Information, discrimination and divergence in cytology. VI. Biases and errors of measurement in small samples

Total discrimination and total divergence have been shown to be useful measures of performance in diagnostic cytology. The sample size, Ns (observed number of cytology-histology pairs, essential components of a confusion matrix), may be small for the comparison of two or more laboratories or periodic quality control using observed values. From actual data from previous reports in this series, the best estimation of the confusion matrix of a population was obtained by fitting a Gaussian-type curve after pseudoscalar transform of ranks (row and column numbers). Small sample confusion matrices were generated by Monte Carlo simulation to 2.5 x 10(-7) resolution. To keep measurement biases within +/- 0.5 decits, we found that 100-200 samples of cytology-histology pairs were required in the best classifications of three, four and five category-states. At these sample sizes, measurement errors (standard errors) were also contained within +/- 0.5 decits. This study also confirmed that previously reported overestimated propagated errors in small samples were in fact overestimation and that their use for testing a null hypothesis was valid. The number of samples with indefinable statistics due to a zero denominator can be as high as 30% when the sample sizes are 500 for three, four and five category-state classifications. Biases due to small samples were positive for most category-states except for the optimum three category-states, in which bias changed to negative ("bias inversion"), and observed errors of discrimination and divergence paradoxically decreased as Ns decreased ("error-sample paradox") for a small sample size (Ns less than 700).(ABSTRACT TRUNCATED AT 250 WORDS)