A meta-analysis uses standardized differences, i.e.,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d = (\bar{y}_{\text{test}} - \bar{y}_{\text{control}} )/s_{\text{p}}$$\end{document}d=(y¯test-y¯control)/spwhere \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{y}_{\text{test}}$$\end{document}y¯test and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{y}_{\text{control}}$$\end{document}y¯control are the sample mean of the test and control, respectively, and s p is the pooled standard deviation, which is calculated from the individual test and control standard deviations. Thus, the standard errors were converted into standard deviations. The database spreadsheets were imported into the software Comprehensive Meta-Analysis™ (version 2, 2011; Biostat™, Englewood, NJ). Separate meta-analyses were conducted for each of the three test materials within each of the two regulatory phases (Experimental and Pilot) using random-effects models (Cochran and Cox 1957). In some cases, there were studies where the standard deviation for the test and/or the control was zero. These studies were excluded from the meta-analysis because s p in Eq. (1) is assumed to be calculated from nonzero standard deviations. The meta-analysis used standardized differences from each individual study to compute a combined study effect. The combined study effect is a weighted standardized difference between test and control across studies, and the weights are functions of the sample sizes (Hedges and Olkin 1985). A random-effects model was used in each meta-analysis based on the assumption that the material effect interacts with the changing environments (sites), which is a common assumption in agronomic studies. The combined study effect obtained under the random-effects model is an estimate of the overall effect (standardized difference between test and control) across all potential environments. (The significance testing of this overall effect took the material-by-site interaction effect into account.) A 95 % confidence interval along with the p value was also obtained to describe the combined study effect. If the 95 % confidence interval contains zero, then the standardized difference favors neither the test nor the control. If the interval does not contain zero and is positive, then the standardized difference favors the test (test minus control is positive); if the interval does not contain zero and is negative, then the standardized difference favors the control (test minus control is negative). Statistical significance is defined by a p value <0.05. If the p value is less than 0.05, then the combined study effect is significantly different from zero, which means that the test and control are significantly different.