Single-case designs (also called N=1 designs, within-subject designs, or single-case experimental designs) are a methodological tradition with decades of history in psychology, especially in applied behavior analysis and in the evaluation of clinical interventions. Unlike group research designs in psychology, where you compare the means of two or more conditions with many participants, in a single-case design you study the effect of an intervention on a single individual (or a very small number of individuals) through the systematic comparison of phases with and without the intervention.
The logic of these designs is that each participant serves as their own control. In the most basic design, the AB design, the dependent variable is recorded repeatedly during a baseline phase (A) and then during an intervention phase (B). If the variable changes when the intervention is introduced, an effect is inferred. The problem with the AB design is that it does not allow ruling out that the change is due to temporal factors (maturation, external events) coinciding with the introduction of the intervention. That is why more rigorous designs include reversals (ABAB, where the intervention is withdrawn and reintroduced) or staggered introductions (multiple baseline design, where the intervention is introduced at different times for different behaviors, settings, or participants).
Statistical analysis of single-case data
Historically, single-case data have been analyzed through visual inspection: the researcher examines the time series graphs and judges whether there is a change in level, trend, or variability between phases. Visual inspection has the advantage of being intuitive and of detecting complex patterns that statistical analyses may miss. However, it also has important limitations: inter-rater reliability is low (different raters may reach different conclusions from the same data), and it is insensitive to small or moderate effects, especially when the data are variable.
In recent decades there has been a considerable effort to develop statistical methods appropriate for single-case data. One of the most widely used approaches involves non-overlap effect size indices, which quantify the extent to which data from the intervention phase do not overlap with those from the baseline. The PND (Percentage of Non-overlapping Data) is the simplest: it calculates the percentage of data points in phase B that exceed the most extreme value in phase A. The NAP (Nonoverlap of All Pairs) and Tau-U are improved versions that are more robust to outliers and can adjust for trend in the baseline.
Another more sophisticated approach is the use of multilevel models or linear mixed-effects models for single-case data. These models allow estimation of the change in level and trend between phases, while controlling for the serial autocorrelation that is inherent in time series data. The advantage of these models is that they provide parameter estimates with confidence intervals and allow the quantitative synthesis of multiple cases within a study or across studies (known as single-case meta-analysis). The SingleCaseES package in R offers functions for calculating multiple effect sizes for single-case designs.
When to use single-case designs
Single-case designs are especially appropriate in situations where group designs are impractical or inappropriate. In rare clinical populations (infrequent diseases, developmental disorders with highly heterogeneous presentations), it may be impossible to assemble a sufficient sample for a randomized controlled trial. In everyday clinical practice, a therapist who wants to evaluate whether a specific intervention works with a particular patient, for instance using the reliable change index (RCI), does not need a trial with 100 participants, but rather a well-implemented single-case design.
They are also valuable as a preliminary step before group trials. Before investing the resources necessary for a randomized controlled trial, a single-case design can provide preliminary evidence about whether the intervention has potential. If it does not work with a few carefully studied cases, it is unlikely to work at the group level. And if it does work, the single-case data can inform the group trial design (for example, by helping to determine the expected effect size and therefore the necessary sample size).
Recommendations for implementation
If you decide to use a single-case design, there are several important practical considerations. The first is the length of the baseline: you need enough data points in phase A to establish a stable pattern against which to evaluate change. The minimum recommendation is five data points per phase, although more is always better. The second is the choice of design: if the target behavior is reversible (such as the frequency of an observable behavior), an ABAB design is appropriate. If it is not reversible (such as learning a skill), a multiple baseline design is more suitable.
Regarding the analysis, my recommendation is to combine visual inspection with at least one statistical effect size index (you can use our effect size calculator). Visual inspection gives you a qualitative understanding of the pattern of change, while the statistical index provides a quantification that facilitates communication and comparison across studies. The What Works Clearinghouse standards and the SCRIBE guidelines provide detailed directions on how to design, implement, and report single-case studies with sufficient methodological rigor to be considered valid scientific evidence.
Before you submit it: single-case papers rarely get rejected over the statistics themselves, they get rejected over how the design and the analysis are reported. A three-point baseline with no explanation. A non-overlap index chosen without saying why that one and not another. A phase change that is described in words but never quantified. No mention of autocorrelation. If your manuscript is already drafted, paste the methods and results into the free AI paper reviewer: it returns the objections a Q1 reviewer would actually raise, ordered by how likely each one is to sink the paper, so you can fix them while it still costs you an afternoon and not four months of review.