For basic researchers that operate day in and day out with small sample sizes, the answer is to use non-parametric statistics. Non-parametric statistical tests such as the Mann-Whitney U, Kruskal-Wallis, Wilcoxon, and Friedman's ANOVA are robust to violations of statistical assumptions and skewed distributions. These tests can yield interpretable medians, interquartile ranges, and p-values.
Non-parametric statistics are also useful in the social sciences due to the inherent measurement error associated with assessing human behaviors, thoughts, feelings, intelligence, and emotional states. The underlying algebra associated with psychometrics relies on intercorrelations amongst constructs or items. Correlations can easily be skewed by outlying observations and measurement error. Therefore, in concordance with mathematical and empirical reasoning, non-parametric statistics should be used often for between-subjects comparisons of surveys, instruments, and psychological measures.