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For the individuals sampled with a positive interaction, the individual analysis is very sensitive with the average power greater than .9 even at the lowest levels of the effect. The individual-level analysis is also sensitive even to small effects near zero, from individuals sampled with a null interaction. Effectively, the analysis is sensitive enough to occasionally detect that the interaction effect is different from zero even when that effect is rather small.
Our Design Process
According to this paradigm, the goal of experimentation is to draw inferences about the properties of an underlying population or populations from measurements made on samples drawn from those populations. Expressed in model-comparison terms (Maxwell & Delaney, 1990), the goal of inference is to decide between two models of the psychological phenomenon under investigation, or more precisely, to decide between two models of the data-generating process that gave rise to the observed experimental outcomes. One model is a null model, in which the value of a parameter in the data-generating process is zero; the other is an alternative model, in which the value of the parameter is nonzero. This parameter is conceptualized as the numerical value that would be obtained if a population-wide census could feasibly be undertaken. The additive factors method originated as a way to determine the presence or not of sequential or serial stages of processing in response time (RT) tasks (Sternberg, 1969). Two factors, varied factorially, which influence different processes, will have additive effects on response time under the assumption that the processes are arrayed sequentially.
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In view of our finite individual and collective resources for collecting data, we suggest that small-N designs are often a better and more informative way to allocate them. On the other hand, studies of speeded decision-making are often carried out on group data created by averaging quantiles of response time distributions across participants (Ratcliff & Smith, 2004). Fits of the diffusion decision model to quantile-averaged group data typically agree fairly well the averages of fits to individual participant data (Ratcliff et al., 2003; Ratcliff et al., 2004).
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This new hardware ecosystem will run on Meta Horizon OS, the mixed reality operating system that powers our Meta Quest headsets. Meta Horizon OS combines the core technologies that power today’s mixed reality experiences with a suite of features that put social presence at the center of the platform. Not all rehabilitation clinicians will participate in traditional large-N group comparison experimental research designed to test hypotheses or refine theory.
Simulation results
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Phenomenon-based versus process-based research
As a corollary to this interpretation, we might expect that the areas of psychology that were slowest in taking advantage of Fisher’s methodological innovations would be those in which the replication crisis is now deepest. An experimenter who runs a small number of participants probably does so in the expectation of finding a high degree of interparticipant agreement, as is often found in sensory science, animal learning studies, and some areas of cognitive neuroscience. However, in situations like the one in our simulation in which there is appreciable heterogeneity in the underlying population, the expected consistency is unlikely to eventuate, or not completely.
We then used model selection (i.e., a G2 test) to determine whether the more general model fit significantly better than the constrained model. The key strengths of the AB design are its applicability to almost any clinical setting or problem, as well as its simplicity in evaluating whether changes occurred in the outcome following the transition from baseline to intervention. The basic design in this classification involves an AB structure, wherein “A” represents the baseline (non-treatment) phase and “B” refers to the intervention phase.
These might include issues such as intensity or duration or combining multiple components of the intervention and testing them across various patients and settings. In making these claims for findings like Fechher’s and Ebbinghaus’s laws, we are of course not attempting to suggest that all of the historical studies carried out using small-N or single-participant designs yielded enduring and reliable knowledge. That would be like claiming that all the best songs were written in the sixties because the songs from the sixties that continue to be played today are better than the songs being written now—and would embody the same kind of logical error. Rather, it is to claim that these examples show that use of single-participant designs is in no way inimical to the discovery of precise quantitative relationships of enduring psychological significance. Indeed, it might have been much more difficult for Fechner and Ebbinghaus to have discovered their laws had they worked with large-N designs.
In this form of replication, participants are matched as closely as possible on subject characteristics. The aim is to establish, as clearly as possible, that a given intervention can have an effect on a certain kind of patient within a specific setting. If a series of direct replication small-N studies produces consistently positive results, then the replication process moves to the next level. The figure is adapted from Carey and Matyas’ study17 on direct and transfer effects of stimulus-specific training on joint proprioception in five patients with stroke.
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Clinically-derived evidence can serve as the catalyst for investigators to design high-quality research that is relevant to clinical practice (see article by Whyte and others in this issue). Small-N designs represent one approach that is available to practitioners and that may allow them to contribute to the advancement of rehabilitation science and practice. Since randomly selecting a representative sample from a large target population is not a component of small-N designs, replication is the alternative strategy used to establish the generalizability of small-N research findings. Barlow and Hersen34 describe three strategies for establishing generalizability in small-N research. The first form of generalizability involves the accumulation of a number of direct replications of the specific treatment effect on one well-defined outcome measure within a defined clinical setting.
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There are other forms of small-N designs and many variations within each category of design. Identifying which design is the best fit for a particular research question or context depends on many factors. They can be useful in the early developmental phase of research as well as in refining the application of research findings to individual patients. While we fully understand the arguments in favor of such models, to us, many of the published examples of their use have tended to obscure rather than to emphasize the quality of the fits at the individual level. However, our ultimate goal throughout this article is not to criticize these or any other particular methods, but to highlight that psychology is not a homogeneous discipline. The lesson is that a common feature of small-N methods, and the increased power and precision of inference they offer, is only realizable in data-rich environments.
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