Research for the Development of Guidelines for Conducting and Analyzing an Environmental Water Quality Study to Determine Statistically Meaningful Results

This report presents and discusses the basic statistical models and methods which are useful to researchers in the field of water resources research, as well as in other fields. These models and methods are presented from the standpoint of type (parametric and nonparametric - or distribution free) and purpose (e.g., simultaneous comparison of several means, comparison of two or more variances, establishment of a difference between two means with a specified confidence, etc.). The material is presented with emphasis primarily upon methodology, including the necessary assumptions upon which each model is based. No derivations or proofs are given, since these are found in numerous textbooks on statistics readily accessible to the reader. Emphasis is also placed upon the need for the researcher to determine before obtaining data the type of statistical model and analysis required, so that he can use that model or method which is most powerful, and so that he will have the proper data to permit the most efficient analysis. Failure to carry out such preliminary planning relevant to the selection and application of a statistical model will almost always result in either a lack of sufficient relevant data or in the gathering of extraneous data, either of which is unnecessarily costly. Each method is illustrated by an example, together with an interpretation of the result

Bayesian Confidence Limits For The Reliability Of Mixed Cascade And Parallel Independent Exponential Subsystems

This paper deals with the theoretical problem of deriving Bayesian confidence intervals for the reliability of a system consisting of both cascade and parallel subsystems where each subsystem is independent and has an exponential failure probability density function (pdf). This approach is applicable when test data are available for each individual subsystem and not for the entire system. The Mellin integral transform is used to analyze the system in a step-by-step procedure until the posterior pdf of the system reliability is obtained. The posterior cumulative distribution function is then obtained in the usual manner by integrating the pdf, which serves the dual purpose of yielding system reliability confidence limits while at the same time providing a check on the accuracy of the derived pdf. A computer program has been written in FORTRAN IV to evaluate the confidence limits. An example is presented which uses the computer program. Copyright © 1974 by The Institute of Electrical and Electronics Engineers, Inc

Statistics of Bipolar Representation of CMB maps

Gaussianity of temperature fluctuations in the Cosmic Microwave Background(CMB) implies that the statistical properties of the temperature field can be completely characterized by its two point correlation function. The two point correlation function can be expanded in full generality in the bipolar spherical harmonic(BipoSH) basis. Looking for significant deviations from zero for Bipolar Spherical Harmonic(BipoSH) Coefficients derived from observed CMB maps forms the basis of the strategy used to detect isotropy violation. In order to quantify "significant deviation" we need to understand the distributions of these coefficients. We analytically evaluate the moments and the distribution of the coefficients of expansion($A^{LM}_{l_1 l_2}$), using characteristic function approach. We show that for BipoSH coefficients with M=0 an analytical form for the moments up to any arbitrary order can be derived. For the remaining BipoSH coefficients with $M\neq0$, the moments derived using the characteristic function approach need to be supplemented with a correction term. The correction term is found to be important particularly at low multipoles. We provide a general prescription for calculating these corrections, however we restrict the explicit calculations only up to kurtosis. We confirm our results with measurements of BipoSH coefficients on numerically simulated statistically isotropic CMB maps

Late posterior hip instability after lumbar spinopelvic fusion

The kinematic relationship between the hip and the axial skeleton is dynamic and can be variable based on individual anatomy. It has been shown [1] that pelvic incidence (sacral slope + pelvic tilt) can be used as a proxy to determine the ability of the pelvis to accommodate changes in sagittal balance. Individuals have varied pelvic incidence and thus may adapt differently degenerative and/or iatrrogenic to changes that occur in the axial spine. This is a case report in which surgical changes to the lumbopelvic spine resulted in chronic posterior periprosthetic hip instability. The focus of this discussion reflects the intimate relationship between the hip and spine and highlights the role between sagittal balance and acetabular version, specifically as it pertains to total hip arthroplasty