smallsample

Smallsample, or small-sample analysis, refers to statistical analyses conducted on datasets with a limited number of observations. In such contexts, the usual large-sample approximations may fail, and results can be highly sensitive to model assumptions and outliers. The term is not strictly defined by a numeric threshold; instead, it describes scenarios where n is small relative to model complexity or variability.

Challenges and methods: Key challenges include high variance, potential bias, non-normality, and unreliable variance estimates. Common approaches include exact tests like Fisher's exact test for contingency tables, t-tests with appropriate degrees of freedom, nonparametric methods (such as the Mann-Whitney test), and bootstrap or permutation methods with caution. Bayesian methods with informative priors or hierarchical models can borrow strength across related data to improve inferences.

Applications and design: Small samples occur in rare diseases, early-phase experiments, pilot studies, or cost-constrained research. Experimental design considerations emphasize replication, randomization, and robust analysis plans; sequential or adaptive designs can improve efficiency, while meta-analysis or data pooling may help if compatible data exist.

Limitations and terminology: Findings from small-sample analyses are often less precise and generalizable. Power analyses are harder, and pre-study planning is critical. The term is used across statistics, psychology, medicine, and social sciences, with practitioners stressing careful model checking and transparent reporting.