Statistical Power in Plant Pathology Research.

In null hypothesis testing, failure to reject a null hypothesis may have two potential interpretations. One interpretation is that the treatments being evaluated do not have a significant effect, and a correct conclusion was reached in the analysis. Alternatively, a treatment effect may have existed but the conclusion of the study was that there was none. This is termed a Type II error, which is most likely to occur when studies lack sufficient statistical power to detect a treatment effect. In basic terms, the power of a study is the ability to identify a true effect through a statistical test. The power of a statistical test is 1 - (the probability of Type II errors), and depends on the size of treatment effect (termed the effect size), variance, sample size, and significance criterion (the probability of a Type I error, α). Low statistical power is prevalent in scientific literature in general, including plant pathology. However, power is rarely reported, creating uncertainty in the interpretation of nonsignificant results and potentially underestimating small, yet biologically significant relationships. The appropriate level of power for a study depends on the impact of Type I versus Type II errors and no single level of power is acceptable for all purposes. Nonetheless, by convention 0.8 is often considered an acceptable threshold and studies with power less than 0.5 generally should not be conducted if the results are to be conclusive. The emphasis on power analysis should be in the planning stages of an experiment. Commonly employed strategies to increase power include increasing sample sizes, selecting a less stringent threshold probability for Type I errors, increasing the hypothesized or detectable effect size, including as few treatment groups as possible, reducing measurement variability, and including relevant covariates in analyses. Power analysis will lead to more efficient use of resources and more precisely structured hypotheses, and may even indicate some studies should not be undertaken. However, the conclusions of adequately powered studies are less prone to erroneous conclusions and inflated estimates of treatment effectiveness, especially when effect sizes are small.

Spatial and temporal assessment of pollen- and seed-mediated gene flow from genetically engineered plum Prunus domestica.

Pollen flow from a 0.46 ha plot of genetically engineered (GE) Prunus domestica located in West Virginia, USA was evaluated from 2000-2010. Sentinel plum trees were planted at distances ranging from 132 to 854 m from the center of the GE orchard. Plots of mixed plum varieties and seedlings were located at 384, 484 and 998 m from the GE plot. Bee hives (Apis mellifera) were dispersed between the GE plum plot and the pollen flow monitoring sites. Pollen-mediated gene flow from out of the GE plum plot to non-GE plums under the study conditions was low, only occurring at all in 4 of 11 years and then in only 0.31% of the 12,116 seeds analyzed. When it occurred, gene flow, calculated as the number of GUS positive embryos/total embryos sampled, ranged from 0.215% at 132 m from the center of the GE plum plot (28 m from the nearest GE plum tree) to 0.033-0.017% at longer distances (384-998 m). Based on the percentage of GUS positive seeds per individual sampled tree the range was 0.4% to 12%. Within the GE field plot, gene flow ranged from 4.9 to 39%. Gene flow was related to distance and environmental conditions. A single year sample from a sentinel plot 132 m from the center of the GE plot accounted for 65% of the total 11-year gene flow. Spatial modeling indicated that gene flow dramatically decreased at distances over 400 m from the GE plot. Air temperature and rainfall were, respectively, positively and negatively correlated with gene flow, reflecting the effects of weather conditions on insect pollinator activity. Seed-mediated gene flow was not detected. These results support the feasibility of coexistence of GE and non-GE plum orchards.