Abstract
Research papers represent an important and rich source of comparative data. The change is to extract the information of interest. Herein, we look at the possibilities to construct confidence intervals for sample averages when only ranges are available with maximum likelihood estimation with order statistics (MLEOS). Using Monte Carlo simulation, we looked at the confidence interval coverage characteristics for likelihood ratio and Wald-type approximate 95% confidence intervals. We saw indication that the likelihood ratio interval had better coverage and narrower intervals. For single parameter distributions, MLEOS is directly applicable. For location-scale distribution is recommended that the variance (or combination of it) to be estimated using standard formulas and used as a plug-in.
Highlights
One of the tasks statisticians face is extracting and possibly inferring biologically/clinically relevant information from published papers
Concomitant estimation of both means and associated standard deviations leads a substantial under-coverage of likelihood ratio intervals based on ranges
We showed that it is possible to construct likelihood-based confidence intervals for means when the only available data is the minimum and maximum value of a sample
Summary
One of the tasks statisticians face is extracting and possibly inferring biologically/clinically relevant information from published papers This aspect of applied statistics is well developed, and one can choose to form many easy to use and performant algorithms that aid problem solving. Often, these algorithms aim to aid statisticians/practitioners to extract variability of different measures or biomarkers that is needed for power calculation and research design [1,2]. While these algorithms are efficient and easy to use, they mostly are not probabilistic in nature, they do not offer means for statistical inference Another field of applied statistics that aims to help practitioners in extracting relevant information when only partial data is available propose a probabilistic approach with order statistics. Thereafter we list the results of the simulation, an illustrative application and conclude with a brief general discussion
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