An empirical study to check the accuracy of approximating averages of ratios using ratios of averages

TL;DR

This study empirically evaluates the accuracy of approximating the average of ratios by the ratio of averages using simulated data, finding minimal differences and identifying a suitable distribution fit.

Contribution

It provides empirical evidence on the validity of using ratios of averages as approximations in bibliometric data analysis.

Findings

Bootstrap confidence intervals show no significant difference between the two methods.

The Kolmogorov-Smirnov test indicates similar distributions for both approaches.

Log-logistic distribution fits the ratio data well.

Abstract

For a number of researchers a number of publications for each author is simulated using the zeta distribution and then for each publication a number of citations per publication simulated. Bootstrap confidence intervals indicate that the difference between the average of ratios and the ratio of averages are not significant, and there are no significant differences in the distributions in realistic problems when using the two-sample Kolmogorov-Smirnov test to compare distributions. It was found that the log-logistic distribution which is a general form for the ratio of two correlated Pareto random variables, give a good fit to the estimated ratios.