The Statistical Analysis of Small Data Sets

Abstract We live in the era of big data. However, small data sets are still common for ethical, financial, and practical reasons. Small sample sizes can cause researchers to particularly seek the most powerful methods to analyse their data; but they may be wary that some methodologies rely on assumptions that may not be appropriate when samples are small. The book offers advice on the statistical analysis of small data sets for various designs and levels of measurement. This should help researchers to analyse such data sets, but also to evaluate and interpret others' analyses. Potential challenges associated with a small sample and how these challenges can be mitigated are discussed. Generally, approaches that are often not especially difficult to apply are preferred; a focus is on permutation tests and bootstrap methods. However, topics such as meta-analysis, sequential and adaptive designs, and multiple testing are also discussed. The focus is on frequentist methods, but Bayesian analyses are also covered. R code is presented to carry out the proposed methods; many of them are not limited to use on small data sets. Approaches for computing the power or the necessary sample size, respectively, are also given.