Sample Size

BackgroundChoosing a suitable sample size in qualitative research is an area of conceptual debate and practical uncertainty. That sample size principles, guidelines and tools have been developed to enable researchers to set, and justify the acceptability of, their sample size is an indication that the issue constitutes an important marker of the quality of qualitative research. Nevertheless, research shows that sample size sufficiency reporting is often poor, if not absent, across a range of disciplinary fields.MethodsA systematic analysis of single-interview-per-participant designs within three health-related journals from the disciplines of psychology, sociology and medicine, over a 15-year period, was conducted to examine whether and how sample sizes were justified and how sample size was characterised and discussed by authors. Data pertinent to sample size were extracted and analysed using qualitative and quantitative analytic techniques.ResultsOur findings demonstrate that provision of sample size justifications in qualitative health research is limited; is not contingent on the number of interviews; and relates to the journal of publication. Defence of sample size was most frequently supported across all three journals with reference to the principle of saturation and to pragmatic considerations. Qualitative sample sizes were predominantly - and often without justification - characterised as insufficient (i.e., 'small') and discussed in the context of study limitations. Sample size insufficiency was seen to threaten the validity and generalizability of studies' results, with the latter being frequently conceived in nomothetic terms.ConclusionsWe recommend, firstly, that qualitative health researchers be more transparent about evaluations of their sample size sufficiency, situating these within broader and more encompassing assessments of data adequacy. Secondly, we invite researchers critically to consider how saturation parameters found in prior methodological studies and sample size community norms might best inform, and apply to, their own project and encourage that data adequacy is best appraised with reference to features that are intrinsic to the study at hand. Finally, those reviewing papers have a vital role in supporting and encouraging transparent study-specific reporting.

Data saturation is the most commonly employed concept for estimating sample sizes in qualitative research. Over the past 20 years, scholars using both empirical research and mathematical/statistical models have made significant contributions to the question: How many qualitative interviews are enough? This body of work has advanced the evidence base for sample size estimation in qualitative inquiry during the design phase of a study, prior to data collection, but it does not provide qualitative researchers with a simple and reliable way to determine the adequacy of sample sizes during and/or after data collection. Using the principle of saturation as a foundation, we describe and validate a simple-to-apply method for assessing and reporting on saturation in the context of inductive thematic analyses. Following a review of the empirical research on data saturation and sample size estimation in qualitative research, we propose an alternative way to evaluate saturation that overcomes the shortcomings and challenges associated with existing methods identified in our review. Our approach includes three primary elements in its calculation and assessment: Base Size, Run Length, and New Information Threshold. We additionally propose a more flexible approach to reporting saturation. To validate our method, we use a bootstrapping technique on three existing thematically coded qualitative datasets generated from in-depth interviews. Results from this analysis indicate the method we propose to assess and report on saturation is feasible and congruent with findings from earlier studies.

BackgroundExternal pilot or feasibility studies can be used to estimate key unknown parameters to inform the design of the definitive randomised controlled trial (RCT). However, there is little consensus on how large pilot studies need to be, and some suggest inflating estimates to adjust for the lack of precision when planning the definitive RCT.MethodsWe use a simulation approach to illustrate the sampling distribution of the standard deviation for continuous outcomes and the event rate for binary outcomes. We present the impact of increasing the pilot sample size on the precision and bias of these estimates, and predicted power under three realistic scenarios. We also illustrate the consequences of using a confidence interval argument to inflate estimates so the required power is achieved with a pre-specified level of confidence. We limit our attention to external pilot and feasibility studies prior to a two-parallel-balanced-group superiority RCT.ResultsFor normally distributed outcomes, the relative gain in precision of the pooled standard deviation (SDp) is less than 10% (for each five subjects added per group) once the total sample size is 70. For true proportions between 0.1 and 0.5, we find the gain in precision for each five subjects added to the pilot sample is less than 5% once the sample size is 60. Adjusting the required sample sizes for the imprecision in the pilot study estimates can result in excessively large definitive RCTs and also requires a pilot sample size of 60 to 90 for the true effect sizes considered here.ConclusionsWe recommend that an external pilot study has at least 70 measured subjects (35 per group) when estimating the SDp for a continuous outcome. If the event rate in an intervention group needs to be estimated by the pilot then a total of 60 to 100 subjects is required. Hence if the primary outcome is binary a total of at least 120 subjects (60 in each group) may be required in the pilot trial. It is very much more efficient to use a larger pilot study, than to guard against the lack of precision by using inflated estimates.

Effect size measures are important complements to P values, providing information about the magnitude and practical relevance of research findings. While widely discussed in the context of parametric tests, effect size estimation for nonparametric tests remains less explored. This article reviews standardized effect size measures applicable to four common nonparametric tests: Mann-Whitney, Wilcoxon signed-rank, Kruskal-Wallis, and Friedman. Commonly suggested classifications for these effect sizes are also discussed. This article aims to support researchers in reporting and interpreting effect sizes more effectively in nonparametric contexts.