We have conducted population size estimation study among KAP (key affected population) using different methods. So we have got various estimates, although with overlapping acceptable intervals. Then we hypothesized the median of the various estimates could be the most plausible size estimate. It has also been suggested to use an average. How do we reassure, was it the best decision in our case?
It looks like location estimation right? Then, the mean is the best estimator if the data shows Gaussian distribution. You can compute the residuals and perform a statistical test if your assumption (Gaussian) was not wrong.
The median works superior if your data shows some outliers. You can use boxplots with notches to compare the location of different data sets. There is also a 'conversion' for the median so that it meets the result of the mean if the data is Gaussian.
There is a third location estimator, called shortest half.
The drawback of median is, that it has slower convergence.
Two references that might help.
mean vs median vs shortest half, Chapter 4:
@BOOK{Rousseeuw1987,
title = {Robust regression and outlier detection},
publisher = {Wiley},
year = {1987},
author = {Rousseeuw, P.J. and Leroy, A.M.},
series = {Wiley series in probability and mathematical statistics : Applied
probability and statistics},
doi = {10.1002/0471725382},
}
boxplots:
@ARTICLE{McGill1978,
author = {McGill, R. and Tukey, J.W. and Larsen, W.A.},
title = {Variations of Box Plots},
journal = {The American Statistician},
year = {1978},
volume = {32},
pages = {12--16},
number = {1},
doi = {10.2307/2683468},
issn = {00031305},
publisher = {Taylor \& Francis, Ltd. on behalf of the American Statistical Association},
}
I hope this was somehow helpful.
You can compare the precision of different methods for KAP.
Median is positional averages, and whether it is suitable for KAP!
Agree with Stephan Rhode, Rousseeuw is a good reference for robust statistics.
Dear Stephan, Rajiv and David, thanks a lot. You really helped me.
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