Effect Of Random Measurement Errors Research Articles

Extension of self-modeling curve resolution to mixtures of more than three components: Part 3. Atmospheric aerosol data simulation studies

In the previous two papers [R.C. Henry, B.M. Kim, Extension of self-modeling curve resolution to mixtures of more than three components: Part 1. Finding the basic feasible region, Chemom. Intell. Lab. Syst. 8 (1990) 205–216; B.M. Kim, R.C. Henry, Extension of self-modeling curve resolution to mixtures of more than three components: Part 2. Finding the complete solution, Chemom. Intell. Lab. Syst. 49 (1999) 67–77.], a method was described to extend the self-modeling curve resolution (SMCR) technique to mixtures of more than three components, one set of data was created without errors to examine the performance of the model when no random measurement errors exist. In this paper, simulation studies were conducted to examine the performance of the model and to determine the effects of random measurement errors, both in source compositions and in ambient concentrations, on the estimated source compositions. The bias and errors in the estimated source compositions were also determined. Five sources (roadway, marine, secondary, crustal, and residual oil) were assumed in the simulation. It was shown that the model estimates source compositions with acceptable error and bias. The maximum percentage uncertainties in the estimated compositions of the roadway and secondary sources were less than 10% for most of the major species, except elemental carbon in the roadway and organic carbon (OC) in the secondary sources, which are 20%. The maximum uncertainties in the estimated marine compositions were about 30% for major species.

Conditional sampling revisited

There is a continued need for simple, robust, yet accurate methods for measuring the surface/atmosphere exchange of a wide variety of trace gases and particulates. Conditional sampling is a relatively new method that has received increasing attention in recent years because it is related to theoretically attractive eddy covariance, but does not require a rapid response sensor for the covariate. It does require rapid measurement of the vertical wind speed, w, and sorting of sampled air into two separate lines based on the direction of w. As originally proposed, the flux was then calculated as F= βΔ Cσ w, where Δ C is the mean difference in concentration between the upward and downward moving eddies, σ w the standard deviation of the vertical wind speed, and β an empirical coefficient. Subsequent exposition showed that β was derivable from the statistics of joint Gaussian distribution, although field experiments have consistently found values in the range of 0.56 to 0.58, somewhat lower than the theoretical expectation of ≈0.62–0.63. Here, we reexamine the method, and show that if the flux is instead expressed as F= b 1 σ w 2, where b 1 is the regression-estimated slope of the concentration vs. wind speed relation, then it is exactly equivalent to eddy covariance. The aim of conditional sampling then becomes an estimation of b 1 as Δ C/Δ W. We show that this quantity has a consistent positive bias when samples are sorted simply into positive and negative excursions from mean w. Inclusion of a sampling deadband, symmetric about the mean w, improves the accuracy of the slope estimate and decreases its variance as well. A potential problem with conditional sampling, regardless of which formulation may be used, is the effect of random measurement error (noise) in the wind speed measurement. We show that this introduces systematic errors into conditional sampling, while eddy covariance measurements are unaffected. Direct and indirect assessments indicate that these errors are too small to be significant for the sonic anemometer that we used, but it is probably wise for practitioners of the method to make certain that such is the case for the instruments used in their particular systems. We conclude that conditional sampling is a maturing method, with an increasing body of evidence indicating that the underlying relationships between scalar concentration and wind speed are sufficiently robust to support widespread use.

Reliability in Experimental Sociology

Although scientists from various disciplines stress the importance of estimating random measurement error, these discussions have little effect on experimenters who do behavioral sociological research. There have been two important results: (i) many experimenters continue to adopt a laissez-faire approach to measurement error, and (ii) there are very few discussions that illustrate its practical importance in laboratory research. In this article I examine the role of abstract measurement theory in modern experimental sociology, giving particular emphasis to the improvement of data analysis and theory building. I detail the cause and effect of random measurement error in the laboratory and review how the reliability of behavioral data is estimated and interpreted. Discussed are issues of statistical power, Type I and Type II errors, internal and external validity, and the prospects for cumulative theory

The effect of random measurement error on receiver operating characteristic (ROC) curves

The effect of random measurement error on receiver operating characteristic (ROC) curves

Optimization of TOMS wavelength channels for ozone and sulfur dioxide retrievals

The wavelengths of the TOMS channels can be optimized to minimize the effects of random measurement errors on simultaneous ozone and sulfur dioxide retrievals. The inversion matrix is extremely sensitive to the spectral position of the channels due to mathematical singularities related to O3 and SO2 absorption coefficients. None of the current sets of wavelengths in the TOMS instruments are optimal for the low latitude retrievals considered. Minor adjustment of the wavelengths can reduce retrieval errors by more than a factor of two.

Effect of measurement errors on cardiac output calculated with O2 and modified CO2 Fick methods.

We have investigated the effect of measurement errors on cardiac output, calculated via three different Fick methods. In method 1, the classic O2 Fick equation is expressed in terms of oxygen uptake (VO2), arterial pulse (SaO2) and venous oximetry (SVO2) saturations. The second method, a modified CO2 Fick method, is obtained by replacing VO2 in method 1 with carbon dioxide production (VCO2) divided by the respiratory quotient. In method 3, cardiac output is expressed as VCO2 divided by the product of the SaO2-SVO2 difference and a constant. This constant is determined from initial measurements of VCO2, SaO2, SVO2, and thermodilution cardiac output (Qth). This determination of the constant results in equality of the initial cardiac output of method 3 with the simultaneously determined Qth and, therefore, is similar to performing an autocalibration. For each of the three preceding Fick methods, we derive general expressions that explicitly show how measurement errors (random and systematic) in the Fick variables (VO2, VCO2, SaO2, and SVO2) propagate into errors in calculated cardiac output. The errors in theoretically calculated cardiac output decrease as the SaO2-SVO2 difference increases, except for the systematic error in method 3. The systematic error of method 3 is constant and depends only upon the accuracy of the initial Qth. Analytic expressions for the sensitivity of calculated cardiac output to errors in individual Fick variables are also obtained. Using estimates from the literature for typical systematic and random measurement errors in the Fick variables, the resultant errors in cardiac output are numerically calculated. The effect of random measurement errors on errors in calculated cardiac output was comparable among the three methods. However, the systematic error was least with method 3. Total errors (random and systematic) were comparable among the three methods. Using these numerical measurement errors, we conclude that continuous cardiac output may be calculated with comparable accuracy with each of these methods.

Error Analysis for Pseudodynamic Test Method. II: Application

Error propagation characteristics for the pseudodynamic test method based on implicit time‐integration schemes are evaluated and compared to those for an explicit time‐integration scheme. For random errors and a linear structure with one degree of freedom, the error amplification factor for the implicit scheme is generally lower than that for the explicit scheme. The difference is small when the time step is small compared to the period of oscillation of the structure, and increases for larger time steps. The advantages of the implicit scheme become more apparent for an N‐degree‐of‐freedom structure consisting of N equal masses connected by shear springs of equal stiffness, and errors that occur independently from one story to the next. In this case, the error amplification factor at first increases as the number of degrees of freedom is increased, but then decreases and appears to approach an asymptotic value of unity when the number of degrees of freedom becomes very large. As an example of an inelastic system, the effect of random measurement errors on the response of an elastic‐perfectly plastic oscillator is evaluated. This example serves to verify the range over which linearity of the error structure is applicable.

Analysis of role conflict and role ambiguity in a structural equations framework.

In this study a confirmatory methodology was implemented to analyze a model that uses the Rizzo, House, and Lirtzman (1970) scales of role conflict (RC) and role ambiguity (RA; i.e., the Bedeian and Armenakis, 1981, model). The validity of the RC and RA scales were examined through structural equations analysis, and a nested models approach was used to compare the Bedeian and Armenakis model with a model suggesting a more parsimonious representation of the data. Furthermore, path estimates from models incorporating random measurement error were compared with estimates from a model not incorporating the effects of random measurement error

Measurement of Fenestration Net Energy Performance: Considerations Leading to Development of the Mobile Window Thermal Test (MoWitt) Facility

We present a detailed consideration of the energy flows entering a building space and the effect of random measurement errors on determining fenestration performance. Estimates of error magnitudes are made for a passive test cell; we show that a more accurate test facility is needed for reliable measurements on fenestration systems with thermal resistance 2–10 times that of single glazing or with shading coefficients less than 0.7. A test facility of this type, built at Lawrence Berkeley Laboratory, is described. The effect of random errors in this facility is discussed and computer calculations of its performance are presented. The discussion shows that, for any measurement facility, random errors are most serious in nighttime measurements, and systematic errors are most important in daytime measurements. It is concluded that, for this facility, errors from both sources should be small.

Interval estimates for correlation coefficients corrected for within-person variation: implications for study design and hypothesis testing.

It is well known that random measurement error can attenuate the correlation coefficient between two variables. One possible solution to this problem is to estimate the correlation coefficient based on an average of a large number of replicates for each individual. As an alternative, several authors have proposed an unattenuated (or corrected) correlation coefficient which is an estimate of the true correlation between two variables after removing the effect of random measurement error. In this paper, the authors obtain an estimate of the standard error for the corrected correlation coefficient and an associated 100% x (1-alpha) confidence interval. The standard error takes into account the variability of the observed correlation coefficient as well as the estimated intraclass correlation coefficient between replicates for one or both variables. The standard error is useful in hypothesis testing for comparisons of correlation coefficients based on data with different degrees of random error. In addition, the standard error can be used to evaluate the relative efficiency of different study designs. Specifically, an investigator often has the option of obtaining either a few replicates on a large number of individuals, or many replicates on a small number of individuals. If one establishes the criterion of minimizing the standard error of the corrected coefficient while fixing the total number of measurements obtained, in almost all instances it is optimal to obtain no more than five replicates per individual. If the intraclass correlation is greater than or equal to 0.5, it is usually optimal to obtain no more than two replicates per individual.

Air pollution-mortality models: A demonstration of the effects of random measurement error

Errors of measurement have long been recognized as a chronic problem in statistical analysis. Although there is a vast statistical literature of multiple regression models estimating the air pollution-mortality relationship, this problem has been largely ignored. It is well known that pollution measures contain error, but the consequences of this error for regression estimates is not known. We use Lave and Seskin's air pollution model to demonstrate the consequences of random measurement error. We assume a range of 0% to 50% of the variance of the pollution measures is due to error. We find large differences in the estimated effects on mortality of the pollution variables as well as the other explanatory variables once this measurement error is taken into account. These results cast doubt on the usual regression estimates of the mortality effects of air pollution. More generally our results demonstrate the consequences of random measurement error in the explanatory variable of a multiple regression analysis and the misleading conclusions that may result in policy research if this error is ignored.

Error analysis of in situ field tests of fenestration net energy performance

The need for information about fenestration net energy performance under realistic conditions is discussed and the method of measuring it in a “field test” on a complete building is reviewed. A detailed consideration of the energy flows entering the energy balance on a building space adjacent to a fenestration system and the effect of random measurement errors on the determination of fenestration performance is presented. Estimates of the error magnitudes are made for prototypical field tests utilizing a residential and a moderate-sized commercial building. In both cases, it is shown that these errors make it difficult to isolate the fenestration performance even for relatively low-performance windows (1 – 2 times the resistance of single glazing). It is concluded that whole-building measurements are not well adapted to measuring the performance of advanced fesestration system (thermal resistance 2 – 10 times that of single glazing or shading coefficient less than 0.7).

Effects of measurement errors on an individual tree-based growth projection system

Systematic and random measurement errors were placed on the input variables of a distance-independent individual tree-based growth and mortality projection model to study how sensitive the system was to measurement error. The study was conducted in three parts. First, the effects of systematic measurement errors on individual model components of the growth projection were investigated. Second, systematic errors were placed on the input variables of the growth projection system and the performance of the overall system was observed. Third, a Monte Carlo study was performed to examine the effects of random measurement errors of varying magnitude on the projection system estimates. Overall, the projection system was most sensitive to measurement errors in site index. Measurement errors in diameter at breast height were only critical when projecting basal area, but were not critical when projecting number of trees. The system was insensitive to errors in crown ratio.

Dosimetric analysis of stereo and orthogonal reconstruction of interstitial implants

We have evaluated the performance of stereo and orthogonal computerized three-dimensional implant reconstruction algorithms. Sets of orthogonal and stereo radiographs of a simulated interstitial seed implant were taken. Computer reconstructed coordinates of each source were compared with their measured positions in order to assess the geometric accuracy of the two methods. We find that the effect of random measurement errors on reconstructed coordinates from stereo films is 3–5 times that of the orthogonal method. Although relataive individual seed positions may be in error by as much as 1 cm, these errors do not significantly change the shape or area of isodose curves surrounding the implant periphery.

Precision Lattice Parameter Measurements with Guinier Camera and Counter Diffractometer: Comparison and Reconciliation of Results

Different procedures used in precision measurements of lattice parameters are, strictly, only valid if they can be shown to give results that are mutually reproducible. For this purpose reproducibility is defined in terms of the parameters a. and standard deviations a. obtained for X-ray specimens of one or more reference materials. The requirement is that all systematic errors should be minimized to a level below that of the random measurement errors. Where these have a Gaussian distribution the significance of the difference, Δa°, between two , measurements can then be Let;Led by evaluating . Thus, if K < 2 the difference, Δa°, cannot be distinguished from the effects of random measurement errors. This condition should be met for specimens of the same sample if reproducibility is good. For K ≥ 3 the value of Δa° is then taken to reflect real differences in the crystalline Jattice of two X-ray specimens of a given compound. A basis is thus created for the study of solid solubility and for the precise characterization of crystalline compounds.

Simulation of the effects of random measurement errors (teaching)

The authors propose a simulation (Monte Carlo) method similar to the computer oriented approach of La Fara (1973), which can be implemented by a group of students and which requires only scientific calculators and tables of random digits. Each student can then simulate the random behaviour of the component variables in the function and, by combining the group results, the outline of the sampling distribution of the function can be obtained.

Position Location: Triangulation Versus Circulation

Position location algorithms, using data from electronic surveillance systems have, for the most part, been based upon statistical analysis of the points of intersection of the lines of bearing. These triangulation ion algorithms may well minimize the effect of random measurement errors on the location estimate, but few existing algorithms account for systematic (bias) errors. An algorithm based upon intersecting circles which eliminates certain types of systematic error is presented with simulation data utilized to compare the position location estimates obtained from both triangulation and circulation algorithms.