Meta-analysis data : application of quantile function techniques

Abstract

The development of quantitive research intergation for a large number of studies on a given topic leading to Glass's technique of meta-analysis using calculated effect size is examined. Nonparametric statistical data analysis methods are examined and illustrated, including Tukey's box-and-whiskers plot, quantile functions, and Parzen's quantile-box plots and goodness-of-fit techniques. A quantile-box plot method of analyzing effect size data from meta-analysis is described for use in determining the nature of the distribution form of effect size data before full-scale meta-analysis. In particular, the quantile-box plot method is applied to real meta-analysis data sets from pretest sensitization studies. The quantile-box plot analysis illustrates near-normality of these effect size data, lending credibility to the original assumption of normality of the effect size data for pretest sensitization effects. How a 21-number summary of effect size data can quickly provide information on their distribution characteristics is examined. It is recommended that all effect size data sets be summarized using the 21-numbers and that these and a quantile-box plot be routinely published in any meta-analysis study for which original effect size cannot be included.