’s length, maintaining a fixed base of support in the standing position; higher scores indicating better performance) significantly improved during intervention for Participants 1 and 3 without further improvement observed following withdrawal of the intervention (during baseline phase A 2 ). Data were extracted from Freeman et al. (2010) 16 utilizing Rohatgi’s WebPlotDigitizer software. 78

An example of results from a single-case A 1 B 1 A 2 B 2 study conducted on two participants with severe unilateral neglect after a right-hemisphere stroke. Two weeks of conventional treatment (baseline phases A 1, A 2 ) alternated with two weeks of visuo-spatio-motor cueing (intervention phases B 1 , B 2 ). Performance was assessed in two tests of lateral neglect, the Bells Cancellation Test (Figure A; lower scores indicating better performance) and the Line Bisection Test (Figure B; higher scores indicating better performance). There was a statistically significant intervention-related improvement in participants’ performance on the Line Bisection Test, but not on the Bells Test. Data were extracted from Samuel at al. (2000) 17 utilizing Rohatgi’s WebPlotDigitizer software. 78

A recent study used an ABA reversal SC study to determine the effectiveness of core stability training in 8 participants with multiple sclerosis. 16 During the first four weekly data collections, the researchers ensured a stable baseline, which was followed by eight weekly intervention data points, and concluded with four weekly withdrawal data points. Intervention significantly improved participants’ walking and reaching performance ( Figure 2 ). 16 This A 1 BA 2 design could have been strengthened by the addition of a second intervention phase for replication (A 1 B 1 A 2 B 2 ). For instance, a single-case A 1 B 1 A 2 B 2 withdrawal design aimed to assess the efficacy of rehabilitation using visuo-spatio-motor cueing for two participants with severe unilateral neglect after a severe right-hemisphere stroke. 17 Each phase included 8 data points. Statistically significant intervention-related improvement was observed, suggesting that visuo-spatio-motor cueing might be promising for treating individuals with very severe neglect ( Figure 3 ). 17

The reversal design can also incorporate a cross over design where each participant experiences more than one type of intervention. For instance, a B 1 C 1 B 2 C 2 design could be used to study the effects of two different interventions (B and C) on outcome measures. Challenges with including more than one intervention involve potential carry-over effects from earlier interventions and order effects that may impact the measured effectiveness of the interventions. 2 , 12 Including multiple participants and randomizing the order of intervention phase presentations are tools to help control for these types of effects. 19

When an intervention permanently changes an individual’s ability, a return to baseline performance is not feasible and reversal designs are not appropriate. Multiple Baseline Designs (MBDs) are useful in these situations ( Figure 4 ). 20 MBDs feature staggered introduction of the intervention across time: each participant is randomly assigned to one of at least 3 experimental conditions characterized by the length of the baseline phase. 21 These studies involve more than one participant, thus functioning as SC studies with replication across participants. Staggered introduction of the intervention allows for separation of intervention effects from those of maturation, experience, learning, and practice. For example, a multiple baseline SC study was used to investigate the effect of an anti-spasticity baclofen medication on stiffness in five adult males with spinal cord injury. 20 The subjects were randomly assigned to receive 5–9 baseline data points with a placebo treatment prior to the initiation of the intervention phase with the medication. Both participants and assessors were blind to the experimental condition. The results suggested that baclofen might not be a universal treatment choice for all individuals with spasticity resulting from a traumatic spinal cord injury ( Figure 4 ). 20

An example of results from a single-case multiple baseline study conducted on five participants with spasticity due to traumatic spinal cord injury. Total duration of data collection was nine weeks. The first participant was switched from placebo treatment (baseline) to baclofen treatment (intervention) after five data collection sessions, whereas each consecutive participant was switched to baclofen intervention at the subsequent sessions through the ninth session. There was no statistically significant effect of baclofen on viscous stiffness at the ankle joint. Data were extracted from Hinderer at al. (1990) 20 utilizing Rohatgi’s WebPlotDigitizer software. 78

The impact of two or more interventions can also be assessed via Alternating Treatment Designs (ATDs) . In ATDs, after establishing the baseline, the experimenter exposes subjects to different intervention conditions administered in close proximity for equal intervals ( Figure 5 ). 22 ATDs are prone to “carry-over effects” when the effects of one intervention influence the observed outcomes of another intervention. 1 As a result, such designs introduce unique challenges when attempting to determine the effects of any one intervention and have been less commonly utilized in rehabilitation. An ATD was used to monitor disruptive behaviors in the school setting throughout a baseline followed by an alternating treatment phase with randomized presentation of a control condition or an exercise condition. 23 Results showed that 30 minutes of moderate to intense physical activity decreased behavioral disruptions through 90 minutes after the intervention. 23 An ATD was also used to compare the effects of commercially available and custom-made video prompts on the performance of multi-step cooking tasks in four participants with autism. 22 Results showed that participants independently performed more steps with the custom-made video prompts ( Figure 5 ). 22

An example of results from a single case alternating treatment study conducted on four participants with autism (data on two participants were used for this example). After the observation phase (baseline), effects of commercially available and custom-made video prompts on the performance of multi-step cooking tasks were identified (treatment phase), after which only the best treatment was used (best treatment phase). Custom-made video prompts were most effective for improving participants’ performance of multi-step cooking tasks. Data were extracted from Mechling at al. (2013) 22 utilizing Rohatgi’s WebPlotDigitizer software. 78

Regardless of the SC study design, replication and randomization should be incorporated when possible to improve internal and external validity. 11 The reversal design is an example of replication across study phases. The minimum number of phase replications needed to meet quality standards is three (A 1 B 1 A 2 B 2 ), but having four or more replications is highly recommended (A 1 B 1 A 2 B 2 A 3 …). 11 , 14 In cases when interventions aim to produce lasting changes in participants’ abilities, replication of findings may be demonstrated by replicating intervention effects across multiple participants (as in multiple-participant AB designs), or across multiple settings, tasks, or service providers. When the results of an intervention are replicated across multiple reversals, participants, and/or contexts, there is an increased likelihood a causal relationship exists between the intervention and the outcome. 2 , 12

Randomization should be incorporated in SC studies to improve internal validity and the ability to assess for causal relationships among interventions and outcomes. 11 In contrast to traditional group designs, SC studies often do not have multiple participants or units that can be randomly assigned to different intervention conditions. Instead, in randomized phase-order designs , the sequence of phases is randomized. Simple or block randomization is possible. For example, with simple randomization for an A 1 B 1 A 2 B 2 design, the A and B conditions are treated as separate units and are randomly assigned to be administered for each of the pre-defined data collection points. As a result, any combination of A-B sequences is possible without restrictions on the number of times each condition is administered or regard for repetitions of conditions (e.g., A 1 B 1 B 2 A 2 B 3 B 4 B 5 A 3 B 6 A 4 A 5 A 6 ). With block randomization for an A 1 B 1 A 2 B 2 design, two conditions (e.g., A and B) would be blocked into a single unit (AB or BA), randomization of which to different time periods would ensure that each condition appears in the resulting sequence more than two times (e.g., A 1 B 1 B 2 A 2 A 3 B 3 A 4 B 4 ). Note that AB and reversal designs require that the baseline (A) always precedes the first intervention (B), which should be accounted for in the randomization scheme. 2 , 11

In randomized phase start-point designs , the lengths of the A and B phases can be randomized. 2 , 11 , 24 – 26 For example, for an AB design, researchers could specify the number of time points at which outcome data will be collected, (e.g., 20), define the minimum number of data points desired in each phase (e.g., 4 for A, 3 for B), and then randomize the initiation of the intervention so that it occurs anywhere between the remaining time points (points 5 and 17 in the current example). 27 , 28 For multiple-baseline designs, a dual-randomization, or “regulated randomization” procedure has been recommended. 29 If multiple-baseline randomization depends solely on chance, it could be the case that all units are assigned to begin intervention at points not really separated in time. 30 Such randomly selected initiation of the intervention would result in the drastic reduction of the discriminant and internal validity of the study. 29 To eliminate this issue, investigators should first specify appropriate intervals between the start points for different units, then randomly select from those intervals, and finally randomly assign each unit to a start point. 29

Single Case Analysis Techniques for Intervention Research

The What Works Clearinghouse (WWC) single-case design technical documentation provides an excellent overview of appropriate SC study analysis techniques to evaluate the effectiveness of intervention effects. 1 , 18 First, visual analyses are recommended to determine whether there is a functional relation between the intervention and the outcome. Second, if evidence for a functional effect is present, the visual analysis is supplemented with quantitative analysis methods evaluating the magnitude of the intervention effect. Third, effect sizes are combined across cases to estimate overall average intervention effects which contributes to evidence-based practice, theory, and future applications. 2 , 18

Visual Analysis

Traditionally, SC study data are presented graphically. When more than one participant engages in a study, a spaghetti plot showing all of their data in the same figure can be helpful for visualization. Visual analysis of graphed data has been the traditional method for evaluating treatment effects in SC research. 1 , 12 , 31 , 32 The visual analysis involves evaluating level, trend, and stability of the data within each phase (i.e., within-phase data examination) followed by examination of the immediacy of effect, consistency of data patterns, and overlap of data between baseline and intervention phases (i.e., between-phase comparisons). When the changes (and/or variability) in level are in the desired direction, are immediate, readily discernible, and maintained over time, it is concluded that the changes in behavior across phases result from the implemented treatment and are indicative of improvement. 33 Three demonstrations of an intervention effect are necessary for establishing a functional relation. 1

Within-phase examination

Level, trend, and stability of the data within each phase are evaluated. Mean and/or median can be used to report the level, and trend can be evaluated by determining whether the data points are monotonically increasing or decreasing. Within-phase stability can be evaluated by calculating the percentage of data points within 15% of the phase median (or mean). The stability criterion is satisfied if about 85% (80% – 90%) of the data in a phase fall within a 15% range of the median (or average) of all data points for that phase. 34

Between-phase examination

Immediacy of effect, consistency of data patterns, and overlap of data between baseline and intervention phases are evaluated next. For this, several nonoverlap indices have been proposed that all quantify the proportion of measurements in the intervention phase not overlapping with the baseline measurements. 35 Nonoverlap statistics are typically scaled as percent from 0 to 100, or as a proportion from 0 to 1. Here, we briefly discuss the Nonoverlap of All Pairs ( NAP ), 36 the Extended Celeration Line ( ECL ), the Improvement Rate Difference ( IRD) , 37 and the TauU and the TauU-adjusted, TauU adj , 35 as these are the most recent and complete techniques. We also examine the Percentage of Nonoverlapping Data ( PND ) 38 and the Two Standard Deviations Band Method, as these are frequently used techniques. In addition, we include the Percentage of Nonoverlapping Corrected Data ( PNCD ) – an index applying to the PND after controlling for baseline trend. 39

Nonoverlap of all pairs (NAP)

Each baseline observation can be paired with each intervention phase observation to make n pairs (i.e., N = n A * n B ). Count the number of overlapping pairs, n o , counting all ties as 0.5. Then define the percent of the pairs that show no overlap. Alternatively, one can count the number of positive (P), negative (N), and tied (T) pairs 2 , 36 :

Extended Celeration Line (ECL)

ECL or split middle line allows control for a positive Phase A trend. Nonoverlap is defined as the proportion of Phase B ( n b ) data that are above the median trend plotted from Phase A data ( n B< sub > Above Median trend A </ sub > ), but then extended into Phase B: ECL = n B Above Median trend A n b ∗ 100

As a consequence, this method depends on a straight line and makes an assumption of linearity in the baseline. 2 , 12

Improvement rate difference (IRD)

This analysis is conceptualized as the difference in improvement rates (IR) between baseline ( IR B ) and intervention phases ( IR T ). 38 The IR for each phase is defined as the number of “improved data points” divided by the total data points in that phase. IRD, commonly employed in medical group research under the name of “risk reduction” or “risk difference” attempts to provide an intuitive interpretation for nonoverlap and to make use of an established, respected effect size, IR B - IR B , or the difference between two proportions. 37

TauU and TauU adj

Each baseline observation can be paired with each intervention phase observation to make n pairs (i.e., n = n A * n B ). Count the number of positive (P), negative (N), and tied (T) pairs, and use the following formula: TauU = P - N P + N + τ

The TauU adj is an adjustment of TauU for monotonic trend in baseline. Each baseline observation can be paired with each intervention phase observation to make n pairs (i.e., n = n A * n B ). Each baseline observation can be paired with all later baseline observations (n A *(n A -1)/2). 2 , 35 Then the baseline trend can be computed: TauU adf = P - N - S trend P + N + τ ; S trend = P A – NA

Online calculators might assist researchers in obtaining the TauU and TauU adjusted coefficients ( http://www.singlecaseresearch.org/calculators/tau-u ).

Percentage of nonoverlapping data (PND)

If anticipating an increase in the outcome, locate the highest data point in the baseline phase and then calculate the percent of the intervention phase data points that exceed it. If anticipating a decrease in the outcome, find the lowest data point in the baseline phase and then calculate the percent of the treatment phase data points that are below it: PND = n B Overlap A n b ∗ 100 . A PND < 50 would mark no observed effect, PND = 50–70 signifies a questionable effect, and PND > 70 suggests the intervention was effective. 40 The percentage of nonoverlapping (PNDC) corrected was proposed in 2009 as an extension of the PND. 39 Prior to applying the PND, a data correction procedure is applied eliminating pre-existing baseline trend. 38

Two Standard Deviation Band Method

When the stability criterion described above is met within phases, it is possible to apply the two standard deviation band method. 12 , 41 First, the mean of the data for a specific condition is calculated and represented with a solid line. In the next step, the standard deviation of the same data is computed and two dashed lines are represented: one located two standard deviations above the mean and the other – two standard deviations below. For normally distributed data, few points (less than 5%) are expected to be outside the two standard deviation bands if there is no change in the outcome score due to the intervention. However, this method is not considered a formal statistical procedure, as the data cannot typically be assumed to be normal, continuous, or independent. 41

Statistical Analysis

If the visual analysis indicates a functional relationship (i.e., three demonstrations of the effectiveness of the intervention effect), it is recommended to proceed with the quantitative analyses, reflecting the magnitude of the intervention effect. First, effect sizes are calculated for each participant (individual-level analysis). Moreover, if the research interest lies in the generalizability of the effect size across participants, effect sizes can be combined across cases to achieve an overall average effect size estimate (across-case effect size).

Note that quantitative analysis methods are still being developed in the domain of SC research 1 and statistical challenges of producing an acceptable measure of treatment effect remain. 14 , 42 , 43 Therefore, the WWC standards strongly recommend conducting sensitivity analysis and reporting multiple effect size estimators. If consistency across different effect size estimators is identified, there is stronger evidence for the effectiveness of the treatment. 1 , 18

Individual-level effect size analysis

The most common effect sizes recommended for SC analysis are: 1) standardized mean difference Cohen’s d ; 2) standardized mean difference with correction for small sample sizes Hedges’ g ; and 3) the regression-based approach which has the most potential and is strongly recommended by the WWC standards. 1 , 44 , 45 Cohen’s d can be calculated using following formula: d = X A ¯ - X B ¯ s p , with X A ¯ being the baseline mean, X B ¯ being the treatment mean, and s p indicating the pooled within-case standard deviation. Hedges’ g is an extension of Cohen’s d , recommended in the context of SC studies as it corrects for small sample sizes. The piecewise regression-based approach does not only reflect the immediate intervention effect, but also the intervention effect across time:

i stands for the measurement occasion ( i = 0, 1,… I ). The dependent variable is regressed on a time indicator, T , which is centered around the first observation of the intervention phase, D , a dummy variable for the intervention phase, and an interaction term of these variables. The equation shows that the expected score, Ŷ i , equals β 0 + β 1 T i in the baseline phase, and ( β 0 + β 2 ) + ( β 1 + β 3 ) T i in the intervention phase. β 0 , therefore, indicates the expected baseline level at the start of the intervention phase (when T = 0), whereas β 1 marks the linear time trend in the baseline scores. The coefficient β 2 can then be interpreted as an immediate effect of the intervention on the outcome, whereas β 3 signifies the effect of the intervention across time. The e i ’s are residuals assumed to be normally distributed around a mean of zero with a variance of σ e 2 . The assumption of independence of errors is usually not met in the context of SC studies because repeated measures are obtained within a person. As a consequence, it can be the case that the residuals are autocorrelated, meaning that errors closer in time are more related to each other compared to errors further away in time. 46 – 48 As a consequence, a lag-1 autocorrelation is appropriate (taking into account the correlation between two consecutive errors: e i and e i –1 ; for more details see Verbeke & Molenberghs, (2000). 49 In Equation 1 , ρ indicates the autocorrelation parameter. If ρ is positive, the errors closer in time are more similar; if ρ is negative, the errors closer in time are more different, and if ρ equals zero, there is no correlation between the errors.

Across-case effect sizes

Two-level modeling to estimate the intervention effects across cases can be used to evaluate across-case effect sizes. 44 , 45 , 50 Multilevel modeling is recommended by the WWC standards because it takes the hierarchical nature of SC studies into account: measurements are nested within cases and cases, in turn, are nested within studies. By conducting a multilevel analysis, important research questions can be addressed (which cannot be answered by single-level analysis of SC study data), such as: 1) What is the magnitude of the average treatment effect across cases? 2) What is the magnitude and direction of the case-specific intervention effect? 3) How much does the treatment effect vary within cases and across cases? 4) Does a case and/or study level predictor influence the treatment’s effect? The two-level model has been validated in previous research using extensive simulation studies. 45 , 46 , 51 The two-level model appears to have sufficient power (> .80) to detect large treatment effects in at least six participants with six measurements. 21

Furthermore, to estimate the across-case effect sizes, the HPS (Hedges, Pustejovsky, and Shadish) , or single-case educational design ( SCEdD)-specific mean difference, index can be calculated. 52 This is a standardized mean difference index specifically designed for SCEdD data, with the aim of making it comparable to Cohen’s d of group-comparison designs. The standard deviation takes into account both within-participant and between-participant variability, and is typically used to get an across-case estimator for a standardized change in level. The advantage of using the HPS across-case effect size estimator is that it is directly comparable with Cohen’s d for group comparison research, thus enabling the use of Cohen’s (1988) benchmarks. 53

Valuable recommendations on SC data analyses have recently been provided. 54 , 55 They suggest that a specific SC study data analytic technique can be chosen based on: (1) the study aims and the desired quantification (e.g., overall quantification, between-phase quantifications, randomization, etc.), (2) the data characteristics as assessed by visual inspection and the assumptions one is willing to make about the data, and (3) the knowledge and computational resources. 54 , 55 Table 1 lists recommended readings and some commonly used resources related to the design and analysis of single-case studies.

Recommend readings and resources related to the design and analysis of single-case studies.

Quality Appraisal Tools for Single-Case Design Research

Quality appraisal tools are important to guide researchers in designing strong experiments and conducting high-quality systematic reviews of the literature. Unfortunately, quality assessment tools for SC studies are relatively novel, ratings across tools demonstrate variability, and there is currently no “gold standard” tool. 56 Table 2 lists important SC study quality appraisal criteria compiled from the most common scales; when planning studies or reviewing the literature, we recommend readers consider these criteria. Table 3 lists some commonly used SC quality assessment and reporting tools and references to resources where the tools can be located.

Summary of important single-case study quality appraisal criteria.

Quality assessment and reporting tools related to single-case studies.

When an established tool is required for systematic review, we recommend use of the What Works Clearinghouse (WWC) Tool because it has well-defined criteria and is developed and supported by leading experts in the SC research field in association with the Institute of Education Sciences. 18 The WWC documentation provides clear standards and procedures to evaluate the quality of SC research; it assesses the internal validity of SC studies, classifying them as “Meeting Standards”, “Meeting Standards with Reservations”, or “Not Meeting Standards”. 1 , 18 Only studies classified in the first two categories are recommended for further visual analysis. Also, WWC evaluates the evidence of effect, classifying studies into “Strong Evidence of a Causal Relation”, “Moderate Evidence of a Causal Relation”, or “No Evidence of a Causal Relation”. Effect size should only be calculated for studies providing strong or moderate evidence of a causal relation.

The Single-Case Reporting Guideline In BEhavioural Interventions (SCRIBE) 2016 is another useful SC research tool developed recently to improve the quality of single-case designs. 57 SCRIBE consists of a 26-item checklist that researchers need to address while reporting the results of SC studies. This practical checklist allows for critical evaluation of SC studies during study planning, manuscript preparation, and review.

Single-case studies can be designed and analyzed in a rigorous manner that allows researchers strength in assessing causal relationships among interventions and outcomes, and in generalizing their results. 2 , 12 These studies can be strengthened via incorporating replication of findings across multiple study phases, participants, settings, or contexts, and by using randomization of conditions or phase lengths. 11 There are a variety of tools that can allow researchers to objectively analyze findings from SC studies. 56 While a variety of quality assessment tools exist for SC studies, they can be difficult to locate and utilize without experience, and different tools can provide variable results. The WWC quality assessment tool is recommended for those aiming to systematically review SC studies. 1 , 18

SC studies, like all types of study designs, have a variety of limitations. First, it can be challenging to collect at least five data points in a given study phase. This may be especially true when traveling for data collection is difficult for participants, or during the baseline phase when delaying intervention may not be safe or ethical. Power in SC studies is related to the number of data points gathered for each participant so it is important to avoid having a limited number of data points. 12 , 58 Second, SC studies are not always designed in a rigorous manner and, thus, may have poor internal validity. This limitation can be overcome by addressing key characteristics that strengthen SC designs ( Table 2 ). 1 , 14 , 18 Third, SC studies may have poor generalizability. This limitation can be overcome by including a greater number of participants, or units. Fourth, SC studies may require consultation from expert methodologists and statisticians to ensure proper study design and data analysis, especially to manage issues like autocorrelation and variability of data. 2 Fifth, while it is recommended to achieve a stable level and rate of performance throughout the baseline, human performance is quite variable and can make this requirement challenging. Finally, the most important validity threat to SC studies is maturation. This challenge must be considered during the design process in order to strengthen SC studies. 1 , 2 , 12 , 58

SC studies can be particularly useful for rehabilitation research. They allow researchers to closely track and report change at the level of the individual. They may require fewer resources and, thus, can allow for high-quality experimental research, even in clinical settings. Furthermore, they provide a tool for assessing causal relationships in populations and settings where large numbers of participants are not accessible. For all of these reasons, SC studies can serve as an effective method for assessing the impact of interventions.

Acknowledgments

This research was supported by the National Institute of Health, Eunice Kennedy Shriver National Institute of Child Health & Human Development (1R21HD076092-01A1, Lobo PI) and the Delaware Economic Development Office (Grant #109).

Some of the information in this manuscript was presented at the IV Step Meeting in Columbus, OH, June 2016.

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Case Study – Methods, Examples and Guide

Table of Contents

A case study is a research method that involves an in-depth examination and analysis of a particular phenomenon or case, such as an individual, organization, community, event, or situation.

It is a qualitative research approach that aims to provide a detailed and comprehensive understanding of the case being studied. Case studies typically involve multiple sources of data, including interviews, observations, documents, and artifacts, which are analyzed using various techniques, such as content analysis, thematic analysis, and grounded theory. The findings of a case study are often used to develop theories, inform policy or practice, or generate new research questions.

Types of Case Study

Types and Methods of Case Study are as follows:

Single-Case Study

A single-case study is an in-depth analysis of a single case. This type of case study is useful when the researcher wants to understand a specific phenomenon in detail.

For Example , A researcher might conduct a single-case study on a particular individual to understand their experiences with a particular health condition or a specific organization to explore their management practices. The researcher collects data from multiple sources, such as interviews, observations, and documents, and uses various techniques to analyze the data, such as content analysis or thematic analysis. The findings of a single-case study are often used to generate new research questions, develop theories, or inform policy or practice.

Multiple-Case Study

A multiple-case study involves the analysis of several cases that are similar in nature. This type of case study is useful when the researcher wants to identify similarities and differences between the cases.

For Example, a researcher might conduct a multiple-case study on several companies to explore the factors that contribute to their success or failure. The researcher collects data from each case, compares and contrasts the findings, and uses various techniques to analyze the data, such as comparative analysis or pattern-matching. The findings of a multiple-case study can be used to develop theories, inform policy or practice, or generate new research questions.

Exploratory Case Study

An exploratory case study is used to explore a new or understudied phenomenon. This type of case study is useful when the researcher wants to generate hypotheses or theories about the phenomenon.

For Example, a researcher might conduct an exploratory case study on a new technology to understand its potential impact on society. The researcher collects data from multiple sources, such as interviews, observations, and documents, and uses various techniques to analyze the data, such as grounded theory or content analysis. The findings of an exploratory case study can be used to generate new research questions, develop theories, or inform policy or practice.

Descriptive Case Study

A descriptive case study is used to describe a particular phenomenon in detail. This type of case study is useful when the researcher wants to provide a comprehensive account of the phenomenon.

For Example, a researcher might conduct a descriptive case study on a particular community to understand its social and economic characteristics. The researcher collects data from multiple sources, such as interviews, observations, and documents, and uses various techniques to analyze the data, such as content analysis or thematic analysis. The findings of a descriptive case study can be used to inform policy or practice or generate new research questions.

Instrumental Case Study

An instrumental case study is used to understand a particular phenomenon that is instrumental in achieving a particular goal. This type of case study is useful when the researcher wants to understand the role of the phenomenon in achieving the goal.

For Example, a researcher might conduct an instrumental case study on a particular policy to understand its impact on achieving a particular goal, such as reducing poverty. The researcher collects data from multiple sources, such as interviews, observations, and documents, and uses various techniques to analyze the data, such as content analysis or thematic analysis. The findings of an instrumental case study can be used to inform policy or practice or generate new research questions.

Case Study Data Collection Methods

Here are some common data collection methods for case studies:

Interviews involve asking questions to individuals who have knowledge or experience relevant to the case study. Interviews can be structured (where the same questions are asked to all participants) or unstructured (where the interviewer follows up on the responses with further questions). Interviews can be conducted in person, over the phone, or through video conferencing.

Observations

Observations involve watching and recording the behavior and activities of individuals or groups relevant to the case study. Observations can be participant (where the researcher actively participates in the activities) or non-participant (where the researcher observes from a distance). Observations can be recorded using notes, audio or video recordings, or photographs.

Documents can be used as a source of information for case studies. Documents can include reports, memos, emails, letters, and other written materials related to the case study. Documents can be collected from the case study participants or from public sources.

Surveys involve asking a set of questions to a sample of individuals relevant to the case study. Surveys can be administered in person, over the phone, through mail or email, or online. Surveys can be used to gather information on attitudes, opinions, or behaviors related to the case study.

Artifacts are physical objects relevant to the case study. Artifacts can include tools, equipment, products, or other objects that provide insights into the case study phenomenon.

How to conduct Case Study Research

Conducting a case study research involves several steps that need to be followed to ensure the quality and rigor of the study. Here are the steps to conduct case study research:

• Define the research questions: The first step in conducting a case study research is to define the research questions. The research questions should be specific, measurable, and relevant to the case study phenomenon under investigation.
• Select the case: The next step is to select the case or cases to be studied. The case should be relevant to the research questions and should provide rich and diverse data that can be used to answer the research questions.
• Collect data: Data can be collected using various methods, such as interviews, observations, documents, surveys, and artifacts. The data collection method should be selected based on the research questions and the nature of the case study phenomenon.
• Analyze the data: The data collected from the case study should be analyzed using various techniques, such as content analysis, thematic analysis, or grounded theory. The analysis should be guided by the research questions and should aim to provide insights and conclusions relevant to the research questions.
• Draw conclusions: The conclusions drawn from the case study should be based on the data analysis and should be relevant to the research questions. The conclusions should be supported by evidence and should be clearly stated.
• Validate the findings: The findings of the case study should be validated by reviewing the data and the analysis with participants or other experts in the field. This helps to ensure the validity and reliability of the findings.
• Write the report: The final step is to write the report of the case study research. The report should provide a clear description of the case study phenomenon, the research questions, the data collection methods, the data analysis, the findings, and the conclusions. The report should be written in a clear and concise manner and should follow the guidelines for academic writing.

Examples of Case Study

Here are some examples of case study research:

• The Hawthorne Studies : Conducted between 1924 and 1932, the Hawthorne Studies were a series of case studies conducted by Elton Mayo and his colleagues to examine the impact of work environment on employee productivity. The studies were conducted at the Hawthorne Works plant of the Western Electric Company in Chicago and included interviews, observations, and experiments.
• The Stanford Prison Experiment: Conducted in 1971, the Stanford Prison Experiment was a case study conducted by Philip Zimbardo to examine the psychological effects of power and authority. The study involved simulating a prison environment and assigning participants to the role of guards or prisoners. The study was controversial due to the ethical issues it raised.
• The Challenger Disaster: The Challenger Disaster was a case study conducted to examine the causes of the Space Shuttle Challenger explosion in 1986. The study included interviews, observations, and analysis of data to identify the technical, organizational, and cultural factors that contributed to the disaster.
• The Enron Scandal: The Enron Scandal was a case study conducted to examine the causes of the Enron Corporation’s bankruptcy in 2001. The study included interviews, analysis of financial data, and review of documents to identify the accounting practices, corporate culture, and ethical issues that led to the company’s downfall.
• The Fukushima Nuclear Disaster : The Fukushima Nuclear Disaster was a case study conducted to examine the causes of the nuclear accident that occurred at the Fukushima Daiichi Nuclear Power Plant in Japan in 2011. The study included interviews, analysis of data, and review of documents to identify the technical, organizational, and cultural factors that contributed to the disaster.

Application of Case Study

Case studies have a wide range of applications across various fields and industries. Here are some examples:

Business and Management

Case studies are widely used in business and management to examine real-life situations and develop problem-solving skills. Case studies can help students and professionals to develop a deep understanding of business concepts, theories, and best practices.

Case studies are used in healthcare to examine patient care, treatment options, and outcomes. Case studies can help healthcare professionals to develop critical thinking skills, diagnose complex medical conditions, and develop effective treatment plans.

Case studies are used in education to examine teaching and learning practices. Case studies can help educators to develop effective teaching strategies, evaluate student progress, and identify areas for improvement.

Social Sciences

Case studies are widely used in social sciences to examine human behavior, social phenomena, and cultural practices. Case studies can help researchers to develop theories, test hypotheses, and gain insights into complex social issues.

Law and Ethics

Case studies are used in law and ethics to examine legal and ethical dilemmas. Case studies can help lawyers, policymakers, and ethical professionals to develop critical thinking skills, analyze complex cases, and make informed decisions.

Purpose of Case Study

The purpose of a case study is to provide a detailed analysis of a specific phenomenon, issue, or problem in its real-life context. A case study is a qualitative research method that involves the in-depth exploration and analysis of a particular case, which can be an individual, group, organization, event, or community.

The primary purpose of a case study is to generate a comprehensive and nuanced understanding of the case, including its history, context, and dynamics. Case studies can help researchers to identify and examine the underlying factors, processes, and mechanisms that contribute to the case and its outcomes. This can help to develop a more accurate and detailed understanding of the case, which can inform future research, practice, or policy.

Case studies can also serve other purposes, including:

• Illustrating a theory or concept: Case studies can be used to illustrate and explain theoretical concepts and frameworks, providing concrete examples of how they can be applied in real-life situations.
• Developing hypotheses: Case studies can help to generate hypotheses about the causal relationships between different factors and outcomes, which can be tested through further research.
• Providing insight into complex issues: Case studies can provide insights into complex and multifaceted issues, which may be difficult to understand through other research methods.
• Informing practice or policy: Case studies can be used to inform practice or policy by identifying best practices, lessons learned, or areas for improvement.

Advantages of Case Study Research

There are several advantages of case study research, including:

• In-depth exploration: Case study research allows for a detailed exploration and analysis of a specific phenomenon, issue, or problem in its real-life context. This can provide a comprehensive understanding of the case and its dynamics, which may not be possible through other research methods.
• Rich data: Case study research can generate rich and detailed data, including qualitative data such as interviews, observations, and documents. This can provide a nuanced understanding of the case and its complexity.
• Holistic perspective: Case study research allows for a holistic perspective of the case, taking into account the various factors, processes, and mechanisms that contribute to the case and its outcomes. This can help to develop a more accurate and comprehensive understanding of the case.
• Theory development: Case study research can help to develop and refine theories and concepts by providing empirical evidence and concrete examples of how they can be applied in real-life situations.
• Practical application: Case study research can inform practice or policy by identifying best practices, lessons learned, or areas for improvement.
• Contextualization: Case study research takes into account the specific context in which the case is situated, which can help to understand how the case is influenced by the social, cultural, and historical factors of its environment.

Limitations of Case Study Research

There are several limitations of case study research, including:

• Limited generalizability : Case studies are typically focused on a single case or a small number of cases, which limits the generalizability of the findings. The unique characteristics of the case may not be applicable to other contexts or populations, which may limit the external validity of the research.
• Biased sampling: Case studies may rely on purposive or convenience sampling, which can introduce bias into the sample selection process. This may limit the representativeness of the sample and the generalizability of the findings.
• Subjectivity: Case studies rely on the interpretation of the researcher, which can introduce subjectivity into the analysis. The researcher’s own biases, assumptions, and perspectives may influence the findings, which may limit the objectivity of the research.
• Limited control: Case studies are typically conducted in naturalistic settings, which limits the control that the researcher has over the environment and the variables being studied. This may limit the ability to establish causal relationships between variables.
• Time-consuming: Case studies can be time-consuming to conduct, as they typically involve a detailed exploration and analysis of a specific case. This may limit the feasibility of conducting multiple case studies or conducting case studies in a timely manner.
• Resource-intensive: Case studies may require significant resources, including time, funding, and expertise. This may limit the ability of researchers to conduct case studies in resource-constrained settings.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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• Perspective
• Published: 22 November 2022

Single case studies are a powerful tool for developing, testing and extending theories

• Lyndsey Nickels   ORCID: orcid.org/0000-0002-0311-3524 1 , 2 ,
• Simon Fischer-Baum   ORCID: orcid.org/0000-0002-6067-0538 3 &
• Wendy Best   ORCID: orcid.org/0000-0001-8375-5916 4  

Nature Reviews Psychology volume  1 ,  pages 733–747 ( 2022 ) Cite this article

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• Neurological disorders

Psychology embraces a diverse range of methodologies. However, most rely on averaging group data to draw conclusions. In this Perspective, we argue that single case methodology is a valuable tool for developing and extending psychological theories. We stress the importance of single case and case series research, drawing on classic and contemporary cases in which cognitive and perceptual deficits provide insights into typical cognitive processes in domains such as memory, delusions, reading and face perception. We unpack the key features of single case methodology, describe its strengths, its value in adjudicating between theories, and outline its benefits for a better understanding of deficits and hence more appropriate interventions. The unique insights that single case studies have provided illustrate the value of in-depth investigation within an individual. Single case methodology has an important place in the psychologist’s toolkit and it should be valued as a primary research tool.

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The authors thank all of those pioneers of and advocates for single case study research who have mentored, inspired and encouraged us over the years, and the many other colleagues with whom we have discussed these issues.

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Nickels, L., Fischer-Baum, S. & Best, W. Single case studies are a powerful tool for developing, testing and extending theories. Nat Rev Psychol 1 , 733–747 (2022). https://doi.org/10.1038/s44159-022-00127-y

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The Advantages and Limitations of Single Case Study Analysis

As Andrew Bennett and Colin Elman have recently noted, qualitative research methods presently enjoy “an almost unprecedented popularity and vitality… in the international relations sub-field”, such that they are now “indisputably prominent, if not pre-eminent” (2010: 499). This is, they suggest, due in no small part to the considerable advantages that case study methods in particular have to offer in studying the “complex and relatively unstructured and infrequent phenomena that lie at the heart of the subfield” (Bennett and Elman, 2007: 171). Using selected examples from within the International Relations literature[1], this paper aims to provide a brief overview of the main principles and distinctive advantages and limitations of single case study analysis. Divided into three inter-related sections, the paper therefore begins by first identifying the underlying principles that serve to constitute the case study as a particular research strategy, noting the somewhat contested nature of the approach in ontological, epistemological, and methodological terms. The second part then looks to the principal single case study types and their associated advantages, including those from within the recent ‘third generation’ of qualitative International Relations (IR) research. The final section of the paper then discusses the most commonly articulated limitations of single case studies; while accepting their susceptibility to criticism, it is however suggested that such weaknesses are somewhat exaggerated. The paper concludes that single case study analysis has a great deal to offer as a means of both understanding and explaining contemporary international relations.

The term ‘case study’, John Gerring has suggested, is “a definitional morass… Evidently, researchers have many different things in mind when they talk about case study research” (2006a: 17). It is possible, however, to distil some of the more commonly-agreed principles. One of the most prominent advocates of case study research, Robert Yin (2009: 14) defines it as “an empirical enquiry that investigates a contemporary phenomenon in depth and within its real-life context, especially when the boundaries between phenomenon and context are not clearly evident”. What this definition usefully captures is that case studies are intended – unlike more superficial and generalising methods – to provide a level of detail and understanding, similar to the ethnographer Clifford Geertz’s (1973) notion of ‘thick description’, that allows for the thorough analysis of the complex and particularistic nature of distinct phenomena. Another frequently cited proponent of the approach, Robert Stake, notes that as a form of research the case study “is defined by interest in an individual case, not by the methods of inquiry used”, and that “the object of study is a specific, unique, bounded system” (2008: 443, 445). As such, three key points can be derived from this – respectively concerning issues of ontology, epistemology, and methodology – that are central to the principles of single case study research.

First, the vital notion of ‘boundedness’ when it comes to the particular unit of analysis means that defining principles should incorporate both the synchronic (spatial) and diachronic (temporal) elements of any so-called ‘case’. As Gerring puts it, a case study should be “an intensive study of a single unit… a spatially bounded phenomenon – e.g. a nation-state, revolution, political party, election, or person – observed at a single point in time or over some delimited period of time” (2004: 342). It is important to note, however, that – whereas Gerring refers to a single unit of analysis – it may be that attention also necessarily be given to particular sub-units. This points to the important difference between what Yin refers to as an ‘holistic’ case design, with a single unit of analysis, and an ’embedded’ case design with multiple units of analysis (Yin, 2009: 50-52). The former, for example, would examine only the overall nature of an international organization, whereas the latter would also look to specific departments, programmes, or policies etc.

Secondly, as Tim May notes of the case study approach, “even the most fervent advocates acknowledge that the term has entered into understandings with little specification or discussion of purpose and process” (2011: 220). One of the principal reasons for this, he argues, is the relationship between the use of case studies in social research and the differing epistemological traditions – positivist, interpretivist, and others – within which it has been utilised. Philosophy of science concerns are obviously a complex issue, and beyond the scope of much of this paper. That said, the issue of how it is that we know what we know – of whether or not a single independent reality exists of which we as researchers can seek to provide explanation – does lead us to an important distinction to be made between so-called idiographic and nomothetic case studies (Gerring, 2006b). The former refers to those which purport to explain only a single case, are concerned with particularisation, and hence are typically (although not exclusively) associated with more interpretivist approaches. The latter are those focused studies that reflect upon a larger population and are more concerned with generalisation, as is often so with more positivist approaches[2]. The importance of this distinction, and its relation to the advantages and limitations of single case study analysis, is returned to below.

Thirdly, in methodological terms, given that the case study has often been seen as more of an interpretivist and idiographic tool, it has also been associated with a distinctly qualitative approach (Bryman, 2009: 67-68). However, as Yin notes, case studies can – like all forms of social science research – be exploratory, descriptive, and/or explanatory in nature. It is “a common misconception”, he notes, “that the various research methods should be arrayed hierarchically… many social scientists still deeply believe that case studies are only appropriate for the exploratory phase of an investigation” (Yin, 2009: 6). If case studies can reliably perform any or all three of these roles – and given that their in-depth approach may also require multiple sources of data and the within-case triangulation of methods – then it becomes readily apparent that they should not be limited to only one research paradigm. Exploratory and descriptive studies usually tend toward the qualitative and inductive, whereas explanatory studies are more often quantitative and deductive (David and Sutton, 2011: 165-166). As such, the association of case study analysis with a qualitative approach is a “methodological affinity, not a definitional requirement” (Gerring, 2006a: 36). It is perhaps better to think of case studies as transparadigmatic; it is mistaken to assume single case study analysis to adhere exclusively to a qualitative methodology (or an interpretivist epistemology) even if it – or rather, practitioners of it – may be so inclined. By extension, this also implies that single case study analysis therefore remains an option for a multitude of IR theories and issue areas; it is how this can be put to researchers’ advantage that is the subject of the next section.

Having elucidated the defining principles of the single case study approach, the paper now turns to an overview of its main benefits. As noted above, a lack of consensus still exists within the wider social science literature on the principles and purposes – and by extension the advantages and limitations – of case study research. Given that this paper is directed towards the particular sub-field of International Relations, it suggests Bennett and Elman’s (2010) more discipline-specific understanding of contemporary case study methods as an analytical framework. It begins however, by discussing Harry Eckstein’s seminal (1975) contribution to the potential advantages of the case study approach within the wider social sciences.

Eckstein proposed a taxonomy which usefully identified what he considered to be the five most relevant types of case study. Firstly were so-called configurative-idiographic studies, distinctly interpretivist in orientation and predicated on the assumption that “one cannot attain prediction and control in the natural science sense, but only understanding ( verstehen )… subjective values and modes of cognition are crucial” (1975: 132). Eckstein’s own sceptical view was that any interpreter ‘simply’ considers a body of observations that are not self-explanatory and “without hard rules of interpretation, may discern in them any number of patterns that are more or less equally plausible” (1975: 134). Those of a more post-modernist bent, of course – sharing an “incredulity towards meta-narratives”, in Lyotard’s (1994: xxiv) evocative phrase – would instead suggest that this more free-form approach actually be advantageous in delving into the subtleties and particularities of individual cases.

Eckstein’s four other types of case study, meanwhile, promote a more nomothetic (and positivist) usage. As described, disciplined-configurative studies were essentially about the use of pre-existing general theories, with a case acting “passively, in the main, as a receptacle for putting theories to work” (Eckstein, 1975: 136). As opposed to the opportunity this presented primarily for theory application, Eckstein identified heuristic case studies as explicit theoretical stimulants – thus having instead the intended advantage of theory-building. So-called p lausibility probes entailed preliminary attempts to determine whether initial hypotheses should be considered sound enough to warrant more rigorous and extensive testing. Finally, and perhaps most notably, Eckstein then outlined the idea of crucial case studies , within which he also included the idea of ‘most-likely’ and ‘least-likely’ cases; the essential characteristic of crucial cases being their specific theory-testing function.

Whilst Eckstein’s was an early contribution to refining the case study approach, Yin’s (2009: 47-52) more recent delineation of possible single case designs similarly assigns them roles in the applying, testing, or building of theory, as well as in the study of unique cases[3]. As a subset of the latter, however, Jack Levy (2008) notes that the advantages of idiographic cases are actually twofold. Firstly, as inductive/descriptive cases – akin to Eckstein’s configurative-idiographic cases – whereby they are highly descriptive, lacking in an explicit theoretical framework and therefore taking the form of “total history”. Secondly, they can operate as theory-guided case studies, but ones that seek only to explain or interpret a single historical episode rather than generalise beyond the case. Not only does this therefore incorporate ‘single-outcome’ studies concerned with establishing causal inference (Gerring, 2006b), it also provides room for the more postmodern approaches within IR theory, such as discourse analysis, that may have developed a distinct methodology but do not seek traditional social scientific forms of explanation.

Applying specifically to the state of the field in contemporary IR, Bennett and Elman identify a ‘third generation’ of mainstream qualitative scholars – rooted in a pragmatic scientific realist epistemology and advocating a pluralistic approach to methodology – that have, over the last fifteen years, “revised or added to essentially every aspect of traditional case study research methods” (2010: 502). They identify ‘process tracing’ as having emerged from this as a central method of within-case analysis. As Bennett and Checkel observe, this carries the advantage of offering a methodologically rigorous “analysis of evidence on processes, sequences, and conjunctures of events within a case, for the purposes of either developing or testing hypotheses about causal mechanisms that might causally explain the case” (2012: 10).

Harnessing various methods, process tracing may entail the inductive use of evidence from within a case to develop explanatory hypotheses, and deductive examination of the observable implications of hypothesised causal mechanisms to test their explanatory capability[4]. It involves providing not only a coherent explanation of the key sequential steps in a hypothesised process, but also sensitivity to alternative explanations as well as potential biases in the available evidence (Bennett and Elman 2010: 503-504). John Owen (1994), for example, demonstrates the advantages of process tracing in analysing whether the causal factors underpinning democratic peace theory are – as liberalism suggests – not epiphenomenal, but variously normative, institutional, or some given combination of the two or other unexplained mechanism inherent to liberal states. Within-case process tracing has also been identified as advantageous in addressing the complexity of path-dependent explanations and critical junctures – as for example with the development of political regime types – and their constituent elements of causal possibility, contingency, closure, and constraint (Bennett and Elman, 2006b).

Bennett and Elman (2010: 505-506) also identify the advantages of single case studies that are implicitly comparative: deviant, most-likely, least-likely, and crucial cases. Of these, so-called deviant cases are those whose outcome does not fit with prior theoretical expectations or wider empirical patterns – again, the use of inductive process tracing has the advantage of potentially generating new hypotheses from these, either particular to that individual case or potentially generalisable to a broader population. A classic example here is that of post-independence India as an outlier to the standard modernisation theory of democratisation, which holds that higher levels of socio-economic development are typically required for the transition to, and consolidation of, democratic rule (Lipset, 1959; Diamond, 1992). Absent these factors, MacMillan’s single case study analysis (2008) suggests the particularistic importance of the British colonial heritage, the ideology and leadership of the Indian National Congress, and the size and heterogeneity of the federal state.

Most-likely cases, as per Eckstein above, are those in which a theory is to be considered likely to provide a good explanation if it is to have any application at all, whereas least-likely cases are ‘tough test’ ones in which the posited theory is unlikely to provide good explanation (Bennett and Elman, 2010: 505). Levy (2008) neatly refers to the inferential logic of the least-likely case as the ‘Sinatra inference’ – if a theory can make it here, it can make it anywhere. Conversely, if a theory cannot pass a most-likely case, it is seriously impugned. Single case analysis can therefore be valuable for the testing of theoretical propositions, provided that predictions are relatively precise and measurement error is low (Levy, 2008: 12-13). As Gerring rightly observes of this potential for falsification:

“a positivist orientation toward the work of social science militates toward a greater appreciation of the case study format, not a denigration of that format, as is usually supposed” (Gerring, 2007: 247, emphasis added).

In summary, the various forms of single case study analysis can – through the application of multiple qualitative and/or quantitative research methods – provide a nuanced, empirically-rich, holistic account of specific phenomena. This may be particularly appropriate for those phenomena that are simply less amenable to more superficial measures and tests (or indeed any substantive form of quantification) as well as those for which our reasons for understanding and/or explaining them are irreducibly subjective – as, for example, with many of the normative and ethical issues associated with the practice of international relations. From various epistemological and analytical standpoints, single case study analysis can incorporate both idiographic sui generis cases and, where the potential for generalisation may exist, nomothetic case studies suitable for the testing and building of causal hypotheses. Finally, it should not be ignored that a signal advantage of the case study – with particular relevance to international relations – also exists at a more practical rather than theoretical level. This is, as Eckstein noted, “that it is economical for all resources: money, manpower, time, effort… especially important, of course, if studies are inherently costly, as they are if units are complex collective individuals ” (1975: 149-150, emphasis added).

Limitations

Single case study analysis has, however, been subject to a number of criticisms, the most common of which concern the inter-related issues of methodological rigour, researcher subjectivity, and external validity. With regard to the first point, the prototypical view here is that of Zeev Maoz (2002: 164-165), who suggests that “the use of the case study absolves the author from any kind of methodological considerations. Case studies have become in many cases a synonym for freeform research where anything goes”. The absence of systematic procedures for case study research is something that Yin (2009: 14-15) sees as traditionally the greatest concern due to a relative absence of methodological guidelines. As the previous section suggests, this critique seems somewhat unfair; many contemporary case study practitioners – and representing various strands of IR theory – have increasingly sought to clarify and develop their methodological techniques and epistemological grounding (Bennett and Elman, 2010: 499-500).

A second issue, again also incorporating issues of construct validity, concerns that of the reliability and replicability of various forms of single case study analysis. This is usually tied to a broader critique of qualitative research methods as a whole. However, whereas the latter obviously tend toward an explicitly-acknowledged interpretive basis for meanings, reasons, and understandings:

“quantitative measures appear objective, but only so long as we don’t ask questions about where and how the data were produced… pure objectivity is not a meaningful concept if the goal is to measure intangibles [as] these concepts only exist because we can interpret them” (Berg and Lune, 2010: 340).

The question of researcher subjectivity is a valid one, and it may be intended only as a methodological critique of what are obviously less formalised and researcher-independent methods (Verschuren, 2003). Owen (1994) and Layne’s (1994) contradictory process tracing results of interdemocratic war-avoidance during the Anglo-American crisis of 1861 to 1863 – from liberal and realist standpoints respectively – are a useful example. However, it does also rest on certain assumptions that can raise deeper and potentially irreconcilable ontological and epistemological issues. There are, regardless, plenty such as Bent Flyvbjerg (2006: 237) who suggest that the case study contains no greater bias toward verification than other methods of inquiry, and that “on the contrary, experience indicates that the case study contains a greater bias toward falsification of preconceived notions than toward verification”.

The third and arguably most prominent critique of single case study analysis is the issue of external validity or generalisability. How is it that one case can reliably offer anything beyond the particular? “We always do better (or, in the extreme, no worse) with more observation as the basis of our generalization”, as King et al write; “in all social science research and all prediction, it is important that we be as explicit as possible about the degree of uncertainty that accompanies out prediction” (1994: 212). This is an unavoidably valid criticism. It may be that theories which pass a single crucial case study test, for example, require rare antecedent conditions and therefore actually have little explanatory range. These conditions may emerge more clearly, as Van Evera (1997: 51-54) notes, from large-N studies in which cases that lack them present themselves as outliers exhibiting a theory’s cause but without its predicted outcome. As with the case of Indian democratisation above, it would logically be preferable to conduct large-N analysis beforehand to identify that state’s non-representative nature in relation to the broader population.

There are, however, three important qualifiers to the argument about generalisation that deserve particular mention here. The first is that with regard to an idiographic single-outcome case study, as Eckstein notes, the criticism is “mitigated by the fact that its capability to do so [is] never claimed by its exponents; in fact it is often explicitly repudiated” (1975: 134). Criticism of generalisability is of little relevance when the intention is one of particularisation. A second qualifier relates to the difference between statistical and analytical generalisation; single case studies are clearly less appropriate for the former but arguably retain significant utility for the latter – the difference also between explanatory and exploratory, or theory-testing and theory-building, as discussed above. As Gerring puts it, “theory confirmation/disconfirmation is not the case study’s strong suit” (2004: 350). A third qualification relates to the issue of case selection. As Seawright and Gerring (2008) note, the generalisability of case studies can be increased by the strategic selection of cases. Representative or random samples may not be the most appropriate, given that they may not provide the richest insight (or indeed, that a random and unknown deviant case may appear). Instead, and properly used , atypical or extreme cases “often reveal more information because they activate more actors… and more basic mechanisms in the situation studied” (Flyvbjerg, 2006). Of course, this also points to the very serious limitation, as hinted at with the case of India above, that poor case selection may alternatively lead to overgeneralisation and/or grievous misunderstandings of the relationship between variables or processes (Bennett and Elman, 2006a: 460-463).

As Tim May (2011: 226) notes, “the goal for many proponents of case studies […] is to overcome dichotomies between generalizing and particularizing, quantitative and qualitative, deductive and inductive techniques”. Research aims should drive methodological choices, rather than narrow and dogmatic preconceived approaches. As demonstrated above, there are various advantages to both idiographic and nomothetic single case study analyses – notably the empirically-rich, context-specific, holistic accounts that they have to offer, and their contribution to theory-building and, to a lesser extent, that of theory-testing. Furthermore, while they do possess clear limitations, any research method involves necessary trade-offs; the inherent weaknesses of any one method, however, can potentially be offset by situating them within a broader, pluralistic mixed-method research strategy. Whether or not single case studies are used in this fashion, they clearly have a great deal to offer.

References 

Bennett, A. and Checkel, J. T. (2012) ‘Process Tracing: From Philosophical Roots to Best Practice’, Simons Papers in Security and Development, No. 21/2012, School for International Studies, Simon Fraser University: Vancouver.

Bennett, A. and Elman, C. (2006a) ‘Qualitative Research: Recent Developments in Case Study Methods’, Annual Review of Political Science , 9, 455-476.

Bennett, A. and Elman, C. (2006b) ‘Complex Causal Relations and Case Study Methods: The Example of Path Dependence’, Political Analysis , 14, 3, 250-267.

Bennett, A. and Elman, C. (2007) ‘Case Study Methods in the International Relations Subfield’, Comparative Political Studies , 40, 2, 170-195.

Bennett, A. and Elman, C. (2010) Case Study Methods. In C. Reus-Smit and D. Snidal (eds) The Oxford Handbook of International Relations . Oxford University Press: Oxford. Ch. 29.

Berg, B. and Lune, H. (2012) Qualitative Research Methods for the Social Sciences . Pearson: London.

Bryman, A. (2012) Social Research Methods . Oxford University Press: Oxford.

David, M. and Sutton, C. D. (2011) Social Research: An Introduction . SAGE Publications Ltd: London.

Diamond, J. (1992) ‘Economic development and democracy reconsidered’, American Behavioral Scientist , 35, 4/5, 450-499.

Eckstein, H. (1975) Case Study and Theory in Political Science. In R. Gomm, M. Hammersley, and P. Foster (eds) Case Study Method . SAGE Publications Ltd: London.

Flyvbjerg, B. (2006) ‘Five Misunderstandings About Case-Study Research’, Qualitative Inquiry , 12, 2, 219-245.

Geertz, C. (1973) The Interpretation of Cultures: Selected Essays by Clifford Geertz . Basic Books Inc: New York.

Gerring, J. (2004) ‘What is a Case Study and What Is It Good for?’, American Political Science Review , 98, 2, 341-354.

Gerring, J. (2006a) Case Study Research: Principles and Practices . Cambridge University Press: Cambridge.

Gerring, J. (2006b) ‘Single-Outcome Studies: A Methodological Primer’, International Sociology , 21, 5, 707-734.

Gerring, J. (2007) ‘Is There a (Viable) Crucial-Case Method?’, Comparative Political Studies , 40, 3, 231-253.

King, G., Keohane, R. O. and Verba, S. (1994) Designing Social Inquiry: Scientific Inference in Qualitative Research . Princeton University Press: Chichester.

Layne, C. (1994) ‘Kant or Cant: The Myth of the Democratic Peace’, International Security , 19, 2, 5-49.

Levy, J. S. (2008) ‘Case Studies: Types, Designs, and Logics of Inference’, Conflict Management and Peace Science , 25, 1-18.

Lipset, S. M. (1959) ‘Some Social Requisites of Democracy: Economic Development and Political Legitimacy’, The American Political Science Review , 53, 1, 69-105.

Lyotard, J-F. (1984) The Postmodern Condition: A Report on Knowledge . University of Minnesota Press: Minneapolis.

MacMillan, A. (2008) ‘Deviant Democratization in India’, Democratization , 15, 4, 733-749.

Maoz, Z. (2002) Case study methodology in international studies: from storytelling to hypothesis testing. In F. P. Harvey and M. Brecher (eds) Evaluating Methodology in International Studies . University of Michigan Press: Ann Arbor.

May, T. (2011) Social Research: Issues, Methods and Process . Open University Press: Maidenhead.

Owen, J. M. (1994) ‘How Liberalism Produces Democratic Peace’, International Security , 19, 2, 87-125.

Seawright, J. and Gerring, J. (2008) ‘Case Selection Techniques in Case Study Research: A Menu of Qualitative and Quantitative Options’, Political Research Quarterly , 61, 2, 294-308.

Stake, R. E. (2008) Qualitative Case Studies. In N. K. Denzin and Y. S. Lincoln (eds) Strategies of Qualitative Inquiry . Sage Publications: Los Angeles. Ch. 17.

Van Evera, S. (1997) Guide to Methods for Students of Political Science . Cornell University Press: Ithaca.

Verschuren, P. J. M. (2003) ‘Case study as a research strategy: some ambiguities and opportunities’, International Journal of Social Research Methodology , 6, 2, 121-139.

Yin, R. K. (2009) Case Study Research: Design and Methods . SAGE Publications Ltd: London.

[1] The paper follows convention by differentiating between ‘International Relations’ as the academic discipline and ‘international relations’ as the subject of study.

[2] There is some similarity here with Stake’s (2008: 445-447) notion of intrinsic cases, those undertaken for a better understanding of the particular case, and instrumental ones that provide insight for the purposes of a wider external interest.

[3] These may be unique in the idiographic sense, or in nomothetic terms as an exception to the generalising suppositions of either probabilistic or deterministic theories (as per deviant cases, below).

[4] Although there are “philosophical hurdles to mount”, according to Bennett and Checkel, there exists no a priori reason as to why process tracing (as typically grounded in scientific realism) is fundamentally incompatible with various strands of positivism or interpretivism (2012: 18-19). By extension, it can therefore be incorporated by a range of contemporary mainstream IR theories.

— Written by: Ben Willis Written at: University of Plymouth Written for: David Brockington Date written: January 2013

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Read our research on: Abortion | Podcasts | Election 2024

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What the data says about abortion in the u.s..

Pew Research Center has conducted many surveys about abortion over the years, providing a lens into Americans’ views on whether the procedure should be legal, among a host of other questions.

In a  Center survey  conducted nearly a year after the Supreme Court’s June 2022 decision that  ended the constitutional right to abortion , 62% of U.S. adults said the practice should be legal in all or most cases, while 36% said it should be illegal in all or most cases. Another survey conducted a few months before the decision showed that relatively few Americans take an absolutist view on the issue .

Find answers to common questions about abortion in America, based on data from the Centers for Disease Control and Prevention (CDC) and the Guttmacher Institute, which have tracked these patterns for several decades:

How many abortions are there in the U.S. each year?

How has the number of abortions in the u.s. changed over time, what is the abortion rate among women in the u.s. how has it changed over time, what are the most common types of abortion, how many abortion providers are there in the u.s., and how has that number changed, what percentage of abortions are for women who live in a different state from the abortion provider, what are the demographics of women who have had abortions, when during pregnancy do most abortions occur, how often are there medical complications from abortion.

This compilation of data on abortion in the United States draws mainly from two sources: the Centers for Disease Control and Prevention (CDC) and the Guttmacher Institute, both of which have regularly compiled national abortion data for approximately half a century, and which collect their data in different ways.

The CDC data that is highlighted in this post comes from the agency’s “abortion surveillance” reports, which have been published annually since 1974 (and which have included data from 1969). Its figures from 1973 through 1996 include data from all 50 states, the District of Columbia and New York City – 52 “reporting areas” in all. Since 1997, the CDC’s totals have lacked data from some states (most notably California) for the years that those states did not report data to the agency. The four reporting areas that did not submit data to the CDC in 2021 – California, Maryland, New Hampshire and New Jersey – accounted for approximately 25% of all legal induced abortions in the U.S. in 2020, according to Guttmacher’s data. Most states, though,  do  have data in the reports, and the figures for the vast majority of them came from each state’s central health agency, while for some states, the figures came from hospitals and other medical facilities.

Discussion of CDC abortion data involving women’s state of residence, marital status, race, ethnicity, age, abortion history and the number of previous live births excludes the low share of abortions where that information was not supplied. Read the methodology for the CDC’s latest abortion surveillance report , which includes data from 2021, for more details. Previous reports can be found at  stacks.cdc.gov  by entering “abortion surveillance” into the search box.

For the numbers of deaths caused by induced abortions in 1963 and 1965, this analysis looks at reports by the then-U.S. Department of Health, Education and Welfare, a precursor to the Department of Health and Human Services. In computing those figures, we excluded abortions listed in the report under the categories “spontaneous or unspecified” or as “other.” (“Spontaneous abortion” is another way of referring to miscarriages.)

Guttmacher data in this post comes from national surveys of abortion providers that Guttmacher has conducted 19 times since 1973. Guttmacher compiles its figures after contacting every known provider of abortions – clinics, hospitals and physicians’ offices – in the country. It uses questionnaires and health department data, and it provides estimates for abortion providers that don’t respond to its inquiries. (In 2020, the last year for which it has released data on the number of abortions in the U.S., it used estimates for 12% of abortions.) For most of the 2000s, Guttmacher has conducted these national surveys every three years, each time getting abortion data for the prior two years. For each interim year, Guttmacher has calculated estimates based on trends from its own figures and from other data.

The latest full summary of Guttmacher data came in the institute’s report titled “Abortion Incidence and Service Availability in the United States, 2020.” It includes figures for 2020 and 2019 and estimates for 2018. The report includes a methods section.

In addition, this post uses data from StatPearls, an online health care resource, on complications from abortion.

An exact answer is hard to come by. The CDC and the Guttmacher Institute have each tried to measure this for around half a century, but they use different methods and publish different figures.

The last year for which the CDC reported a yearly national total for abortions is 2021. It found there were 625,978 abortions in the District of Columbia and the 46 states with available data that year, up from 597,355 in those states and D.C. in 2020. The corresponding figure for 2019 was 607,720.

The last year for which Guttmacher reported a yearly national total was 2020. It said there were 930,160 abortions that year in all 50 states and the District of Columbia, compared with 916,460 in 2019.

• How the CDC gets its data: It compiles figures that are voluntarily reported by states’ central health agencies, including separate figures for New York City and the District of Columbia. Its latest totals do not include figures from California, Maryland, New Hampshire or New Jersey, which did not report data to the CDC. ( Read the methodology from the latest CDC report .)
• How Guttmacher gets its data: It compiles its figures after contacting every known abortion provider – clinics, hospitals and physicians’ offices – in the country. It uses questionnaires and health department data, then provides estimates for abortion providers that don’t respond. Guttmacher’s figures are higher than the CDC’s in part because they include data (and in some instances, estimates) from all 50 states. ( Read the institute’s latest full report and methodology .)

While the Guttmacher Institute supports abortion rights, its empirical data on abortions in the U.S. has been widely cited by  groups  and  publications  across the political spectrum, including by a  number of those  that  disagree with its positions .

These estimates from Guttmacher and the CDC are results of multiyear efforts to collect data on abortion across the U.S. Last year, Guttmacher also began publishing less precise estimates every few months , based on a much smaller sample of providers.

The figures reported by these organizations include only legal induced abortions conducted by clinics, hospitals or physicians’ offices, or those that make use of abortion pills dispensed from certified facilities such as clinics or physicians’ offices. They do not account for the use of abortion pills that were obtained  outside of clinical settings .

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The annual number of U.S. abortions rose for years after Roe v. Wade legalized the procedure in 1973, reaching its highest levels around the late 1980s and early 1990s, according to both the CDC and Guttmacher. Since then, abortions have generally decreased at what a CDC analysis called  “a slow yet steady pace.”

Guttmacher says the number of abortions occurring in the U.S. in 2020 was 40% lower than it was in 1991. According to the CDC, the number was 36% lower in 2021 than in 1991, looking just at the District of Columbia and the 46 states that reported both of those years.

(The corresponding line graph shows the long-term trend in the number of legal abortions reported by both organizations. To allow for consistent comparisons over time, the CDC figures in the chart have been adjusted to ensure that the same states are counted from one year to the next. Using that approach, the CDC figure for 2021 is 622,108 legal abortions.)

There have been occasional breaks in this long-term pattern of decline – during the middle of the first decade of the 2000s, and then again in the late 2010s. The CDC reported modest 1% and 2% increases in abortions in 2018 and 2019, and then, after a 2% decrease in 2020, a 5% increase in 2021. Guttmacher reported an 8% increase over the three-year period from 2017 to 2020.

As noted above, these figures do not include abortions that use pills obtained outside of clinical settings.

Guttmacher says that in 2020 there were 14.4 abortions in the U.S. per 1,000 women ages 15 to 44. Its data shows that the rate of abortions among women has generally been declining in the U.S. since 1981, when it reported there were 29.3 abortions per 1,000 women in that age range.

The CDC says that in 2021, there were 11.6 abortions in the U.S. per 1,000 women ages 15 to 44. (That figure excludes data from California, the District of Columbia, Maryland, New Hampshire and New Jersey.) Like Guttmacher’s data, the CDC’s figures also suggest a general decline in the abortion rate over time. In 1980, when the CDC reported on all 50 states and D.C., it said there were 25 abortions per 1,000 women ages 15 to 44.

That said, both Guttmacher and the CDC say there were slight increases in the rate of abortions during the late 2010s and early 2020s. Guttmacher says the abortion rate per 1,000 women ages 15 to 44 rose from 13.5 in 2017 to 14.4 in 2020. The CDC says it rose from 11.2 per 1,000 in 2017 to 11.4 in 2019, before falling back to 11.1 in 2020 and then rising again to 11.6 in 2021. (The CDC’s figures for those years exclude data from California, D.C., Maryland, New Hampshire and New Jersey.)

The CDC broadly divides abortions into two categories: surgical abortions and medication abortions, which involve pills. Since the Food and Drug Administration first approved abortion pills in 2000, their use has increased over time as a share of abortions nationally, according to both the CDC and Guttmacher.

The majority of abortions in the U.S. now involve pills, according to both the CDC and Guttmacher. The CDC says 56% of U.S. abortions in 2021 involved pills, up from 53% in 2020 and 44% in 2019. Its figures for 2021 include the District of Columbia and 44 states that provided this data; its figures for 2020 include D.C. and 44 states (though not all of the same states as in 2021), and its figures for 2019 include D.C. and 45 states.

Guttmacher, which measures this every three years, says 53% of U.S. abortions involved pills in 2020, up from 39% in 2017.

Two pills commonly used together for medication abortions are mifepristone, which, taken first, blocks hormones that support a pregnancy, and misoprostol, which then causes the uterus to empty. According to the FDA, medication abortions are safe  until 10 weeks into pregnancy.

Surgical abortions conducted  during the first trimester  of pregnancy typically use a suction process, while the relatively few surgical abortions that occur  during the second trimester  of a pregnancy typically use a process called dilation and evacuation, according to the UCLA School of Medicine.

In 2020, there were 1,603 facilities in the U.S. that provided abortions,  according to Guttmacher . This included 807 clinics, 530 hospitals and 266 physicians’ offices.

While clinics make up half of the facilities that provide abortions, they are the sites where the vast majority (96%) of abortions are administered, either through procedures or the distribution of pills, according to Guttmacher’s 2020 data. (This includes 54% of abortions that are administered at specialized abortion clinics and 43% at nonspecialized clinics.) Hospitals made up 33% of the facilities that provided abortions in 2020 but accounted for only 3% of abortions that year, while just 1% of abortions were conducted by physicians’ offices.

Looking just at clinics – that is, the total number of specialized abortion clinics and nonspecialized clinics in the U.S. – Guttmacher found the total virtually unchanged between 2017 (808 clinics) and 2020 (807 clinics). However, there were regional differences. In the Midwest, the number of clinics that provide abortions increased by 11% during those years, and in the West by 6%. The number of clinics  decreased  during those years by 9% in the Northeast and 3% in the South.

The total number of abortion providers has declined dramatically since the 1980s. In 1982, according to Guttmacher, there were 2,908 facilities providing abortions in the U.S., including 789 clinics, 1,405 hospitals and 714 physicians’ offices.

The CDC does not track the number of abortion providers.

In the District of Columbia and the 46 states that provided abortion and residency information to the CDC in 2021, 10.9% of all abortions were performed on women known to live outside the state where the abortion occurred – slightly higher than the percentage in 2020 (9.7%). That year, D.C. and 46 states (though not the same ones as in 2021) reported abortion and residency data. (The total number of abortions used in these calculations included figures for women with both known and unknown residential status.)

The share of reported abortions performed on women outside their state of residence was much higher before the 1973 Roe decision that stopped states from banning abortion. In 1972, 41% of all abortions in D.C. and the 20 states that provided this information to the CDC that year were performed on women outside their state of residence. In 1973, the corresponding figure was 21% in the District of Columbia and the 41 states that provided this information, and in 1974 it was 11% in D.C. and the 43 states that provided data.

In the District of Columbia and the 46 states that reported age data to  the CDC in 2021, the majority of women who had abortions (57%) were in their 20s, while about three-in-ten (31%) were in their 30s. Teens ages 13 to 19 accounted for 8% of those who had abortions, while women ages 40 to 44 accounted for about 4%.

The vast majority of women who had abortions in 2021 were unmarried (87%), while married women accounted for 13%, according to  the CDC , which had data on this from 37 states.

In the District of Columbia, New York City (but not the rest of New York) and the 31 states that reported racial and ethnic data on abortion to  the CDC , 42% of all women who had abortions in 2021 were non-Hispanic Black, while 30% were non-Hispanic White, 22% were Hispanic and 6% were of other races.

Looking at abortion rates among those ages 15 to 44, there were 28.6 abortions per 1,000 non-Hispanic Black women in 2021; 12.3 abortions per 1,000 Hispanic women; 6.4 abortions per 1,000 non-Hispanic White women; and 9.2 abortions per 1,000 women of other races, the  CDC reported  from those same 31 states, D.C. and New York City.

For 57% of U.S. women who had induced abortions in 2021, it was the first time they had ever had one,  according to the CDC.  For nearly a quarter (24%), it was their second abortion. For 11% of women who had an abortion that year, it was their third, and for 8% it was their fourth or more. These CDC figures include data from 41 states and New York City, but not the rest of New York.

Nearly four-in-ten women who had abortions in 2021 (39%) had no previous live births at the time they had an abortion,  according to the CDC . Almost a quarter (24%) of women who had abortions in 2021 had one previous live birth, 20% had two previous live births, 10% had three, and 7% had four or more previous live births. These CDC figures include data from 41 states and New York City, but not the rest of New York.

The vast majority of abortions occur during the first trimester of a pregnancy. In 2021, 93% of abortions occurred during the first trimester – that is, at or before 13 weeks of gestation,  according to the CDC . An additional 6% occurred between 14 and 20 weeks of pregnancy, and about 1% were performed at 21 weeks or more of gestation. These CDC figures include data from 40 states and New York City, but not the rest of New York.

About 2% of all abortions in the U.S. involve some type of complication for the woman , according to an article in StatPearls, an online health care resource. “Most complications are considered minor such as pain, bleeding, infection and post-anesthesia complications,” according to the article.

The CDC calculates  case-fatality rates for women from induced abortions – that is, how many women die from abortion-related complications, for every 100,000 legal abortions that occur in the U.S .  The rate was lowest during the most recent period examined by the agency (2013 to 2020), when there were 0.45 deaths to women per 100,000 legal induced abortions. The case-fatality rate reported by the CDC was highest during the first period examined by the agency (1973 to 1977), when it was 2.09 deaths to women per 100,000 legal induced abortions. During the five-year periods in between, the figure ranged from 0.52 (from 1993 to 1997) to 0.78 (from 1978 to 1982).

The CDC calculates death rates by five-year and seven-year periods because of year-to-year fluctuation in the numbers and due to the relatively low number of women who die from legal induced abortions.

In 2020, the last year for which the CDC has information , six women in the U.S. died due to complications from induced abortions. Four women died in this way in 2019, two in 2018, and three in 2017. (These deaths all followed legal abortions.) Since 1990, the annual number of deaths among women due to legal induced abortion has ranged from two to 12.

The annual number of reported deaths from induced abortions (legal and illegal) tended to be higher in the 1980s, when it ranged from nine to 16, and from 1972 to 1979, when it ranged from 13 to 63. One driver of the decline was the drop in deaths from illegal abortions. There were 39 deaths from illegal abortions in 1972, the last full year before Roe v. Wade. The total fell to 19 in 1973 and to single digits or zero every year after that. (The number of deaths from legal abortions has also declined since then, though with some slight variation over time.)

The number of deaths from induced abortions was considerably higher in the 1960s than afterward. For instance, there were 119 deaths from induced abortions in  1963  and 99 in  1965 , according to reports by the then-U.S. Department of Health, Education and Welfare, a precursor to the Department of Health and Human Services. The CDC is a division of Health and Human Services.

Note: This is an update of a post originally published May 27, 2022, and first updated June 24, 2022.

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Key facts about the abortion debate in America

Public opinion on abortion, three-in-ten or more democrats and republicans don’t agree with their party on abortion, partisanship a bigger factor than geography in views of abortion access locally, do state laws on abortion reflect public opinion, most popular.

About Pew Research Center Pew Research Center is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping the world. It conducts public opinion polling, demographic research, media content analysis and other empirical social science research. Pew Research Center does not take policy positions. It is a subsidiary of The Pew Charitable Trusts .

Research on automatic recognition of active landslides using InSAR deformation under digital morphology: A case study of the Baihetan reservoir, China

• Gu, Zhenkui
• Li, Renjiang
• Zhou, Zhenkai
• Liu, Xinghong
• Yao, Chuangchuang
• Wei, Shangfei

Optical remote sensing and field investigations cannot satisfy the accuracy and timeliness requirements of active landslide detection. Interferometric synthetic aperture radar (InSAR) technology has become the mainstream method for observing active landslides in recent years, due to its advantages of a large detection range and high sensitivity to surface deformation. However, quickly and accurately obtaining landslide boundaries from InSAR results is still a key issue for hazard mitigation and watershed management. In this study, first, an automatic recognition method for active landslides based on InSAR results is established to rapidly extract deformed slopes. In the recognition process, using the deformation value map as the object, the optimal threshold is determined using the image gradient edge information to extract the deformed pixels. Second, the contrast limited adaptive histogram equalization (CLAHE) algorithm is employed to improve the contrast of images with weak deformation. Last, morphological rules are applied to optimize the segmentation results to ensure that they are near the boundary of the natural landslide. To verify the effectiveness of the method, the Baihetan Reservoir area, which has frequent landslides in the lower reaches of the Jinsha River Basin, was selected as the test area. Under the conditions of ascending and descending orbits, 336 and 590 landslides, respectively, were recognized. Through unmanned aerial vehicle (UAV) and field investigations, the recognition accuracy of 76% is reached without sample training, and the maximum intersection over union (IOU) of a single landslide is increased by 0.3. This finding shows that the automatic recognition method can quickly identify dangerous active landslides at large spatial scales and with complex topographies.

• Landslide automatic recognition;
• Mathematical morphology;
• Baihetan reservoir area;
• Jinsha River

On the History of Single-Case Methodology: A Data-Based Analysis

• Original Paper
• Published: 29 April 2022
• Volume 33 , pages 163–183, ( 2024 )

Cite this article

• Collin Shepley   ORCID: orcid.org/0000-0003-1967-9714 1 ,
• Sally B. Shepley 1 &
• Amy D. Spriggs 1  

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To provide context surrounding the history of single-case research and to act as a benchmark for which future changes across the fields and disciplines that use single-case methods may be compared, we conducted this study to serve as an update and extension on the trends and prevalence of single-case research in the peer-reviewed literature. Our analytical sample was derived from 20 peer-reviewed journals over a 40-year timespan. Results indicate that since 1978, approximately one in six publications within our examined body of research employed a single-case research design. Exploratory moderator analyses revealed that a journal’s focus on behavior analytic research, and a journal’s impact factor moderated the prevalence of single-case publications within a journal. We discuss our findings in relation to prior studies examining the prevalence and trends of single-case research and future directions for single-case researchers to improve the quality, value, and understanding of single-case methodology ( https://osf.io/fns3m/ ).

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Acknowledgements

We would like to thank Maddie Calzi, Rachel Jacob, Hannah Keene, Katelyn Nicklow, Kaitlin O’Neil, Meredith Davis, Bryn Handley, and Hannah Dollinger for their assistance with this project.

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Collin Shepley, Sally B. Shepley & Amy D. Spriggs

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Shepley, C., Shepley, S.B. & Spriggs, A.D. On the History of Single-Case Methodology: A Data-Based Analysis. J Behav Educ 33 , 163–183 (2024). https://doi.org/10.1007/s10864-022-09477-2

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Accepted : 13 April 2022

Published : 29 April 2022

Issue Date : March 2024

DOI : https://doi.org/10.1007/s10864-022-09477-2

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