Balanced Sampling Design Research Articles

Estimating the Variability of Active‐Layer Thaw Depth in Two Physiographic Regions of Northern Alaska

The active layer is the zone above permafrost that experiences seasonal freeze and thaw. Active‐layer thickness varies annually in response to air and surface temperature, and generally decreases poleward. Substantially less is known about thaw variability across small lateral distances in response to topography, parent material, vegetation, and subsurface hydrology.A graduated steel rod was used to measure the 1998 end‐of‐season thaw depth across several transects. A balanced hierarchical sampling design was used to estimate the contribution to total variance in active‐layer depth at separating distances of 1, 3, 9, 27, and 100 meters. A second sampling scheme was used to examine variation at shorter distances of 0.3 and 0.1 meter. This seven‐stage sample design was applied to two sites in the Arctic Foothills physiographic province, and four sites on the Arctic Coastal Plain province in northern Alaska. The spatial variability for each site was determined using ANOVA and variogram methods to compare intersite and inter‐province variation.Spatial variation in thaw depth was different in the Foothills and Coastal Plain sites. A greater percentage of the total variance occurs at short lag distances (0–3 meters) at the Foothills sites, presumably reflecting the influence of frost boils and tussock vegetation on ground heat flow. In contrast, thaw variation at the Coastal Plain sites occurs at distances exceeding 10 meters, and is attributed to the influence of well‐developed networks of ice‐wedge polygons and the presence of drained thaw‐lake basins. This information was used to determine an ongoing sampling scheme for each site and to assess the suitability of each method of analysis.

Spatial variability of soil microbial biomass measured by the fumigation extraction method, and KEC as affected by depth and manure application

The horizontal and vertical variability of “total” soil microbial biomass measured by the fumigation-extraction method (FEM), and the extraction efficiency coefficient K EC, were investigated at the plot scale in an unfertilized soil and in a dairy manure-treated (100 t ha −1) soil. Soil cores (0–60 cm) were taken according to a balanced nested sampling design and were sectioned into 20-cm increments. Microbial biomass was measured by the fumigation-extraction method (FEM), and the K EC was determined by in situ 14C-labelling; total and soluble C were also measured on all samples. Manure application increased the variability of all measured properties at the 0–20 cm and 20–40 cm depths. The range was generally inferior to 0.1 m in the unfertilized plot and between 0.1 and 1 m in the manure-treated plot. Microbial biomass spatial variability was similar to that of total C, and was highly correlated with total C throughout the soil profile. At the plot scale, sampling distances of greater than 1 m were required to adequately measure biomass. K EC values did not correlate with organic carbon, soluble carbon, clay or silt content. K EC values for soils sampled from all depths fell within the range of 0.30 to 0.43, close to the commonly used consensus value of about 0.4. However, the K EC for subsurface soil samples was significantly lower and more variable than that for surface soils. The results of this study suggest that using K EC values for surface soils to calculate subsurface soil biomass using the FEM would result in a significant underestimate of the true subsurface soil biomass value.

Balanced designs in longitudinal population pharmacokinetic studies.

A simulation study was performed using a balanced design to determine the sample size required for accurate and precise estimation of a parameter at a given level of intersubject variability in a longitudinal population pharmacokinetic study. A two-compartment model parameterized in terms of clearance (Cl), volumes of the central (V1) and peripheral (V2) compartments, and intercompartmental clearance (Q) with multiple intravenous bolus inputs was assumed. Six samples were obtained from each subject using the informative profile (block) randomized design. Variability (in terms of coefficient of variation, CV) in model parameters was varied between 30% and 100%, and residual variability was fixed at 15%. Sample sizes ranging from 30 to 1,000 subjects were studied, and a hundred replicate data sets were generated and analyzed with NONMEM for each sample size at each CV. A sample size of 30 was required for accurate and precise estimation of structural model parameters when CV < or = 75%, except for Cl where it is adequate for CV < or = 100%. A sample size of 80 was required for intersubject variability estimation with CV < or = 60%. Robust estimates of variability in Cl were obtained with sample sizes of 30 (CV < or = 45%), 60 (CV 60-75%), and 100 (CV > or = 75%). Positively biased estimates of residual variability were obtained irrespective of sample size at > or = 60% CV. This indicates that estimates of residual variability obtained in study situations where CV > or = 60% should be interpreted with caution. In such situations model misspecification may not be the issue, because in this simulation study concentration-time profiles were generated and analyzed with the same model. Although these results should be interpreted within the context of the study, they provide a framework for addressing the issue of sample size in longitudinal population pharmacokinetic study with a balanced sampling design. The result of a population pharmacokinetic study can be anticipated by comparing the results of several simulations in which the various input factors have been varied.

Balanced versus unbalanced designs for linear structural relations in two‐level data

A general two‐level model for multivariate data is described and illustrated by specializations to a common factor model and a path model with latent variables. The problem of estimation is treated, and in the special case of a balanced sampling design, a likelihood‐based discrepancy function and a test of goodness of fit are obtained in terms of some simple sufficient statistics.

Construction of Some Non-Invariant Balanced Sampling Designs

The problem considered in this paper is that of construcHng fixed size sampling designs having constant inclusion probabilities of first two orders. Some such sampling designs are developed in situations where the population units are subject to classification in one or more ways eliminating the chance of selection of samples for which the units have too lopsided a distribution over the classes.

On the Construction of Non­Invariant Balanced Sampling Designs

The problem of constructing non­invariant balanced sampling designs of fixed effective size has been considered and solutions have been suggested to cover all possible combinations of values of the population and the sample sizes, The methods also illustrate that fixed effective size designs can easily be constructed with constant inclusion probabilities of first two orders and with the number of possible samples much smaller than that for the usual SRSWOR procedure.

Statistical problems in multi‐variate (etiological) surveys

AbstractA number of multi‐variate etiological surveys are analyzed for recurrent sources of bias in balanced and purposive sampling designs. Three nonsampling components emerge that may dominate the total error of a sample survey estimate. Outstanding among these appear to be administrative consideration of cost and convenience which may actually determine a sampling procedure, especially by reliance on voluntary participation, proxy responses and case‐finding methods that restrict the sample. Next is lack of comparability of population series that differ on some initial state (as to smoking). Finally, errors are caused by strong beliefs in what results should be. Extensive experience has now shown that it may not be possible to conduct a satisfactory etiological inquiry by use of surveys using nonrandom population samples.