The probability of a rare event is usually estimated directly as the number of times the event occurs divided by the total sample size. Unfortunately, the precision of this estimate is low. For typical sample sizes of N , 100 in ecological studies, the coefficient of variation (CV) of this estimate of the probability of a rare event can exceed 300%. Sample sizes on the order of 103–104 observat...

Analysis of variance (Anova) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (for example, splitplot designs), it is not always easy to set up an appropriate Anova. We propose a hierarchical analysis that automatically gives the correct Anova comparisons even in complex scenarios. The inferences for all means and variances are p...

Perceived blur is an important measure of image quality and clinical visual function. The magnitude of image blur varies across space and time under natural viewing conditions owing to changes in pupil size and accommodation. Blur is frequently studied in the laboratory with a variety of digital filters, without comparing how the choice of filter affects blur perception. We examine the percepti...

Analysis of variance (ANOVA) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (e.g., split-plot designs), it is not always easy to set up an appropriate ANOVA. We propose a hierarchical analysis that automatically gives the correct ANOVA comparisons even in complex scenarios. The inferences for all means and variances are perform...

To determine if deoxynivalenol (DON) is concentrated in small corn screenings, fourteen to twenty-three 1.1 kg test samples were taken from each of 10 barges of shelled corn. Each of the 181 test samples was divided into 2 components (fines and clean) using a 5 mm screen. The clean component sample rode the 5 mm screen and the fines component sample passed through the 5 mm screen. The DON conce...

Single and joint inclusion probabilities are generally available and known for complex survey designs up to the point where survey weights are modified due to nonresponse and population controls. Best practice by sophisticated survey practitioners generally includes weight modifications, first by calibration, ratio adjustment or raking to correct for nonresponse, next by further steps to impose...

Motivated by steady-state simulation experiments, we consider the problem of estimating the marginal variance of a stationary time series. The usual estimator, the sample variance is biased for autocorrelated data. To reduce bias, other authors have suggested interlaced estimators. These estimators which like the sample variance are sums of squares are a generalization of the sample variance an...