Effects of experimental nitrogen additions on plant diversity in tropical forests of contrasting disturbance regimes in southern China

Responses of understory plant diversity to nitrogen (N) additions were investigated in reforested forests of contrasting disturbance regimes in southern China from 2003 to 2008: disturbed forest (withharvesting of understory vegetation and litter) and rehabilitated forest (without harvesting). Experimental additions of N were administered as the following treatments: Control, 50 kg N ha1yr1, and 100kg N ha1yr1. Nitrogen additions did not significantly affect understory plant richness, density,and cover in the disturbed forest. Similarly, no significant response was found for canopy closure in thisforest. In the rehabilitated forest, species richness and density showed no significant response to Nadditions; however, understory cover decreased significantly in the N-treated plots, largely a functionof a significant increase in canopy closure. Our results suggest that responses of plant diversity to N deposition may vary with different land-use history, and rehabilitated forests may be more sensitive to N deposition.

Power Calculations for Preclinical Studies Using a K-Sample Rank Test and the Lehmann Alternative Hypothesis

Power calculations in a small sample comparative study, with a continuous outcome measure, are typically undertaken using the asymptotic distribution of the test statistic. When the sample size is small, this asymptotic result can be a poor approximation. An alternative approach, using a rank based test statistic, is an exact power calculation. When the number of groups is greater than two, the number of calculations required to perform an exact power calculation is prohibitive. To reduce the computational burden, a Monte Carlo resampling procedure is used to approximate the exact power function of a k-sample rank test statistic under the family of Lehmann alternative hypotheses. The motivating example for this approach is the design of animal studies, where the number of animals per group is typically small.

Multiple Testing With an Empirical Alternative Hypothesis

An optimal multiple testing procedure is identified for linear hypotheses under the general linear model, maximizing the expected number of false null hypotheses rejected at any significance level. The optimal procedure depends on the unknown data-generating distribution, but can be consistently estimated. Drawing information together across many hypotheses, the estimated optimal procedure provides an empirical alternative hypothesis by adapting to underlying patterns of departure from the null. Proposed multiple testing procedures based on the empirical alternative are evaluated through simulations and an application to gene expression microarray data. Compared to a standard multiple testing procedure, it is not unusual for use of an empirical alternative hypothesis to increase by 50% or more the number of true positives identified at a given significance level.