Calculation Of Standard Errors Research Articles

The reliability and validity of measurements of human dental casts made by an intra-oral 3D scanner, with conventional hand-held digital callipers as the comparison measure

AimIntra-oral 3D scanning of dentitions has the potential to provide a fast, accurate and non-invasive method of recording dental information. The aim of this study was to assess the reliability of measurements of human dental casts made using a portable intra-oral 3D scanner appropriate for field use. MethodTwo examiners each measured 84 tooth and 26 arch features of 50 sets of upper and lower human dental casts using digital hand-held callipers, and secondly using the measuring tool provided with the Zfx IntraScan intraoral 3D scanner applied to the virtual dental casts. The measurements were repeated at least one week later. Reliability and validity were quantified concurrently by calculation of intra-class correlation coefficients (ICC) and standard errors of measurement (SEM). ResultsThe measurements of the 110 landmark features of human dental casts made using the intra-oral 3D scanner were virtually indistinguishable from measurements of the same features made using conventional hand-held callipers. The difference of means as a percentage of the average of the measurements by each method ranged between 0.030% and 1.134%. The intermethod SEMs ranged between 0.037% and 0.535%, and the inter-method ICCs ranged between 0.904 and 0.999, for both the upper and the lower arches. The inter-rater SEMs were one-half and the intra-method/rater SEMs were one-third of the inter-method values. ConclusionThis study demonstrates that the Zfx IntraScan intra-oral 3D scanner with its virtual on-screen measuring tool is a reliable and valid method for measuring the key features of dental casts.

Analytic Small Sample Bias and Standard Error Calculations for Tests of Serial Correlation in Market Returns

This article derives analytic finite sample approximations to the bias and standard error of a class of statistics which test the hypothesis of no serial correlation in market returns. They offer an alternative to both the widely used Monte Carlo approach for calculating the bias, as well as asymptotic standard error calculations. These approximations are calculated under the assumption that returns are spherically symmetrically distributed (such as Gaussian) and also under the weaker assumption that returns follow any arbitrary continuous distribution. The class of statistics examined here includes many of those employed in the finance and macroeconomics literature to test for the existence of random walk, including the variance ratio and the multi-period return regression on past returns. The accuracy of the approximations is benchmarked using simulated data, where arbitrarily tight estimates of the bias and standard error can be calculated. The approximations are then applied to adjust the statistics calculated using returns on the NYSE firom 1926-1991.

Intsvy: An R Package for Analyzing International Large-Scale Assessment Data

This paper introduces intsvy, an R package for working with international assessment data (e.g., PISA, TIMSS, PIRLS). The package includes functions for importing data, performing data analysis, and visualizing results. The paper describes the underlying methodology and provides real data examples. Tools for importing data allow useRs to select variables from student, home, school, and teacher survey instruments as well as for specific countries. Data analysis functions take into account the complex sample design (with replicate weights) and rotated test forms (with plausible values of achievement scores) in the calculation of point estimates and standard errors of means, standard deviations, regression coefficients, correlation coefficients, and frequency tables. Visualization tools present data aggregates in standardized graphical form.

Extensions of Tests of Indirect Effect in Mediation Analysis

This study seeks to determine economic variables that jointly mediate upon government expenditure and unemployment in Nigeria and in proven cases of mediation, determine the type of mediation that exist. It compares the two methods of calculating indirect effect which are product of coefficient and difference of coefficients respectively. Furthermore, the study compares the three methods of testing the significance of indirect effect vis-a-vis Sobel’s test, Aroian test and Goodman’s test. The differences in these three tests are due to variations in the methods of standard error computation. This study further proposed extensions for the three variations in methods of standard error computation for a case of two mediator which may also be extended for more than two mediator cases. The results show that a combination of any two of labour force population, interest rate and inflation showed a significant evidence of partial mediation. The result of indirect effect computation shows that the method of product of coefficient gave a slightly higher result when compared to that of difference of coefficient. The proposed extension of Sobel, Aroian and Goodman tests gave the same result for all cases as their standard errors are the same. The study thus recommends employing some variable selection techniques in subsequent studies which may improve mediational results; further studies may to be carried out to seek methods of ascertaining the direction of relationship of indirect effect, other than those of the regression models; and finally studies may be carried out to determine the effect of multicolinearity on mediation results.

Model Uncertainty and Robustness

Model uncertainty is pervasive in social science. A key question is how robust empirical results are to sensible changes in model specification. We present a new approach and applied statistical software for computational multimodel analysis. Our approach proceeds in two steps: First, we estimate the modeling distribution of estimates across all combinations of possible controls as well as specified functional form issues, variable definitions, standard error calculations, and estimation commands. This allows analysts to present their core, preferred estimate in the context of a distribution of plausible estimates. Second, we develop a model influence analysis showing how each model ingredient affects the coefficient of interest. This shows which model assumptions, if any, are critical to obtaining an empirical result. We demonstrate the architecture and interpretation of multimodel analysis using data on the union wage premium, gender dynamics in mortgage lending, and tax flight migration among U.S. states. These illustrate how initial results can be strongly robust to alternative model specifications or remarkably dependent on a knife-edge specification.

Comparison of Tests of Indirect Effect in Single Mediation Analysis

This study compares various methods of mediations analysis. Firstly, it compares the two methods of calculating indirect effect which are product of coefficient and difference of coefficients respectively. Secondly, the study compares the three methods of testing the significance of indirect effect vis avis Sobel’s test, Aroian test and Goodman’s test. The differences in these three tests are due to variations in the methods of standard error computation. The findings are discussed. The results show that both methods of product of coefficients and difference of coefficients give approximately the same result. However the product of coefficient gave a slightly higher result. The comparison of test of indirect effect for mediator shows that the tests gave the same result for Sobel’s, Aroian and Goodman test. The study recommended further studies to seek methods of ascertaining the direction of relationship of indirect effect, other than those of the regression models, further studies may be carried out to determine the effect of multicolinearity on mediation results.

Features of the content of carbonates in the ordinary chernozem improved by forest under plantings of false acacia (Robinia pseudoacacia L.)

Carbonate neoplasms are the characteristic feature of the black soil profile. The study of morphological and micromorphological characteristics and chemical composition gives an idea of the black soil genesis and serves as the diagnostic feature of classification units of them. The study of migration carbonate in the chernozem are of great scientific and practical interest (Afanasyeva, 1996). Nowadays the issues of migration carbonates, as well as the extent of the manifestation of this process in the soil profile need further researching, which is important as carbonates has one of the main role in basic soil processes, in particular, they affect the concentration and activity of calcium ions in the soil solution, the composition of the soil absorbing complex and pH in the soil solution. Carbonate neoplasms contribute to the formation of strong coagulation structures, which increases soil fertility and harvest agricultural crops, provides resistance against the wind, prevents reduction of the upper fertile soil layer, increases mobility of some chemical elements and improves such physical characteristics of soil as density, permeability and porosity (Goncharova, 1983). The aim of our work was to study the content of calcium carbonate in the soil profile of the test section 201–L under of the acacia plantations crops of forest ecosystems and to determine of their distribution in the soil genetic horizons. According to the aim of our work of we has the following tasks: to give a general characterization of carbonates of calcium in Chernozem usual, to perform sampling of the genetic horizons of the soil profile of test section 201–L, to determine the content of carbonates by conventional gravimetric methods; to study the features of the content of carbonates in soil profiles of test section 201–L; to conduct statistical processing of the obtained data; to formulate conclusions of the performed research. Soil samples were selected according to the standard technique in genetic horizons of the soil profile on three times (Fedorets, 2009). Determination of the percentage content of carbonates in the soil was performed by the gravimetric method, which is based on weight loss of soil due to discharge of CO2 during the destruction of carbonates with acid. It should be noted that the method can be applied in the case of the carbonates content up to 70 % (Travleev et al., 2009). The average coefficient of variation of carbonates of calcium content in genetic horizons of the soil profile is 77.5 %. This is quite a high rate, so as General it is considered that if the value of the coefficient of variation is less than 33 %, the result is considered homogeneous if more than 33 %, it is inhomogeneous. Based on this observation, we conclude that carbonate calcium has inhomogeneous redistribution of genetic horizons of test section 201–L. Regarding the reliability of the obtained data, we can see that the standard error calculations for each of the horizons does not exceed 0,34, which in turn confirms the accuracy of the our data. According to our calculations the lowest content of calcium carbonate is 1.47 % in the first horizon, and biggest – 16,07 % in the genetic horizon Ph (70–90 cm). These results are extending the current understanding of the processes of formation and distribution of calcium carbonate in the genetic horizons of the soil profile of the Chernozem ordinary. The data of percentage of calcium carbonate may be used in the solution of the question of the genesis, evolution and classification of soils, the obtained data can serve as the basis of the research the conditions of pedogenesis under the influence of natural climatic fluctuations and anthropogenic factors.

Mean-shift outliers model in skew scale-mixtures of normal distributions

ABSTRACTAsymmetric models have been discussed quite extensively in recent years, in situations where the normality assumption is suspected due to lack of symmetry in the data. Techniques for assessing the quality of fit and diagnostic analysis are important for model validation. This paper presents a study of the mean-shift method for the detection of outliers in regression models under skew scale-mixtures of normal distributions. Analytical solutions for the estimators of the parameters are obtained through the use of Expectation–Maximization algorithm. The observed information matrix for the calculation of standard errors is obtained for each distribution. Simulation studies and an application to the analysis of a data have been carried out, showing the efficiency of the proposed method in detecting outliers.

Exponential description of the static pressure-volume curve of normal and diseased lungs.

We examined the practical value of a simple mathematical description of the static pressure-volume (PV) curve of the lungs above functional residual capacity by fitting a monoexponential function of the form V = Vmax - Ae-KP (where Vmax is the volume extrapolated to infinite P, and A and K are constants) to PV curves obtained in 45 normal subjects and 39 patients with emphysema, intermediate α1-antitrypsin deficiency, fibrosing alveolitis, or sarcoidosis. Quality of fit was assessed by calculation of the standard errors of the parameters, by the reduction of original variance (R2), and by the application of sign and runs tests. The runs test proved particularly useful for detecting minor deviations from a monoexponential function; the value of R2 was less discriminating and largely depended on the magnitude of experimental error. The exponential function described the expiratory pressure-volume data well in 42 of the 45 normal subjects and in all of the patients with lung disease. The shape of the pressur...

Unexpected life events as improbable reasons for moving home: a review of two studies' findings

In longitudinal studies of panel data, logistic regression coefficients' standard errors may be sensitive to extremely-skewed data from low response probabilities, and so, statistical findings of those studies may have been compromised. The present study reviews the findings of two published studies as examples of panel-data studies in order to be convinced about residents' moving home during the next one or two years in response to the occurrence of a life event. The present study's conclusion however is that four life events of household or family dissolution, becoming a widow(er), becoming unemployed, and finding employment/changing job, may have been traumatic reasons for moving at most, but not that they were unexpected reasons for moving. This conclusion is based upon a statistical contradiction between predicted likelihoods of moving from calculated probabilities for respondents' subgroups, and inferred probabilities from logistic regression coefficients. Methods for more refined calculation of standard errors of logistic regression coefficients for data with low response probabilities are proposed.

An objective Bayesian estimation of parameters in a log-binomial model

Log-binomial model is commonly recommended for modeling prevalence ratio just as logistic regression is used to model log odds-ratio. However, for the log-binomial model, the parameter space turns out to be restricted causing difficulties for the maximum likelihood estimation in terms of convergence of numerical algorithms and calculation of standard errors. Bayesian approach is a natural choice for modeling log-binomial model as it involves neither maximization nor large sample approximation. We consider two objective or non-informative priors for the parameters in a log-binomial model: an improper flat prior and a proper prior. We give sufficient conditions for the posterior from the improper flat prior to be proper, and compare the two priors in terms of the resulting posterior summaries. We use Markov Chain Monte Carlo via slice sampling to simulate from the posterior distributions.

One side or two?

One side or two?

Modeling of frac flowback and produced water volume from Wattenberg oil and gas field

The objective of this study was to develop models that could be used to predict frac flowback and produced water volumes considering the unique decline rates that exist for different types of oil and gas wells. Specifically, water production data from the Colorado Oil and Gas Conservation Commission (COGCC) and Noble Energy Inc. were used to develop models for water production for vertical and horizontal wells, a distinction made largely due to the different amounts of water used for each. If centralized water treatment and handling facilities are going to be designed and constructed, it is important to have a reliable estimate of the water that will be produced in the future as wells are completed and brought on line. An Excel-based tool was developed utilizing the horizontal and vertical well models for predicting total volume of water production by current and future wells in Wattenberg Field. Two case studies have been conducted including one with all of the Noble wells in Wattenberg Field and one with a subset assuming a regional treatment center might be established. Uncertainty of the predictions was determined using standard error calculations on the two modeling parameters for water flow decline rates. An interactive Excel-based spreadsheet has been developed to allow predictions of water production based on the number of horizontal and vertical wells drilled in the future. • Models developed for vertical and horizontal wells water production. • Water production prediction tool was created to predict total water production. • Uncertainty of predictions was estimated. • Two cases studies with the tool to predict flowback and produced water.

Derivatives and Fisher information of bivariate copulas

Data sets with complex relationships between random variables are increasingly studied in statistical applications. A popular approach to model their dependence is the use of copula functions. Our contribution is to derive expressions for the observed and expected information for several bivariate copula families, in particular for the Student’s $$t$$ -copula. Further likelihood derivatives which are required for numerical implementations are computed and a numerically stable implementation is provided in the R-package VineCopula. Using a real world data set of stock returns, we demonstrate the applicability of our approach for the routinely calculation of standard errors. In particular, we illustrate how this prevents overestimating the time-variation of dependence parameters in a rolling window analysis.

What Do Panel Studies Tell Us About a Deterrent Effect of Capital Punishment? A Critique of the Literature

We provide a critical review of empirical research on the deterrent effect of capital punishment that makes use of state and, in some instances, county-level, panel data. We present the underlying behavioral model that presumably informs the specification of panel data regressions, outline the typical model specification employed, discuss current norms regarding “best-practice” in the analysis of panel data, and engage in a critical review. The connection between the theoretical reasoning underlying general deterrence and the regression models typically specified in this literature is tenuous. Many of the papers purporting to find strong effects of the death penalty on state-level murder rates suffer from basic methodological problems: weak instruments, questionable exclusion restrictions, failure to control for obvious factors, and incorrect calculation of standard errors which in turn has led to faulty statistical inference. The lack of variation in the key underlying explanatory variables and the heavy influence exerted by a few observations in state panel data regressions is a fundamental problem for all panel data studies of this question, leading to overwhelming model uncertainty. We find the recent panel literature on whether there is a deterrent effect of the death penalty to be inconclusive as a whole, and in many cases uninformative. Moreover, we do not see additional methodological tools that are likely to overcome the multiple challenges that face researchers in this domain, including the weak informativeness of the data, a lack of theory on the mechanisms involved, and the likely presence of unobserved confounders.

Calculating errors for measures derived from choice modelling estimates

The calibration of choice models produces a set of parameter estimates and an associated covariance matrix, usually based on maximum likelihood estimation. However, in many cases, the values of interest to analysts are in fact functions of these parameters rather than the parameters themselves. It is thus also crucial to have a measure of variance for these derived quantities and it is preferable that this can be guaranteed to have the maximum likelihood properties, such as minimum variance. While the calculation of standard errors using the Delta method has been described for a number of such measures in the literature, including the ratio of two parameters, these results are often seen to be approximate calculations and do not claim maximum likelihood properties. In this paper, we show that many measures commonly used in transport studies and elsewhere are themselves maximum likelihood estimates and that the standard errors are thus exact, a point we illustrate for a substantial number of commonly used functions. We also discuss less appropriate methods, notably highlighting the issues with using simulation for obtaining the variance of a function of estimates.

How much Confidence can we have in EU-SILC? Complex Sample Designs and the Standard Error of the Europe 2020 Poverty Indicators

If estimates are based on samples, they should be accompanied by appropriate standard errors and confidence intervals. This is true for scientific research in general, and is even more important if estimates are used to inform and evaluate policy measures such as those aimed at attaining the Europe 2020 poverty reduction target. In this article I pay explicit attention to the calculation of standard errors and confidence intervals, with an application to the European Union Statistics on Income and Living Conditions (EU-SILC). The estimation of accurate standard errors requires among others good documentation and proper sample design variables in the dataset. However, this information is not always available. Therefore, I complement the existing documentation on the sample design of EU-SILC and test the effect on estimated standard errors of various simplifying assumptions with regard to the sample design. It is shown that accounting for clustering within households is of paramount importance. Although this results in many cases in a good approximation of the standard error, taking as much as possible account of the entire sample design generally leads to more accurate estimates, even if sample design variables are partially lacking. The effect is illustrated for the official Europe 2020 indicators of poverty and social exclusion and for all European countries included in the EU-SILC 2008 dataset. The findings are not only relevant for EU-SILC users, but also for users of other surveys on income and living conditions which lack accurate sample design variables.

Assessment of PEFC performance by applying harmonized testing procedure

The performance of a polymer electrolyte membrane fuel cell (PEFC) power stack is assessed in terms of polarization measurements under laboratory conditions by applying a harmonized testing procedure. Harmonization at the level of testing procedures allows for an objective and trustworthy comparison of performance data. The harmonization of the procedure took place among the 55 partners of the Fuel Cell Testing and Standardization Network (FCTESTNET). Selected testing procedures are currently validated through experimental campaigns in the successor project (Fuel Cell Testing, Safety and Quality Assurance, FCTESQA) involving research laboratories from Europe, US, China, and Korea. This study reports the results of a test of the campaign for the performance assessment of a PEFC power stack carried out at JRC by applying the harmonized procedure for validation. Following the procedure, the test inputs and outputs are subjected to stability checks a priori and during the actual polarization measurement steps of the test. The assessment of the stack performance is based on a statistical approach of the test outputs, which includes the calculation of averages, measurement range, (relative) standard deviation and standard error as well as of a stability parameter. The study demonstrates the necessity of harmonized testing procedures and of a harmonized methodology of presenting the test results in a commonly agreed format to provide a comprehensive performance assessment for PEFC stacks. Copyright © 2011 John Wiley & Sons, Ltd.

Measuring the accuracy of the Retail Sales Index

A measure of the accuracy of the Retail Sales Index (RSI) has been produced by estimating the standard errors of index movements. This article reports on the calculation of standard errors for one‐month and 12‐month movements in the RSI. It provides an overview of standard errors and their meaning in the context of the RSI.

Multi-Site Integrated Population Modelling

We examine the performance of a method of integrated population modelling for the joint analysis of different types of demographic data on individuals that exist in, and move between, different sites. The value of the approach is demonstrated by a simulation study which shows substantial improvement in parameter estimation when site-specific census data are combined with demographic data. The multivariate normal approximation to a multi-state mark-recapture likelihood is evaluated, and the performance of a diagonal variance-covariance matrix for the approximation is also examined. The work is motivated by a study of great cormorants. Analysis of the cormorant data suggests that breeders survive better than non-breeders, and also that probabilities of recruitment to breeding have been declining over time for all the colonies of the study. Supplementary material, including notes on the computation of standard errors and extended simulation results, are available online.