Small Sample Research Designs for Evidence-based Rehabilitation: Issues and Methods PMC

Table Of Content

• It all starts with a N logo
• Psychophysical methods in cognitive and mathematical psychology
• Opportunities and Challenges for Small-N Designs in Rehabilitation
• N.design Process
• NDesigns is a Tennessee-based company serving customers from New York to Japan.
• Elevating Your Brand
• A Forester Turned Artist Creates Wire Sculptures of Trees

Although there is no necessary connection between the use of small-N designs and these other features of scientific practice, many researchers who engage in highly quantitative psychological science often favor small-N designs because they see them as possessing distinct advantages. Part of our aim is to argue that the focus on sample size as the sole or even the primary cause of unreliable psychological knowledge is to lose sight of much of what makes good science. Parenthetically, we note that while we frequently contrast small-N and large-N designs for expository purposes we really view them as ends of a continuum and, for many researchers, the methodological sweet spot may lie somewhere in between (see e.g., Rouder and Haaf (in press)). The small-N research approach includes a wide variety of designs, similar to the diversity in larger-N group comparison designs.

It all starts with a N logo

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Moreover, the most convincing way to investigate these laws today continues to be at the individual level. Manolov and colleagues29,30 provide examples and describe the strengths and limitations of several effect size calculations including the common standardized mean difference approach, regression-based approaches, and visual-based approaches. 1It is, of course, also important to realize that there are other sources of variability which are typically uncontrolled and add to the error variance in an experiment.

Psychophysical methods in cognitive and mathematical psychology

In this section, we illustrate the difference between individual- and group-level inference in order to highlight the superior diagnostic information available in analyzing individuals in a small-N design and the problems of averaging over qualitatively different individual performance in a group-level analysis. For this exercise, we have chosen to use Sternberg’s additive factors method (Sternberg, 1969). Our primary reason for using the additive factors method is that it occupies something of a middle ground between the kinds of strong mathematical models we emphasized in the preceding sections and the null-hypothesis significance testing approach that was the target of the OSC’s replication study. One likely reason for the historical success of the additive factors method is that it was a proper, nontrivial cognitive model that was simple enough to be testable using the standard statistical methods of the day, namely, repeated-measures factorial analysis of variance. Off-the-shelf repeated-measures ANOVA routines became widely available during the 1970s, the decade after Sternberg proposed his method, resulting in a neat dovetailing of theory and data-analytic practice that undoubtedly contributed to the method’s widespread acceptance and use. By using the additive factors method as a test-bed we can illustrate the effects of model-based inference at the group and individual level in a very simple way while at the same time showing the influence of the kinds of power and sample-size considerations that have been the focus of the recent debate about replicability.

Opportunities and Challenges for Small-N Designs in Rehabilitation

Genuine questions about the distributions of those processes within populations—as distinct from the vaguely defined populations that are invoked in standard inferential statistical methods—naturally lead to larger-sample designs, which allow the properties of those populations to be characterized with precision. As emphasized by Meehl (1967), the style of research that remains most problematic for scientific psychology is research that is focused on demonstrating the existence of some phenomenon, as distinct from characterizing the processes and conditions that give rise to and control it. The dominant paradigm for inference in psychology is a null-hypothesis significance testing one. Recently, the foundations of this paradigm have been shaken by several notable replication failures.

Because the occurrence, sign, and magnitude of such interactions depend on the durations of all of the stages comprising the network, interactions are more common and individual differences in interaction become more plausible than they are in a pure additive factors framework. Some of the same qualities that make RCTs the gold-standard for efficacy research may limit their application in assessing the effectiveness of a given intervention for an individual patient. Effectiveness studies are designed to examine the effects of an intervention with typical patients in everyday situations wherein an investigator cannot control all the extraneous factors. RCTs tend to have strict inclusion and exclusion criteria and typically report average treatment effects obtained from statistical comparisons of group-level (aggregate) data from experimental and control groups.

N.design Process

The design of the letters N and Z is formed from a unique circle with lines that seem to overlap. Very good for use in all colors and media, both print media and as avatars for social media web and mobile applications. The NUMYX is an tech company, that seeks for simplicity, originality, and a recognizable "N" letter based icon.

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NDesigns is a Tennessee-based company serving customers from New York to Japan.

The large-N approach would be to run a big sample of participants who, because of resourcing constraints, are likely at best to be minimally practiced on the task and, consequently, highly variable. After a few iterations, the field as a whole will conclude that the effect is somewhat fragile, requires large resources to demonstrate reliably, and is therefore uninteresting theoretically, and will move on to study something else. By contrast, the group analysis is only showing comparable power when all four of the simulated participants show a positive interaction. When any of the participants in the group is sampled from the null interaction effect, the power of the analysis drops substantially (from near 1.0 to .3). The implication is that the group-level analysis is masking the individual differences in the presentation of the interaction. When half or fewer of the participants show the interaction, the group-level analysis only very rarely detects an interaction.

Elevating Your Brand

The article by Horn and colleagues in this issue, as well as earlier reviews by Grimmer et al.,3 and Kravitz et al.2 provide more details on why it is sometimes difficult to extrapolate findings from RCTs to everyday clinical practice. Similar results on the effects of aggregation were reported in a number of other cognitive tasks by Cohen, Sanborn, and Shiffrin (2008). They investigated models of forgetting, categorization, and information integration and compared the accuracy of parameter recovery by model selection from group and individual data. They found that when there were only a small number of trials per participant parameter recovery from group data was often better than from individual data. Like the response time studies, their findings demonstrate the data-smoothing properties of averaging and the fact that smoother data typically yield better parameter estimates. Cohen et al.’s results also highlight the fact that, while distortion due to aggregation remains a theoretical possibility, there are no universal prescriptions about whether or not to aggregate; aggregation artifacts must be assessed on a case-by-case basis rather than asserted or denied a priori.

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On the one hand, one of the most well-known examples of aggregation artifact is that of learning curves (Estes, 1956; Gallistel et al., 2004; Sidman, 1960). As has long been recognized, averaging a family of discontinuous learning curves of the kind produced by insight-based, all-or-none learning in which the insight point occurs at different times can produce a smoothly increasing group curve of the kind predicted by incremental-learning, linear operator models (Batchelder, 1975). That is, the conclusions one would draw at the group and individual levels are diametrically opposed. Zealously averaging over unknown individual differences can produce results that potentially misdirect the theoretical direction of the entire field. In a recent survey of the role of small-N designs in psychology, Saville and Buskist (2003) pointed out that the use of large-N designs is a comparatively recent phenomenon, which they linked to the publication of R.

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However, it is important to recognize that the bimodality is not at the level of the data but at the level of the parameters of the cognitive model that generated the data. How that bimodality is expressed at the level of the data will depend on a transformation (usually nonlinear, e.g., Eqs. A2 and A3) that expresses the value of the parameter in the observed data. The qualitative expression of bimodality at the level of empirical measurement is merely that some participants display convincing evidence of an interaction while others display weak or no evidence.