Statistical Issues in Meta-Analysis.

Meta-analysis is a quantitative method for research synthesis in which independent studies are combined to estimate treatment effects and their variability. This method can be advantageous because it relies on quantitative information and allows for testing of hypotheses that cannot be answered by a single study. Additionally, in agricultural research there is the potential for a substantial increase in statistical power because in single studies there is a prevalence of small true differences, small Type I errors and few replications, which generate experiments with low statistical power (large Type II Errors). A disadvantage of meta-analysis, as well as of narrative reviews, is that some details of individual studies are necessarily disregarded in exchange for reaching general conclusions.

In meta-analysis the two main sources of variation are within- and between-studies. Within-studies variability is often represented by the factors year and location, which are sometimes combined in a single factor, environment. Traditionally, the factor year has been considered as fixed mainly because of the inability to solve statistical models that included random factors prior to modern statistical software. Considering year as fixed restricts the inference space to the levels chosen in a particular study, which is of limited practical interest. On the other hand, when year is considered as random and only information from two or three years is available, the variance component estimate for year and the interactions with other factors are unreliable. Therefore, when little information is available, there are limitations to considering year as either random or fixed. Using meta-analytic methods has the advantage of including the random variability due to year in the error, but with a relatively larger number of observations.