Extracting Within-Experiment Precision of Horticultural Experiments Useful for Meta-Analysis

Olkin and Shaw (1995) discussed statistical methods for meta-analysis and its applications in horticultural science. They presented methods for combining tests of significance as well as methods for comparing differences between treatments. For the latter, the standardized difference of two normal means is the effect size of interest and Olkin and Shaw (1995) presented the statistical meta-analysis in the fixed effects model, that is, they assumed homogeneous effect sizes in all the experiments eligible for meta-analysis. A major obstacle to conducting meta-analysis is the non-availability of appropriate experimental results in published journal articles. As Olkin and Shaw (1995) said ”The minimum information required for quantitative research synthesis includes means, sample sizes, and either standard errors or standard deviations.” Shaw and Larson (1999) conducted a meta-analysis of strawberry yield response to preplant soil fumigation with combinations of methyl bromide-cloropicrin and several alternative systems. They followed the lines of Olkin and Shaw (1995) and an inclusion criterion was that means, sample sizes, and either standard errors or standard deviations of the treatments had to be reported in the published articles. Since the published results of four studies, basically eligible for that meta-analysis, lacked these necessary parameters for inclusion, these four studies were omitted. The quality of reporting results in the published articles determines the quality of the meta-analysis. Unfortunately, Olkin and Shaw’s summation about the minimum information required for meta-analysis is still often ignored by presenting results of horticultural experiments in publications nowadays. The lack of information about the precisions of the estimated means in most published articles was a major obstacle for the meta-analysis of Porter et al. (2006) on validating the yield performance of alternatives to methyl bromide for preplant fumigation. To circumvent the problem of missing within-experiment precision, Porter et al. (2006) simply assumed that the between-experiment variability is