Bump-hunting for the proficiency tester—searching for multimodality

Abstract

Kernel density estimation is a method for producing a smooth density approximation to a dataset and avoiding some of the problems associated with histograms. If it is used with a degree of smoothing determined by a fitness for purpose criterion, it can be applied to proficiency test data in order to test for multimodality in the z-scores. The bootstrap is an essential additional technique to determine how rugged the initially estimated kernel density is: the random resampling of the data in the bootstrap simulates a complete blind repeat of the proficiency test. In addition, useful estimates of the standard error of a mode can be thus obtained. It is suggested that a mode and its standard error can be used as an assigned value and its standard uncertainty.