Statistical Measurement Errors Research Articles

Elementary Statistical Methods and Measurement Error

How the sources of physical variation interact with a data collection plan determines what can be learned from the resulting dataset, and in particular, how measurement error is reflected in the dataset. The implications of this fact are rarely given much attention in most statistics courses. Even the most elementary statistical methods have their practical effectiveness limited by measurement variation; and understanding how measurement variation interacts with data collection and the methods is helpful in quantifying the nature of measurement error. We illustrate how simple one- and two-sample statistical methods can be effectively used in introducing important concepts of metrology and the implications of those concepts when drawing conclusions from data.

Kinematic fit of dilepton events in top quark mass measurement using the template method

The study of different modifications for the procedure of determining the reconstructed mass based on the kinematic fit for dilepton events to improve the precision of the top quark mass measurement using the template method is described. It is demonstrated that accounting for the top quark decay width from its mass reduces the statistical measurement error by approximately 20%. The possibility of using transfer functions for a detailed description of the connection between the experimentally measured energy characteristics of b jets and the momenta of b quarks that produced these jets is considered. The capabilities of the modified method as used for the “lepton plus track” sample of the CDF experiment are evaluated.

Study of the d (d, n)3He reaction in the astrophysical energy region with the use of the Hall accelerator

The results of the measurements of the astrophysical S -factor and cross-sections of the reaction dd → ^3He+ n in the deuteron energy collision range of 2.3-6.2keV are presented. The experiment was carried out at the high-current deuteron beam of the Hall pulsed accelerator (FSSI “Nuclear Physics Institute”, Tomsk). Deuterated polyethylene (CD2) targets and frozen heavy water (D2O) were used. Neutrons were detected by eight plastic scintillation counters ( 375×100×100 mm^3) located around the target. The results obtained in the present work substantially differ from the results of the experiments conducted with the use of deuterium saturated metal targets (TiD, TaD, ZrD, PtD). Within statistical errors of measurements there is no discrepancy between the present results and the results of the experiments performed with the heavy-water targets and filled with gaseous-deuterium targets.

Estimating stellar parameters from spectra using a hierarchical Bayesian approach

A method is developed for fitting theoretically predicted astronomical spectra to an observed spectrum. Using a hierarchical Bayesian principle, the method takes both systematic and statistical measurement errors into account, which has not been done before in the astronomical literature. The goal is to estimate fundamental stellar parameters and their associated uncertainties. The non-availability of a convenient deterministic relation between stellar parameters and the observed spectrum, combined with the computational complexities this entails, necessitates the curtailment of the continuous Bayesian model to a reduced model based on a grid of synthetic spectra. A criterion for model selection based on the so-called predictive squared error loss function is proposed, together with a measure for the goodness-of-fit between observed and synthetic spectra. The proposed method is applied to the infrared 2.38–2.60 μm Infrared Space Observatory (ISO)–Short Wavelength Spectrometer (SWS) data of the star α Bootis, yielding estimates for the stellar parameters: effective temperature Teff= 4230 ± 83 K, gravity log g= 1.50 ± 0.15 dex and metallicity [Fe/H]=− 0.30 ± 0.21 dex.

A Rejoinder: The Measurement and Stability of State Citizen Ideology

our initial article challenged three of Brace et al.'s (2004) claims: (1) state citizen ideology is stable over time; (2) the Berry et al. (1998) measure of state citizen ideology is invalid; and (3) assessing the effect of state citizen ideology on state policy requires analysts to first parse out national or across-the-board changes in ideology. By stating that “the authors of the preceding article reinforce most of our substantive points,” Brace et al. (2007, 000) leave the impression that we agree with these claims. We do not. In fact, we see no evidence in this exchange to support any of these claims or to rebut our criticisms of them. To substantiate their first claim Brace et al. (2004) report that residuals from fixed-effects regression models of two measures of state ideological self-identification display few significant time trends. In this issue, we show that the results of the residual analysis are almost certainly artifacts of low statistical power and high measurement error and, hence, cannot support their claim. Brace et al. defend their second claim by showing that Berry et al.'s measure of citizen ideology both produces far more statistically significant time trends than do the two measures of ideological self-identification and is weakly correlated with these two measures. In response, we once again point to the artifactual nature of their regression residual results and note that Brace et al. (2001) report incorrect correlations. These empirical criticisms are independent of the distinction we draw between policy mood and self-identification; were we to abandon this distinction completely, which we recommend against on theoretical grounds, these criticisms of Brace et al. (2004) would still apply. We reject Brace et al.'s third claim that changes in state citizen ideology associated with national trends cannot meaningfully influence state public policyon logical grounds, noting that across-the-board changes in state ideology may very well produce changes in state public policy.

Comparison of the ultrahigh energy cosmic ray flux observed by AGASA, HiRes, and Auger

The current measurements of the cosmic ray energy spectrum at ultra-high energies ($\mathrm{E}>{10}^{19}\text{ }\text{ }\mathrm{eV}$) are characterized by large systematic errors and poor statistics. In addition, the experimental results of the two experiments with the largest published data sets, AGASA and HiRes, appear to be inconsistent with each other, with AGASA seeing an unabated continuation of the energy spectrum even at energies beyond the Greisen-Zatsepin-Kuzmin cutoff energy at ${10}^{19.6}\text{ }\text{ }\mathrm{eV}$. Given the importance of the related astrophysical questions regarding the unknown origin of these highly energetic particles, it is crucial that the extent to which these measurements disagree be well understood. Here we evaluate the consistency of the two measurements for the first time with a model-independent method that accounts for the large statistical and systematic errors of current measurements. We further compare the AGASA and HiRes spectra with the recently presented Auger spectrum. The method directly compares two measurements, bypassing the introduction of theoretical models for the shape of the energy spectrum. The inconsistency between the observations is expressed in terms of a Bayes factor, a standard statistic defined as the ratio of a separate parent source hypothesis to a single parent source hypothesis. Application to the data shows that the two-parent hypothesis is disfavored. We expand the method to allow comparisons between an experimental flux and that predicted by any model.

A new method for fast quantitative mapping of absolute water content in vivo

The presence of brain edema, in its various forms, is an accompanying feature of many diseased states. Although the localized occurrence of brain edema may be demonstrated with MRI, the quantitative determination of absolute water content, an aspect that could play an important role in the objective evaluation of the dynamics of brain edema and the monitoring of the efficiency of treatment, is much more demanding. We present a method for the localized and quantitative measurement of absolute water content based on the combination of two fast multi-slice and multi-time point sequences QUTE and TAPIR for mapping the T 2* and T 1 relaxation times, respectively. Incorporation of corrections for local B 1 field miscalibrations, temperature differences between the subject and a reference probe placed in the FOV, receiver profile inhomogeneities and T 1 saturation effects are included and allow the determination of water content with anatomical resolution and a precision >98%. The method was validated in phantom studies and was applied to the localized in vivo measurement of water content in a group of normal individuals and a patient with brain tumor. The results demonstrate that in vivo measurement of regional absolute water content is possible in clinically relevant measurement times with a statistical and systematic measurement error of <2%.

On Probability - Statistical Representation of Pole Figures for Materials with Hexagonal Symmetry

A new method of computing of normal distributions [1] on rotation groups is suggested. Monte Carlo method allows to calculate the orientation of grains function (ODF) and correspondent pole figures (PFs) using approximation by normal distributions [2]. The developed Monte Carlo method is applied for construction of PFs mathematical statistical model corresponding to experimental measurement. This model is based on statistical simulation of normal distributions on SO(3) group for discrete representation of pole figures. It is possible to calculate effective physical properties of polycrystals using the given discrete representation. The mathematical simulation for texture with two components of polycrystalline sample with hexagonal symmetry is developed. Two experimental PFs } 0 1 10 { and } 0002 { for Be measured by X-ray experiment are being used. For this case the effective property as a tensor of elastic compliance was calculated. The mathematical simulation of PFs also allows to determine the statistical errors of pole figures measurement.

Determining sexual dimorphism in frog measurement data: integration of statistical significance, measurement error, effect size and biological significance

Several analytic techniques have been used to determine sexual dimorphism in vertebrate morphological measurement data with no emergent consensus on which technique is superior. A further confounding problem for frog data is the existence of considerable measurement error. To determine dimorphism, we examine a single hypothesis (Ho = equal means) for two groups (females and males). We demonstrate that frog measurement data meet assumptions for clearly defined statistical hypothesis testing with statistical linear models rather than those of exploratory multivariate techniques such as principal components, correlation or correspondence analysis. In order to distinguish biological from statistical significance of hypotheses, we propose a new protocol that incorporates measurement error and effect size. Measurement error is evaluated with a novel measurement error index. Effect size, widely used in the behavioral sciences and in meta-analysis studies in biology, proves to be the most useful single metric to evaluate whether statistically significant results are biologically meaningful. Definitions for a range of small, medium, and large effect sizes specifically for frog measurement data are provided. Examples with measurement data for species of the frog genus Leptodactylus are presented. The new protocol is recommended not only to evaluate sexual dimorphism for frog data but for any animal measurement data for which the measurement error index and observed or a priori effect sizes can be calculated.

Assessment of the Efficiency of the Counting Method for Processing Information in Multichannel Radiometric Testing Systems

A modification of the counting method for the detection of ionizing radiation is proposed. The modification improves functional capacities of multichannel radiometric systems used for nondestructive testing of commercial products. The method involves recording the time needed for the accumulation of pulses that is set for the channel with the lowest counting rate. Statistical errors of measurements are compared and the efficiency of the method proposed is analyzed.

Comparing Bacterial DNA Microarray Fingerprints

Epidemiologic and forensic investigations often require assays to detect subtle genetic differences between closely related microorganisms. Typically, gel electrophoresis is used to compare randomly amplified DNA fragments between microbial samples, where the patterns of DNA fragment sizes are viewed as genotype 'fingerprints'. The limited genomic sample captured on a gel, however, is not always sufficient to discriminate closely related strains. This paper examines the application of microarray technology to DNA fingerprinting as a high-resolution alternative to gel-based methods. The so-called universal microarray, which uses short oligonucleotide probes that do not target specific genes or species, is intended to be applicable to all microorganisms because it does not require prior knowledge of genomic sequence. In principle, closely related strains can be distinguished if enough independent oligonucleotide probes are used on the microarray, i.e., if the genome is sufficiently sampled. In practice, we confront noisy data, imperfectly matched hybridizations, and a high-dimensional inference problem. We describe the statistical problems of microarray fingerprinting, outline similarities with and differences from more conventional microarray applications, and illustrate a statistical measurement error model to fingerprint 10 closely related strains from three Bacillus species, and 3 strains from non-Bacillus species.

Quantitative T1 mapping and absolute water content measurement using MRI

We present two methods for the mapping of the T 1 and T 2* relaxation times. A recently published sequence, T 1 mApping with Partial Inversion Recovery (TAPIR), is used for T 1 mapping in a cohort of patients suffering from hepatic encephalopathy (HE). TAPIR enables the fast and precise measurement of T 1 with whole brain coverage in approximately 5 min, which makes it a favourable tool for clinical applications. A clear correlation between HE severity and T 1 measured with TAPIR is demonstrated for several brain regions. Patients and control subjects could be classified solely based on their T 1 pattern by making use of unsupervised pattern recognition tools. In addition, a newly developed sequence termed QUanTitativE-EPI (QUTE-EPI) is presented for the fast and precise mapping of T 2* without significant image distortions. The information provided by TAPIR and QUTE-EPI can be used to extract an absolute measure of water content in vivo by MRI. The procedure of H 2O content mapping is described and results are presented. We demonstrate that in vivo water measurement is possible in clinically relevant measurement times with a statistical and systematic measurement error <2%.

Measurement error models in chemical mass balance analysis of air quality data

The chemical mass balance (CMB) equations have been used to apportion observed pollutant concentrations to their various pollution sources. Typical analyses incorporate estimated pollution source profiles, estimated source profile error variances, and error variances associated with the ambient measurement process. Often the CMB model is fit to the data using an iteratively re-weighted least-squares algorithm to obtain the effective variance solution. We consider the chemical mass balance model within the framework of the statistical measurement error model (e.g., Fuller, W.A., Measurement Error Models, Wiley, NewYork, 1987), and we illustrate that the models assumed by each of the approaches to the CMB equations are in fact special cases of a general measurement error model. We compare alternative source contribution estimators with the commonly used effective variance estimator when standard assumptions are valid and when such assumptions are violated. Four approaches for source contribution estimation and inference are compared using computer simulation: weighted least squares (with standard errors adjusted for source profile error), the effective variance approach of Watson et al. (Atmos, Environ., 18, 1984, 1347), the Britt and Luecke (Technometrics, 15, 1973, 233) approach, and a method of moments approach given in Fuller (1987, p. 193). For the scenarios we consider, the simplistic weighted least-squares approach performs as well as the more widely used effective variance solution in most cases, and is slightly superior to the effective variance solution when source profile variability is large. The four estimation approaches are illustrated using real PM2.5 data from Fresno and the conclusions drawn from the computer simulation are validated.

Statistical Error Analysis of Time Delay Measurement by Using Phase of Cross-Spectral Density Function

This article presents the principle of time delay measurement employing the phase of cross-spectral density function. Some features of the method are discussed and statistical errors of time delay measurement are analysed.

Directional characteristics of probability distribution of extreme wind speeds by typhoon simulation

Wind directional fluctuations under typhoon condition was studied on the basis of its effect on the directional probability of annual maximum wind speed. A typhoon model that accurately models the average field observations, underestimates the maximum wind speed. Thus, a probability method is proposed for accurately evaluating the maximum wind speed probability distribution. This probability method is extended to corporate wind directional fluctuations. Before modeling is carried out, uncertainties are divided into physical and other conditions. The physical variation of wind direction is modeled probabilistically as directional fluctuations, and its formula is shown. Other uncertainties include statistical uncertainty (e.g., sampling error), modeling uncertainty and measurement error. These uncertainties are modeled considering two general situations: the maximum uncertain situation, where wind speed is used regardless of its direction, and minimum uncertain (definite), where wind direction is accurately evaluated. Taking these situations into account, a directional wind speed evaluation was formulated. Effects of physical wind directional fluctuations and wind directional uncertainties are indicated as a small increase in wind speeds for long-term wind speed recurrence. More effects were shown in the shorter return period range.

Turbulent Vertical Kinetic Energy in the Ocean Mixed Layer

Abstract Vertical velocities in the ocean boundary layer were measured for two weeks at an open ocean, wintertime site using neutrally buoyant floats. Simultaneous measurements of the surface meteorology and surface waves showed a large variability in both wind and wave properties and only weak correlations between them. Buoyancy forcing was weak. The mean square vertical velocity in the boundary layer σ2w measured from the vertical motion of the floats was proportional to the squared friction velocity u2∗ estimated from shipboard meteorological measurements using bulk formulas. Thus σ2w = Au2∗ (the rate of momentum transport from the atmosphere to the ocean is ρu2∗, where ρ is the density of the water). The deviations from this relation can be attributed entirely to statistical variation and measurement error. The measured values of σ2w were corrected for measurement biases and the nonturbulent contributions of internal waves. The value of the turbulent part of A is 1.75–2 times that measured in laborato...

Magnetic sublevel population in 1s-2p excitation of helium by fast electrons and protons

We report experimental and theoretical results for the magnetic sublevel population of the helium atom in collisions with fast (vi = 3-9 au) electrons and protons. Cross sections for excitation of magnetic sublevels with M = 0 and ±1 have been obtained using polarization measurements of emitted radiation in combination with differential cross sections. Calculations have been carried out using the expansion of the transition amplitude in the Born series over the projectile-target interaction through the second order. Results of calculations are in agreement with experimental data. We find that the particle-antiparticle Z± difference exceeds the statistical error of measurement up to collision velocities vi≈6 au for excitation of sublevels with M = 0.

Formal-kinetic evaluation of polyaddition reactions — results of a round-robin test, initialised by the working group ‘Polymers’ of the German Society for Thermal Analysis (GEFTA)

A simple and well-known polyaddition reaction is used as test reaction. The formal-kinetic evaluation of the data sets from 11 participants of laboratories in industry, universities and manufacturing companies permits representative and well-founded conclusions. In spite of always possible statistical and systematic measurement errors and mathematical artefacts, all calculated individual parameter sets for the most probable formal-kinetic model allow reliable predictions of the reaction behaviour for any complex temperature–time conditions. The simultaneous evaluation of non-isothermal measurements at different heating rates and isothermal data sets at various temperatures is not only possible but even highly desirable. The DSC as well as other thermoanalytical methods are in combination with multivariate kinetic analysis, a powerful tool for process prediction and optimisation.

Measurement of porous media component content and heterogeneity using gamma ray tomography

Tomographic images of porous media are complex distributions of linear attenuation coefficients that reflect the combined effects of scanning spatial resolution, photon statistical measurement errors, and true material densities. We address how the true voxel‐scale attenuation distribution and measurement errors are convoluted to yield measured density frequency distributions. A deconvolution algorithm is demonstrated that uses the measured density frequency distributions and known photon statistical errors to quantify average cross‐section volume contents of pure components and a mixed‐component phase. The mixed‐component phase represents regions where components are intertwined or varied in spaces smaller than the scanning resolution. This approach is applied to a complex core of the Culebra Dolomite Member of the Rustler Formation collected at the Waste Isolation Pilot Plant, near Carlsbad, New Mexico. The methodology provides a quantitative measure of the volume content of gypsum, dolomite, and mixed‐components, and heterogeneity in the sample.

Determination of isotopic ratios of osmium and ruthenium in meteorites by pretreatment and radiochemical neutron activation analysis

The isotopic abundance ratios of Os-190/Os-184 and Ru-96/Ru-102 for the metal phases of the Jilin and Taonan stone meteorites were determined by pretreatment and radiochemical neutron activation analysis. All experimental factors affecting Os and Ru isotopic ratios were discussed, including sampling, standard, irradiation, separation and counting. The statistical errors of measurement for the Os-199/Os-184 ratio can be controlled within 1%. The experimental results indicate that the statistically significant anomalies of the Os-190/Os-184 and Ru-96/Ru-102 ratios have not been found relative to the terrestrial Os and Ru standards.