The purpose of this review is to clarify the concepts of bias, precision and accuracy as
they are commonly defined in the biostatistical literature, with our focus on the use of
these concepts in quantitatively testing the performance of point estimators
(specifically species richness estimators). We first describe the general concepts
underlying bias, precision and accuracy, and then describe a number of commonly
used unscaled and scaled performance measures of bias, precision and accuracy (e.g.
mean error, variance, standard deviation, mean square error, root mean square error,
mean absolute error, and all their scaled counterparts) which may be used to evaluate
estimator performance. We also provide mathematical formulas and a worked example
for most performance measures. Since every measure of estimator performance should
be viewed as suggestive, not prescriptive, we also mention several other performance
measures that have been used by biostatisticians or ecologists. We then outline several
guidelines of how to test the performance of species richness estimators: the detailed
description of data simulation models and resampling schemes, the use of real and
simulated data sets on as many different estimators as possible, mathematical
expressions for all estimators and performance measures, and the presentation of
results for each scaled performance measure in numerical tables with increasing levels
of sampling effort. We finish with a literature review of promising new research related
to species richness estimation, and summarize the results of 14 studies that compared
estimator performance, which confirm that with most data sets, non-parametric
estimators (mostly the Chao and jackknife estimators) perform better than other
estimators, e.g. curve models or fitting species-abundance distributions. | |