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Background Choosing 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. Methods A 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. Results Our 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. Conclusions We 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.

An important step when designing an empirical study is to justify the sample size that will be collected. The key aim of a sample size justification for such studies is to explain how the collected data is expected to provide valuable information given the inferential goals of the researcher. In this overview article six approaches are discussed to justify the sample size in a quantitative empirical study: 1) collecting data from (almost) the entire population, 2) choosing a sample size based on resource constraints, 3) performing an a-priori power analysis, 4) planning for a desired accuracy, 5) using heuristics, or 6) explicitly acknowledging the absence of a justification. An important question to consider when justifying sample sizes is which effect sizes are deemed interesting, and the extent to which the data that is collected informs inferences about these effect sizes. Depending on the sample size justification chosen, researchers could consider 1) what the smallest effect size of interest is, 2) which minimal effect size will be statistically significant, 3) which effect sizes they expect (and what they base these expectations on), 4) which effect sizes would be rejected based on a confidence interval around the effect size, 5) which ranges of effects a study has sufficient power to detect based on a sensitivity power analysis, and 6) which effect sizes are expected in a specific research area. Researchers can use the guidelines presented in this article, for example by using the interactive form in the accompanying online Shiny app, to improve their sample size justification, and hopefully, align the informational value of a study with their inferential goals.

Structural equation modeling (SEM) is a widespread and commonly used approach to test substantive hypotheses in the social and behavioral sciences. When performing hypothesis tests, it is vital to rely on a sufficiently large sample size to achieve an adequate degree of statistical power to detect the hypothesized effect. However, applications of SEM rarely consider statistical power in informing sample size considerations or determine the statistical power for the focal hypothesis tests performed. One reason is the difficulty in translating substantive hypotheses into specific effect size values required to perform power analyses, as well as the lack of user-friendly software to automate this process. The present paper presents the second version of the R package semPower which includes comprehensive functionality for various types of power analyses in SEM. Specifically, semPower 2 allows one to perform both analytical and simulated a priori, post hoc, and compromise power analysis for structural equation models with or without latent variables, and also supports multigroup settings and provides user-friendly convenience functions for many common model types (e.g., standard confirmatory factor analysis [CFA] models, regression models, autoregressive moving average [ARMA] models, cross-lagged panel models) to simplify power analyses when a model-based definition of the effect in terms of model parameters is desired.

Cronbach’s alpha is one of the most widely used measures of reliability in the social and organizational sciences. Current practice is to report the sample value of Cronbach’s alpha reliability, but a confidence interval for the population reliability value also should be reported. The traditional confidence interval for the population value of Cronbach’s alpha makes an unnecessarily restrictive assumption that the multiple measurements have equal variances and equal covariances. We propose a confidence interval that does not require equal variances or equal covariances. The results of a simulation study demonstrated that the proposed method performed better than alternative methods. We also present some sample size formulas that approximate the sample size requirements for desired power or desired confidence interval precision. R functions are provided that can be used to implement the proposed confidence interval and sample size methods.

The size of the training data set is a major determinant of classification accuracy. Nevertheless, the collection of a large training data set for supervised classifiers can be a challenge, especially for studies covering a large area, which may be typical of many real-world applied projects. This work investigates how variations in training set size, ranging from a large sample size (n = 10,000) to a very small sample size (n = 40), affect the performance of six supervised machine-learning algorithms applied to classify large-area high-spatial-resolution (HR) (1–5 m) remotely sensed data within the context of a geographic object-based image analysis (GEOBIA) approach. GEOBIA, in which adjacent similar pixels are grouped into image-objects that form the unit of the classification, offers the potential benefit of allowing multiple additional variables, such as measures of object geometry and texture, thus increasing the dimensionality of the classification input data. The six supervised machine-learning algorithms are support vector machines (SVM), random forests (RF), k-nearest neighbors (k-NN), single-layer perceptron neural networks (NEU), learning vector quantization (LVQ), and gradient-boosted trees (GBM). RF, the algorithm with the highest overall accuracy, was notable for its negligible decrease in overall accuracy, 1.0%, when training sample size decreased from 10,000 to 315 samples. GBM provided similar overall accuracy to RF; however, the algorithm was very expensive in terms of training time and computational resources, especially with large training sets. In contrast to RF and GBM, NEU, and SVM were particularly sensitive to decreasing sample size, with NEU classifications generally producing overall accuracies that were on average slightly higher than SVM classifications for larger sample sizes, but lower than SVM for the smallest sample sizes. NEU however required a longer processing time. The k-NN classifier saw less of a drop in overall accuracy than NEU and SVM as training set size decreased; however, the overall accuracies of k-NN were typically less than RF, NEU, and SVM classifiers. LVQ generally had the lowest overall accuracy of all six methods, but was relatively insensitive to sample size, down to the smallest sample sizes. Overall, due to its relatively high accuracy with small training sample sets, and minimal variations in overall accuracy between very large and small sample sets, as well as relatively short processing time, RF was a good classifier for large-area land-cover classifications of HR remotely sensed data, especially when training data are scarce. However, as performance of different supervised classifiers varies in response to training set size, investigating multiple classification algorithms is recommended to achieve optimal accuracy for a project.

Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy, and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optimal policies with low switching cost for stochastic bandits.

Automated cell type identification is a key computational challenge in single‐cell RNA‐sequencing (scRNA‐seq) data. To capitalise on the large collection of well‐annotated scRNA‐seq datasets, we developed scClassify, a multiscale classification framework based on ensemble learning and cell type hierarchies constructed from single or multiple annotated datasets as references. scClassify enables the estimation of sample size required for accurate classification of cell types in a cell type hierarchy and allows joint classification of cells when multiple references are available. We show that scClassify consistently performs better than other supervised cell type classification methods across 114 pairs of reference and testing data, representing a diverse combination of sizes, technologies and levels of complexity, and further demonstrate the unique components of scClassify through simulations and compendia of experimental datasets. Finally, we demonstrate the scalability of scClassify on large single‐cell atlases and highlight a novel application of identifying subpopulations of cells from the Tabula Muris data that were unidentified in the original publication. Together, scClassify represents state‐of‐the‐art methodology in automated cell type identification from scRNA‐seq data. Synopsis scClassify is a multiscale classification framework based on ensemble learning and cell type hierarchies, enabling sample size estimation required for accurate cell type classification and joint classification of cells using multiple references. scClassify performs multiscale cell type classification based on cell type hierarchies constructed from single or multiple reference datasets. It implements a post‐hoc clustering procedure for discovering novel cell types from cells that are unassigned due to the absence of their types in the reference data. It enables the estimation of the number of cells required in a reference dataset to accurately discriminate a given cell type in a cell type hierarchy. Application to large atlas datasets such as Tabula Muris demonstrates its ability to refine cell types and identify cells from sub‐populations. Graphical Abstract scClassify is a multiscale classification framework based on ensemble learning and cell type hierarchies, enabling sample size estimation required for accurate cell type classification and joint classification of cells using multiple references.

This article features online supplementary material. In this article, we propose a computationally efficient approach-space (Sparse PArtial Correlation Estimation)-for selecting nonzero partial correlations under the high-dimension-low-sample-size setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both nonzero partial correlation selection and the identification of hub variables, and also outperforms two existing methods. We then apply space to a microarray breast cancer dataset and identify a set of hub genes that may provide important insights on genetic regulatory networks. Finally, we prove that, under a set of suitable assumptions, the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation.

Background The current CONSORT guidelines for reporting pilot trials do not recommend hypothesis testing of clinical outcomes on the basis that a pilot trial is under-powered to detect such differences and this is the aim of the main trial. It states that primary evaluation should focus on descriptive analysis of feasibility/process outcomes (e.g. recruitment, adherence, treatment fidelity). Whilst the argument for not testing clinical outcomes is justifiable, the same does not necessarily apply to feasibility/process outcomes, where differences may be large and detectable with small samples. Moreover, there remains much ambiguity around sample size for pilot trials. Methods Many pilot trials adopt a ‘traffic light’ system for evaluating progression to the main trial determined by a set of criteria set up a priori. We construct a hypothesis testing approach for binary feasibility outcomes focused around this system that tests against being in the RED zone (unacceptable outcome) based on an expectation of being in the GREEN zone (acceptable outcome) and choose the sample size to give high power to reject being in the RED zone if the GREEN zone holds true. Pilot point estimates falling in the RED zone will be statistically non-significant and in the GREEN zone will be significant; the AMBER zone designates potentially acceptable outcome and statistical tests may be significant or non-significant. Results For example, in relation to treatment fidelity, if we assume the upper boundary of the RED zone is 50% and the lower boundary of the GREEN zone is 75% (designating unacceptable and acceptable treatment fidelity, respectively), the sample size required for analysis given 90% power and one-sided 5% alpha would be around n = 34 (intervention group alone). Observed treatment fidelity in the range of 0–17 participants (0–50%) will fall into the RED zone and be statistically non-significant, 18–25 (51–74%) fall into AMBER and may or may not be significant and 26–34 (75–100%) fall into GREEN and will be significant indicating acceptable fidelity. Discussion In general, several key process outcomes are assessed for progression to a main trial; a composite approach would require appraising the rules of progression across all these outcomes. This methodology provides a formal framework for hypothesis testing and sample size indication around process outcome evaluation for pilot RCTs.

It is incredibly essential that the current clinicians and researchers remain updated with findings of current biomedical literature for evidence-based medicine. However, they come across many types of research that are nonreproducible and are even difficult to interpret clinically. Statistical and clinical significance is one such difficulty that clinicians and researchers face across many instances. In simpler terms, the P value tests all hypothesis about how the data were produced (model as whole), and not just the targeted hypothesis that it is intended to test (such as a null hypothesis) keeping in mind how reliable are the of the research results. Most of the times it is misinterpreted and misunderstood as a measure to judge the results as clinically significant. Hence this review aims to impart knowledge about \"P\" value and its importance in biostatistics, also highlights the importance of difference between statistical and clinical significance for appropriate interpretation of research results.