Statistical power calculation and sample size determination for environmental studies with data below detection limits

Power calculation and sample size determination are critical in designing environmental monitoring programs. The traditional approach based on comparing the mean values may become statistically inappropriate and even invalid when substantial proportions of the response values are below the detection limits or censored because strong distributional assumptions have to be made on the censored observations when implementing the traditional procedures. In this paper, we propose a quantile methodology that is robust to outliers and can also handle data with a substantial proportion of below-detection-limit observations without the need of imputing the censored values. As a demonstration, we applied the methods to a nutrient monitoring project, which is a part of the Perth Long-Term Ocean Outlet Monitoring Program. In this example, the sample size required by our quantile methodology is, in fact, smaller than that by the traditional t-test, illustrating the merit of our method.

A Bayesian decision approach for sample size determination in phase II trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion: of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study.

Crystallite size effects in stacking faulted nickel hydroxide and its electrochemical behaviour

P-Nickel hydroxide comprises a long range periodic arrangement of atoms with a stacking sequence of AC AC AC-having an ideal composition Ni(OH)(2). Variation in the preparative conditions can lead to the changes in the stacking sequence (AC AC BA CB AC AC or AC AC AB AC AC) This type of variation in stacking sequence can result in the formation of stacking fault in nickel hydroxide. The stability of the stacking fault depends on the free energy content of the sample. Stacking faults in nickel hydroxide is essential for better electrochemical activity. Also there are reports correlating particle size to the better electrochemical activity. Here we present the effect of crystallite size on the stacking faulted nickel hydroxide samples. The electrochemical performance of stacking faulted nickel hydroxide with small crystallite size exchanges 0.8e/Ni, while the samples with larger crystallite size exchange 0.4e/Ni. Hence a right combination of crystallite size and stacking fault content has to be controlled for good electrochemical activity of nickel hydroxide. (C) 2008 Elsevier B.V. All rights reserved.

Effect of crystallite size and clustering in influencing the stability of phases of a very large tetragonality ferroelectric system 0.6BiFeO(3)-0.4PbTiO(3)

The role of crystallite size and clustering in influencing the stability of the structures of a large tetragonality ferroelectric system 0.6BiFeO(3)-0.4PbTiO(3) was investigated. The system exhibits cubic phase for a crystallite size similar to 25 nm, three times larger than the critical size reported for one of its end member PbTiO3. With increased degree of clustering for the same average crystallite size, partial stabilization of the ferroelectric tetragonal phase takes place. The results suggest that clustering helps in reducing the depolarization energy without the need for increasing the crystallite size of free particles.

Ferroelectric phase coexistence by crystallite size reduction in BiFeO3-PbTiO3

Size effect in ferroelectrics has been extensively investigated in the past with the general consensus that the long-range ferroelectric ordering gradually disappears with decreasing crystallite size, eventually leading to the paraelectric state. In this paper, we show that the compositions exhibiting giant tetragonality (c/a similar to 1.18) of the ferroelectric alloy system BiFeO3-PbTiO3 transform from a pure tetragonal phase to a state comprising tetragonal and rhombohedral phases as the average crystallite size is reduced from similar to 10 to similar to 1 mu m. It is argued that the increased surface energy in the smaller sized crystallites creates an equivalent compressive stress that drives the system towards tetragonal-rhombohedral criticality.

Carbon-dispersed Pt-Rh nanoparticles for ethanol electro-oxidation. Effect of the crystallite size and of temperature

This work presents results of studies of carbon-dispersed Pt-Rh (1:1) nanoparticles as electrocatalysts for the ethanol electro-oxidation. The influences of the crystallite size and the cell temperature on the yields of CO2, acetaldehyde and acetic acid are investigated. Metal nanoparticles were prepared by two different routes: (1) impregnation on carbon powder followed by thermal reduction on hydrogen atmosphere and (2) chemical reduction of the precursor salts. The surface active area and the electrochemical activity of the electrocatalysts were estimated by CO stripping and cyclic voltammetry in the absence and in the presence of ethanol, respectively. Reaction intermediates and products were analyzed by in situ Fourier Transform Infra-Red Spectroscopy (FTIR) and Differential Electrochemical Mass Spectrometry (DEMS). The electrochemical stripping of CO and the electrochemical ethanol oxidation were slightly faster on the Pt-Rh electrocatalysts compared to Pt/C. Also, in situ FTIR spectra and DEMS measurements evidenced that the CO2/acetaldehyde and the CO2/acetic acid ratios are higher for the Pt-Rh/C materials in relation to Pt/C. This was ascribed to the activation of the C-C bond breaking by Rh, this being more prominent for the materials with smaller crystallite sizes. (C) 2008 Elsevier B.V. All rights reserved.

Sample size determination for kernel regression estimation using sequential fixed-width confidence bands

We consider a random design model based on independent and identically distributed pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths. The sample size was optimized using the purely and two-stage sequential procedures together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confi dence bands based on the local linear estimator have the better performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

The role of testosterone in bib size determination in the male house sparrow Passer domesticus, is age dependent

Secondary sexual signals are thought to indicate individual quality. In order to understand the evolutionary pressures that give rise to such traits it is important to understand the physiological mechanisms underlying their production. The black bib of the house sparrow Passer domesticus is known to function as a badge of social status in males. Past studies have found that the size of the bib in older males is determined, at least partly, by the androgen testosterone. The immunocompetence handicap hypothesis suggests that testosterone has a key role in maintaining honest signalling – it is both involved in the development or expression of sexual signals and is immunosuppressive. In this paper we test experimentally two hypo theses relating to bib size development, whether 1) testosterone is only immunosuppressive in conditions where the natural feedback loop from the testes has been removed, and 2) testosterone is, in addition to influencing the bib size of older males, responsible for the size of the bib in juvenile sparrows. In the first experiment we found that exogenous testosterone administered to intact males during the winter (when LH and FSH levels are very low and were not artificially increased by castration) caused significant immunosuppression, albeit in interaction with the stress hormone corticosterone. Second, we found that exogenous testosterone administration in castrated fledgling male house sparrows had no effect on subsequent post-juvenile moult bib size relative to controls. Our results suggest that in some circumstances testosterone can be immunosuppressive, but that its role in bib size determination is age-dependent.

Adaptive patch size determination for patch-based image completion

Patch-based image completion proceeds by iteratively filling the target (unknown) region by the best matching patches in the source image. In most existing such algorithms, the size of the patches is either fixed and specified by a default number or simply chosen to be inversely proportional to the spatial frequency. However, it is noted that the patch size affects how well the filled patch captures the local characteristics of the source image and thus the final completion accuracy. Thus in this paper we propose a new method to compute appropriate patch sizes for image completion to improve its performance. In particular, we formulate the patch size determination as an optimization problem that minimizes an objective function involving image gradients and distinct and homogenous features. Experimental results show that our method can provide a significant enhancement to patch-based image completion algorithms.

The influence of residual stress and crystallite size on the magnetic properties of electrodepo sited nanocrystalline Pd-Co alloys

Nanocrystalline Pd-Co alloys were obtained by electrodeposition from an ammoniacal chloride bath. The influence of the crystallite size and the residual stress on the magnetic properties of the alloys was investigated. The residual stress increased as the applied current density was increased. It was associated to the high nucleation rate during electrodeposition and correlated to the lattice strain, estimated from the XRD patterns. Also from the XRD patterns the average crystallite size and the lattice constant were determined by Scherrer's and Rietveld's methods, respectively. Both parameters were directly influenced by the applied current density. Magnetic properties such as coercivity, remanence, saturation magnetization and squareness showed strong dependence on the residual stress and crystallite size. Coercivity higher than 1 kOe was achieved when a high current density was applied. High coercivity was attributed to the presence of residual stress and to the small crystallite size of deposits. (C) 2007 Elsevier B.V. All rights reserved.

Study of crystallite size and strain as a function of morphological evolution in zinc oxide powder obtained from hydroxycarbonate precursor

In this work, zinc oxide samples were obtained from hydroxycarbonate by thermal decomposition at 300°C. Zinc hydroxycarbonate samples were produced by homogeneous precipitation over different periods of time. The method used to obtain zinc oxide produces different morphologies as a function of the precursor precipitation time. Among the obtained particle shapes were porous spherical aggregates, spherulitic needle aggregates, and single acicular particles. This work investigated spherulitic needle-aggregate formation and the correlation among morphology, domain size, and microstrain. Transmission electron microscopy data revealed that the acicular particles that form the spherulitic needle aggregates consist of nanometer crystallites. Apparent crystallite size and microstrain in the directions perpendicular to (h00), (h0l), (hk0), and (00l) planes were invariable as a function of precursor precipitation time. From the results, it was possible to conclude that the precursor precipitation period directly influenced the morphology of the zinc oxide but did not influence average crystallite size and microstrain for ZnO samples. Therefore, using this route, it was possible to prepare zinc oxide with different morphologies without microstructural alterations. © 2001 International Centre for Diffraction Data.

Characterization of depolymerized residues from extremely low acid hydrolysis (ELA) of sugarcane bagasse cellulose: Effects of degree of polymerization, crystallinity and crystallite size on thermal decomposition

Sugarcane bagasse cellulose was subjected to the extremely low acid (ELA) hydrolysis in 0.07% H2SO4 at 190, 210 and 225 degrees C for various times. The cellulose residues from this process were characterized by TGA, XRD, GPC, FIR and SEM. A kinetic study of thermal decomposition of the residues was also carried out, using the ASTM and Kissinger methods. The thermal studies revealed that residues of cellulose hydrolyzed at 190, 210 and 225 degrees C for 80,40 and 8 min have initial decomposition temperature and activation energy for the main decomposition step similar to those of Avicel PH-101. XRD studies confirmed this finding by showing that these cellulose residues are similar to Avicel in crystallinity index and crystallite size in relation to the 110 and 200 planes. FTIR spectra revealed no significant changes in the cellulose chemical structure and analysis of SEM micrographs demonstrated that the particle size of the cellulose residues hydrolyzed at 190 and 210 degrees C were similar to that of Avicel. (C) 2011 Elsevier B.V. All rights reserved.