Sample Size Determination for Grouped Exponential Observations: A Cost Function Approach

Calculating the required sample size for a desired power at a given type I error level, we often assume that we know the exact time of all subject responses whenever they occur during our study period. It is very common, however, in practice that we only monitor subjects periodically and, therefore, we know only whether responses occur or not during an interval. This paper includes a quantitative discussion of the effect resulting from data grouping or interval censoring on the required sample size when we have two treatment groups. Furthermore, with the goal of exploring the optimum in the number of subjects, the number of examinations per subject for test responses, and the total length of a study time period, this paper also provides a general guideline about how to determine these to minimize the total cost of a study for a desired power at a given α-level. A specified linear cost function that incorporates the costs of obtaining subjects, periodic examinations for test responses of subjects, and the total length of a study period, is assumed, primarily for illustrative purpose.     

Large-scale,millennial-length temperature reconstructions from tree-rings

Over the past two decades, the dendroclimate community has produced various annually resolved, warm season temperature reconstructions for the extratropical Northern Hemisphere. Here we compare these tree-ring based reconstructions back to 831 CE and present a set of basic metrics to provide guidance for non-specialists on their interpretation and use. We specifically draw attention to (i) the imbalance between (numerous) short and (few) long site chronologies incorporated into the hemispheric means, (ii) the beneficial effects of including maximum latewood density chronologies in the recently published reconstructions, (iii) a decrease in reconstruction covariance prior to 1400 CE, and (iv) the varying amplitudes and trends of reconstructed temperatures over the past 1100 years. Whereas the reconstructions agree on several important features, such as warmth during medieval times and cooler temperatures in the 17th and 19th centuries, they still exhibit substantial differences during 13th and 14th centuries. We caution users who might consider combining the reconstructions through simple averaging that all reconstructions share some of the same underlying tree-ring data, and provide four recommendations to guide future efforts to better understand past millennium temperature variability.     

Testing the Equality of Dependent Variances

The likelihood ratio test for testing equality of vgE;2 correlated variables is developed. In general, evaluation of the test statistic involves the iterative optimization of a likelihood function with 1 + v(v – 1)/2 parameters. The explicit form of the test statistic is derived in the bivariate case, and an iterative algorithm for determining the maximum likelihood estimates is suggested. A limited Monte Carlo study determines the behavior of the proposed procedure under the null hypothesis and variety of parameter values.     

Determinate growth and the scaling of photosynthetic energy intake in the solitary coral Fungia concinna (Verrill)

For many marine invertebrates, the maximum size of an individual is influenced heavily by environmental factors and may be limited by energetic constraints. In this study, an energetic model developed originally for anemones was applied to the free-living scleractinian Fungia concinna (Verrill) from Moorea (French Polynesia) to test the hypothesis that energetic constraints limit the size of this solitary coral. The modified model assumed that photosynthesis was the primary source of metabolic energy, and that metabolic costs were represented by aerobic respiration; these sources and sinks of energy were compared using daily energy budgets that were analyzed using double logarithmic regressions of energy against coral size. With this approach, energy limitation is characterized by a scaling exponent for energetic cost (b_cost) that is larger than the scaling exponent for energy intake (b_intake). For the size range of F. concinna studied, b_intake = 0.73 ± 0.09 and b_cost = 0.46 ± 0.10, thereby demonstrating that large individuals accumulated an energetic surplus, even when the expenditure associated with host tissue and symbiont growth was included in the model. The surplus of energy that this coral acquires as it grows appears to be driven by the scaling of traits associated functionally with the scaling of respiration and photosynthesis. Specifically, tissue biomass displayed a strong positive allometry with respect to surface area (i.e., b > 1), and this constraint on surface area may be the mechanistic basis of the low scaling exponent for metabolic cost. In contrast, the capacity for autotrophy - defined indirectly as Symbiodinium population density and chlorophyll content - increased isometrically with surface area, and likely contributed to the higher scaling exponent for intake relative to cost. Our results suggest that growth in F. concinna is not limited strictly by energy, but instead maximum size must be determined by alternative physiological or ecological constraints.     

The Effects of Misspecification of a Regression Model

The consequences of the misspecification of a regression model are considered. For small effects of covariates a proportional consistency theorem is derived. The consistent estimation of the covariance matrix of the estimates is discussed.