Small-Sample Reference Interval Estimation: A Comparative Analysis of HARISS, Robust, Parametric, and Nonparametric...

Current veterinary guidelines for establishing reference intervals (RIs) from small samples typically recommend the robust method (RM) or, alternatively, parametric or nonparametric methods (PNPM) based on data distribution (Gaussian or not). A web application, HARISS, refines this approach by using visual inspection of distribution histograms to more accurately select the statistical method for small samples, based on a 3-class classification of data distribution (Gaussian, lognormal, left-skewed). Prior simulation studies have shown HARISS's decision rules lead to more accurate RIs, assuming Gaussian, lognormal, or left-skewed population distributions.

This study aimed to compare the accuracy of HARISS, RM, and PNPM in estimating RIs when small samples are drawn from populations with diverse distributions.

We randomly selected samples of n = 40, 50, or 60 values (50 replicates per size) from seven simulated populations (5000 values each): Gaussian, Student's t, lognormal, right-skewed, left-skewed, bimodal, and irregular. No outlier was included. RIs were constructed using HARISS, RM, and PNPM. Their accuracy was compared using repeated-measures ANOVA.

Overall, HARISS significantly improved the accuracy of both RI lower and upper limit estimations (p < 0.001), irrespective of population distribution or sample size. However, the methods' accuracy varied depending on the specific population distribution. Specifically, HARISS significantly outperformed RM for RIs derived from Gaussian and Student's t population samples and was significantly more accurate than PNPM for RIs from skewed population samples.

Overall, HARISS provided the most accurate RI limit estimations from small samples across the seven population distributions simulated.