Summary of Part C

Part C presented the main analytic toolkit for small-sample quantitative work. Across these chapters, the emphasis was on choosing methods that remain defensible when sample sizes are modest, events are rare, distributions are skewed, predictors are numerous, or the set of alternatives is small. Exact and resampling methods, rank-based procedures, sparse-count methods, short time-series approaches, penalised and Bayesian regression, and multi-criteria decision making all served the same purpose: matching the method to the information actually available.

Taken together, these chapters show that small samples do not call for one universal workaround. They call for a careful match between the research question, the structure of the data, the assumptions that can be defended, and the kind of uncertainty that needs to be reported.

Method-Selection Framework

Use this table as a starting point before choosing a procedure. It does not replace design knowledge, but it helps connect common small-sample questions to the chapters that give the worked implementation.

Data structure or question Typical small-sample setting Recommended starting point Main chapter
Two categorical variables with sparse cells 2 x 2 table, expected counts below 5 Fisher’s exact test, with mid-p or unconditional exact tests as sensitivity checks Chapter 10
One sparse event count against a benchmark Few events observed over a known exposure Exact Poisson test and exact confidence interval Chapter 10
Custom statistic or skewed continuous outcome n is too small for stable normal approximation Permutation test when exchangeability is defensible, or bootstrap interval when resampling the statistic is meaningful Chapter 10
Two independent ordinal or skewed groups Ratings, waiting times, or outcomes with outliers Mann–Whitney U with medians, IQRs, and Cliff’s delta Chapter 11
Paired ordinal or skewed measurements Before-after or matched-pair design Wilcoxon signed-rank with the Hodges–Lehmann pseudomedian shift Chapter 11
Three or more independent groups Small groups with ordinal or skewed outcomes Kruskal–Wallis with adjusted pairwise follow-up and epsilon-squared Chapter 11
Repeated conditions for the same participants Three or more within-person conditions Friedman test with Kendall’s W and adjusted paired follow-up Chapter 11
Sparse rates or count outcomes Few events, overdispersion, or short exposure summaries Exact rate methods first, then quasi-Poisson or negative binomial sensitivity checks when model assumptions are defensible Chapter 12
Very short time series 12 to 20 ordered observations with a simple trend question Transparent trend model with residual-bootstrap forecast band only if residuals are approximately independent Chapter 12
Sparse binary regression or separation Few events or fitted probabilities near 0 or 1 Firth logistic regression and clear event-count reporting Chapter 13
Many or correlated predictors relative to n Linear model with unstable slopes Ridge regression for shrinkage, LASSO for screening, and standardisation before penalisation Chapter 13
Bayesian small-sample model Prior information is explicit and defensible Weakly informative priors, convergence diagnostics, posterior predictive checks, and prior sensitivity Chapter 13
Ranking a few alternatives rather than testing a sample effect Fixed set of programmes, suppliers, or designs AHP, TOPSIS, or VIKOR with transparent weights and sensitivity analysis Chapter 14