Specified Level Of Precision Research Articles

Exact two‐sided tolerance interval controlling tail proportions for sample variances

AbstractTolerance intervals (TIs) for variances are useful when we are interested in the precision of the quality characteristic. They can provide a deeper understanding of the process variability corresponding to process improvement and deterioration. In this paper, we consider the exact two‐sided TI for sample variances that simultaneously controls the proportions in each of the two tails of the distribution. The minimum number of subgroups required to achieve a specified level of precision is also computed. Moreover, we minimize the width of the TI through adjusting the tolerance factors, and the performance of the adjusted TI shows some improvement, especially when the amount of reference data is small. Finally, a real application is used to illustrate the construction and implementation of the proposed TIs.

Multivariate Boundaries of a Self Representing Stratum of Large Units in Agricultural Survey Design

In business surveys in general, and in multipurpose agricultural surveys in particular, the problem of designing a sample from a list frame usually consists of two different aspects. The first is concerned with the choice of a rule for stratifying the population when several size variables are available and the second is devoted to sample size determination and sample allocation to a given set of strata. The main property that is required of the sample design is that it delivers a specified level of precision for a set of variables of interest using as few sampling units as possible. This article examines how this can be achieved via a basic partition into two strata, one completely enumerated and the other sampled, defined in such a way as to achieve both these objectives. The procedure was used to design the Italian Milk Products Monthly Survey on the basis of a set of auxiliary variables obtained from an annual census of the same target population. Given the combinatorial optimization nature of the problem, we use stochastic relaxation theory, and in particular, we use simulated annealing because of its flexibility. Our results indicate that in this situation the multivariate partition obtained by using this random search strategy is a suitable solution as it permits identification of boundaries of any shape. Furthermore, numerical comparisons between sampling designs obtained by using these procedures and some simple extensions of univariate stratification rules are made. The gain from using the proposed strategy is nontrivial as it achieves the required precision using a sample size that is notably smaller than that required by simple extensions to univariate stratification rules.

Airborne scanning LiDAR in a double sampling forest carbon inventory

To meet Kyoto Protocol obligations, New Zealand is required to estimate forest carbon stock change over the first commitment period (2008–2012). New Zealand has three subcategories of forest, namely: Natural forest; Pre-1990 forest; and Post-1989 forest. The Post-1989 forest carbon inventory undertaken in 2008 used discrete return airborne LiDAR and ground-based measurements of 0.06 ha circular plots located on a 4-km × 4-km grid. The national carbon stock estimate was based on a double sampling scheme consisting of 246 plots from which both ground and LiDAR data were obtained, supplemented with 46 additional plots assessed using only LiDAR. This paper describes the relationships established between carbon stocks estimated using ground-based measurements and LiDAR metrics. A regression model explaining 74% of the variation in total carbon was developed using LiDAR 30th percentile height (P30ht) and canopy cover (%Cover). The regression estimator improved the precision of the national carbon stock estimate in 2008 by 6% compared to the ground-based estimate. This inventory indicates that it is possible to reduce the cost of obtaining carbon stock estimates to a specified level of precision using a combination of ground-based and LiDAR measurements in a double sampling approach. The theoretical maximum improvement in precision expected in 2012, when additional LiDAR data are expected to be available, is 50–55%.

Relationship between element concentrations and body size in the Lake Maggiore population of Unio pictorum mancus (Mollusca, Bivalvia)

The study focused on using a fresh-water mussel (Unio pictorum mancus) as a bioindicator of various pollutants, and particularly metals. The elements considered were: Al, As, Ca, Cd, Co, Cr, Cu, Fe, Mn, Mo, Ni, Pb, V and Zn. This research was carried out at a site where various other studies have been conducted on important characteristics of the same population of Unio. This site is a small bay called "Sabbie d’Oro" located on the south-east coast of Lake Maggiore. Our study involved quantifying the capacity of this mollusc to concentrate large amounts of metal in its body without evident consequences by using detoxification mechanisms. We analysed not only element concentrations, but also their variability (expressed as CV%) in the soft tissues and in the shell, for two main reasons: i) the sampling design should include a preliminary analysis to determine how many specimens is necessary collect to ensure a specified level of precision; ii) the sample variability value may be combined with the value of analytical precision (BCR) to obtain an estimate of the "experimental" precision. In soft tissue, Ca accumulation tended to increase with size, and Al accumulation decreased with size. In shell, Ca and Ni were stored more than in soft tissue, but not proportionally to size. V, Cr and Mo tended to accumulate in the shell progressively over the years, whereas Co and Al are "diluted" during growth, or are absorbed mainly during the juvenile stage. Partition between shell and soft tissue resulted roughly the same in the juvenile and adult stages for the following elements: Fe, Al, Co, As, Pb. The relationships among the various elements were schematized in a hierarchical tree plot.

Sequential Fixed Width Confidence Intervals for the Offset Between Two Network Clocks

Estimation of the offset between two network clocks has received a lot of attention in the literature, with the motivating force being data networking applications that require synchronous communication protocols. Statistical modeling techniques have been used to develop improved estimation algorithms, with a recent development being the construction of a confidence interval based on a fixed sample size. Lacking in the fixed sample size confidence interval procedures is a useable relationship between sample size and the width of the resulting confidence interval. Were that available, an optimum sample size could be determined to achieve a specified level of precision in the estimator and thereby improve the efficiency of the estimation procedure by reducing unnecessary overhead in the network that is associated with collecting the data used by the estimation schemes. A fixed sample size confidence interval that has a prescribed width is not available for this problem. However, in this paper we develop and compare alternative sequential intervals with fixed width and demonstrate that an effective solution is available.

Sample size requirements for studying small populations in gerontology research

Calculating sample sizes required to achieve a specified level of precision when estimating population parameters is a common statistical task. As consumer surveys become increasingly common for nursing homes, home care agencies, other service providers, and state and local administrative agencies, standard methods to calculate sample size may not be adequate. Standard methods typically assume a normal approximation and require the specification of a plausible value of the unknown population trait. This paper presents a strategy to estimate sample sizes for small finite populations and when a range of possible population values is specified. This sampling strategy is hierarchical, employing first a hypergeometric sampling model, which directly addresses the finite population concern. This level is then coupled with a beta-binomial distribution for the number of population elements possessing the characteristic of interest. This second level addresses the concern that the population trait may range over an interval of values. The utility of this strategy is illustrated using a study of resident satisfaction in nursing homes.

Approximate programmable quantum processors

A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor to approximate a set of unitary operators to a specified level of precision. We measure how well an operation is performed by the process fidelity between the desired operation and the operation produced by the processor. We show how to find the program for a given processor that produces the best approximation of a particular unitary operation. We also place bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.

Cetuximab alone or in combination with irinotecan effective against irinotecan-refractory colorectal cancer

Results of a multicenter European trial indicate that cetuximab has clinically significant activity when given alone or in combination with irinotecan in patients with irinotecan-refractory colorectal cancer. The findings appear in The New England Journal of Medicine. Cetuximab is a monoclonal antibody that specifically blocks the epidermal growth factor receptor (EGFR), which participates in signaling pathways that are deregulated in cancer cells and that commonly appears on colorectal-cancer cells. EGFR, a member of the ErbB family of receptors, is relevant in colorectal cancer because expression or up-regulation of the EGFR gene occurs in 60% to 80% of cases. Moreover, studies show that expression of the gene is associated with poor survival. Dr. David Cunningham of Royal Marsden Hospital, London and Surrey, United Kingdom, and colleagues randomly assigned 329 patients whose disease had progressed during or within 3 months after treatment with an irinotecan-based regimen to receive either cetuximab and irinotecan or cetuximab monotherapy. “Cetuximab (Erbitux, Merck, and Imclone Systems) is a chimeric IgG1 monoclonal antibody that binds to EGFR with high specificity and with a higher affinity than either epidermal growth factor or TGF-α, thus blocking ligand-induced phosphorylation of EGFR,” the report states. “In addition, cetuximab enhances the effects of irinotecan and radiotherapy in experimental systems.” In this trial, the addition of irinotecan to cetuximab monotherapy was permitted in patients whose disease progressed during the investigation. All patients were evaluated radiologically for tumor response and were also evaluated for the time to tumor progression, survival, and side effects of treatment. The authors state that the rate of response in the combination-therapy group was significantly higher than that of the monotherapy group (22.9% [95% confidence interval, 17.5%–29.1%] vs. 10.8% [95% confidence interval, 5.7%–18.1%], P = 0.007). Median time to progression was significantly greater in the combination-therapy group (4.1 vs. 1.5 months, P < 0.001 by the log-rank test). The median survival time was 8.6 months in the combination-therapy group and 6.9 months in the monotherapy group (P = 0.48). Toxic effects were more frequent in the combination-therapy group, but their severity and incidence were similar to those that would be expected with irinotecan. In an accompanying editorial Drs. Charles Erlichman, M.D., and Daniel J. Sargent, Ph.D. of the Mayo Clinic, Rochester, Minnesota, raise a number of issues. They say the trial “implicitly addressed the question of whether adding cetuximab to irinotecan resensitizes tumors that are refractory to irinotecan. In that sense, the findings clearly support the notion that interfering with EGFR signaling can overcome the resistance to irinotecan.” However, they add, “the appropriateness of the authors’ reporting methods warrants discussion. The primary end point of the trial was a tumor response, and the planned sample size was based not on a comparison of groups but on an estimation of the response rate to a specified level of precision. Thus, the trial could be best labeled as a randomized, phase 2 trial.” Based on the response rate, 10.8%, with a median time to progression of 1.5 months, the editorial also questions the magnitude of the benefit of cetuximab alone for patients who may not be able to tolerate the combination. “In essence, the current trial seems to validate the previously reported single-group studies of cetuximab alone and cetuximab plus irinotecan. For these reasons and others that have been well chronicled, the past 3 years have provided no mature data on cetuximab and irinotecan as first-line treatment or in combination with fluorouracil or fluorouracil-and-oxaliplatin regimens. Nonetheless, trials of cetuximab as a component of first-line treatment are ongoing, and the agent is about to be added to an ongoing trial of adjuvant therapy for colon cancer.” More details can be found in N Engl J Med 2004;351:337–345, 391–392.

Efficient sampling designs for microbial processes: a case study

We describe a method for determining optimal sampling designs for experiments involving subsampling in stages. An optimal sampling design either maximizes the precision of the results for a given amount of experimental effort (time, money) or minimizes the effort required to achieve a specified level of precision. The optimization method utilizes information on (i) the cost of obtaining a sample at each stage and (ii) the variability of the data attributable to each sampling stage. To illustrate the method, we use effluent suspended cell data from a packed-bed bioreactor. The sample design involved three stages. First, three primary samples were collected from the reactor. Second, each reactor sample was subsampled in triplicate and a specified volume of each subsample was passed through a filter. Third, the bacteria of the filter were counted in each of ten microscopic fields, each field representing the same proportion of the filter area. The optimization analysis, applied to the mean of the log-transformed bacterial counts, showed that the precision of the sample mean could be substantially improved by expending more sampling effort on the first stage and less on the second and thir stages. We also show how the optimization analysis can be applied to other response measurements (e.g., total organic carbon, soluble organic carbon and glucose concentration) and sampling designs involving other numbers of subsampling stages.

The distribution and estimation of jack pine budworm defoliation

A method to categorize defoliation on current year's shoots of jack pine (Pinusbanksiana Lamb.) was developed. The pattern of defoliation caused by the jack pine budworm (Choristoneurapinuspinus Free.) feeding on jack pine trees was studied in a variety of locations in Manitoba and Saskatchewan over several years. In addition to differences among locations and years, the crown level from which a sample was taken, the branch within a tree, the tree within a plot, and the plot within a study location were consistent sources of variation. In general, the upper crown was most heavily defoliated and the lower crown least so. Branches, trees, and plots are random sources of variation, and the variance components associated with each such source were analyzed to determine their contribution to the overall variance in the estimate of defoliation. The relative importance of each random source of variation varied with the percent defoliation. Variation among plots was significant at defoliation levels below 45% and peaked at 25%, indicating a patchy distribution of feeding within stands in this range of defoliation. Beyond 45% defoliation, feeding was uniformly distributed among plots within a stand. Variation in defoliation among branches and trees peaked in the 50–60% defoliation range and was negligible at the extremes. Advantage can be taken of the consistent patterns of defoliation among crown levels and knowledge of the variance components of the random sources of variation to design defoliation assessment protocols. These data were used to optimize the allocation of effort, among plots, trees, and branches, required to determine the level of defoliation in stands either with fixed level of effort or to a specified level of precision.

Monte Carlo studies of sampling strategies for estimating tributary loads

Monte Carlo techniques were used to evaluate the accuracy and precision of tributary load estimates, as these are affected by sampling frequency and pattern, calculation method, watershed size, and parameter behavior during storm runoff events. Simulated years consisting of 1460 observations were chosen at random with replacement from data sets of more than 4000 samples. Patterned subsampling of these simulated years produced data appropriate to each sampling frequency and pattern, from which load estimates were calculated. Thus results for all sampling strategies were based on the same series of simulated years. Sampling frequencies ranged from 12 to roughly 600 samples per year. Unstratified and flow‐stratified sampling were examined, and loads were calculated with and without the use of the Beale Ratio Estimator. All loads were evaluated by comparison with loads calculated from all 1460 samples in the simulated year. Studies consisting of 1000 iterations were repeated twice for each of five parameters in each of three watersheds. The results show that bias and precision of loading estimates are affected not only by the frequency and pattern of sampling and the calculation approach used, but also by the watershed size and the behavior of the chemical species being monitored. Furthermore, considerable interaction exists between these factors. In every case, loads based on flow‐stratified sampling and calculated using the Beale ratio estimator provided the best results among the strategies examined. Differences in bias and precision among watersheds and among transported materials are related to the variability of instantaneous fluxes in the systems being monitored. These differences are qualitatively predictable from knowledge of the time behavior of the material and hydrological systems involved. Attempts to derive quantitative relationships to predict the sampling effort required to achieve a specified level of precision have not been successful.

Line transect estimators for schooling populations

Line transect estimators are derived for the number of schools and number of individuals in a schooling population where the probability of sighting a school is a non-decreasing function of school size. The sighting curve for all schools is a weighted sum of individual sighting curves. One method of analysis pools data across school size classes to estimate the number of schools in the population, and multiplies by a weighted estimator of average school size to estimate the total number of individuals. A second method post-stratifies data by school size classes. The coefficient of variation of the estimated number of schools from the pooling method is always less than that for the method of post-stratification, but this result does not apply to the estimated number of individuals. Formulae are given for determining the transect length to achieve a specified level of precision. The methods are applied to minke whale data, using the generalized exponential model for sighting probability. The application illustrates the increased sighting probability of larger schools. The estimates of the number of schools are similar for the two methods, but the precision of the method of pooling is higher. The two methods produce different estimates of the number of individuals because of variability in mean school size.

An algebraic method of strain analysis using elliptical markers

A new method is described for finite strain analysis of naturally deformed sub-fabrics of elliptical markers assuming an homogeneous deformation on the scale of the sample. The method is numerical, and relies on derived equations which relate the axial ratios and orientations of elliptical markers to algebraic parameters of finite linear transformations. This treatment provides criteria for the identification in the deformed state of initial random and non-random but symmetric distributions of elliptical markers about the bedding-trace. For these types of deformed fabric, the method allows: 1. (1) numerical evaluation of the finite strain ratio for the plane of section 2. (2) statistical estimation of the error in this determination due to the sample-size of measured markers and the orientation of the section 3. (3) optimal evaluation of the strain ratio in cases where an initial random fabric is identified 4. (4) determination of the pre-tectonic axial ratios and orientations of the elliptical markers relative to the undeformed bedding-trace 5. (5) determination of pre-tectonic compactional strain imposed on a random depositional fabric; and 6. (6) theoretical investigation of the minimum number of measurements required by the method for any specified level of precision in strain determination in relation to various postulated initial distributions of axial ratios and orientations. Some practical applications of the method are described.

On Matching Lists by Samples

Abstract The problem considered is estimation by sampling methods of the number of names common to two or more lists. The situation covered is that in which the lists are found to have been merged and must be sampled as one. A comparison is made with the case in which the lists can be sampled separately. Tables are included giving the sample sizes necessary to achieve a specified level of precision.