Mixed Models Approach to on-Farm Trials: An Alternative to Meta-Analysis for Comparing One Treatment to Possibly Different Controls

Abstract

The estimator of effect size, the sample mean difference divided by the sample standard error of the difference is studied in the context of mixed models and is related to the analysis of on-farm trials. A single treatment is compared against possibly different controls using a completely randomized design on each farm. A lower (l-u)l00% confidence limit on mean difference of the treatment and the average control is obtained. The best linear unbiased predictors (BLUPs) of the mean difference of the treatment and the individual controls as well as the lower {1-a)100% prediction limits are provided. The effect of omitting or not omitting the farm-bytreatment interaction variance component in the weighting process is assessed using two numerical examples.

Analysis of Linear Models with Two Factors Having Both Fixed and Random Levels

“…The former levels of the two factors (weeding and plant population) are fixed effects and the latter levels are random effects. On-farm trials, which are experiments conducted on the farmers' fields (Amir and Knipscheer, 1989;Hildebrand, 1984;Mutsaers et al, 1997;Njuho and Milliken, 1995;Njuho and Chui, 1999;Riley and Fielding, 2001) involve evaluation of new technologies against old technologies (farmers' practices).…”

Analysis of Linear Models with One Factor Having Both Fixed and Random Levels

“…The new technologies are considered fixed effects and the old technologies as random effects where the later are randomly selected from a population of farmers. General procedures on analysis of data from on-farm trials are discussed (Hildebrand, 1984;Hildebrand and Russell, 1996;Mutsaers et al, 1997;Njuho and Milliken, 1995;Njuho and Chui, 1999;Riley and Fielding, 2001).…”

“…On-farm trials are experiments conducted on the farmers' fields with an aim to incorporate the farmers' opinions, management strategies, and environmental conditions into the newly developed technologies (Njuho and Milliken, 1995). The analysis of data from such trials and the subsequent inference drawn depends on the characterization of the factors involved as to whether they are either fixed or random.…”