Tests of Independence and Zero Correlations Among P Random Variables

Suppose it is desired to determine whether there is an association between any pair of p random variables. A common approach is to test H₀ : R = I, where R is the usual population correlation matrix. A closely related approach is to test H₀ : R_pb = I, where R_pb is the matrix of percentage bend correlations. In so far as type I errors are a concern, at a minimum any test of H₀ should have a type I error probability close to the nominal level when all pairs of random variables are independent. Currently, the Gupta-Rathie method is relatively successful at controlling the probability of a type I error when testing H₀: R = I, but as illustrated in this paper, it can fail when sampling from nonnormal distributions. The main goal in this paper is to describe a new test of H₀: R_pb = I that continues to give reasonable control over the probability of a type I error in the situations where the Gupta-Rathie method fails. Even under normality, the new method has advantages when the sample size is small relative to p. Moreover, when there is dependence, but all correlations are equal to zero, the new method continues to give good control over the probability of a type I error while the Gupta-Rathie method does not. The paper also reports simulation results on a bootstrap confidence interval for the percentage bend correlation.     

Is Body Mass Index a Measure of Adiposity in Elderly Women?

Objective: To evaluate the accuracy of body mass index (BMI) as a predictor of body fat in elderly women. Research Methods and Procedures: A total of 1423 women aged 67 ± 5 (mean ± SD, range: 60 to 88) years were consecutively enrolled into the study. Fat mass (FM) was measured using DXA. Results: BMI explained 72.9% of FM variance (p < 0.0001), with a root mean square error of estimate (RMSE) of 3.5 kg. After standardization of RMSE on the dependent variable as RMSE%, the prediction error equaled 15%. BMI explained 54.8% of FM% variance (p < 0.0001), with an RMSE of 4.1%, corresponding to an RMSE% of 11%. Discussion: The relatively high RMSE% of the FM and FM%‐BMI associations caution against the use of BMI as an adiposity index in individual elderly women. However, an error corresponding to 11% of FM% may be accepted for population studies of body fat in elderly women.     

Sampling error as a misleading artifact in “key factor analysis”

The influences of sampling error in key factor analysis are investigated statistically. The error involved in the data distorts the results in various misleading ways. In the course of detecting key factors by correlation analysis, the distortion arises in the following two ways: (1) the contributions made by the first and the last components of population trend index (log I or K) to the total variation are overrated as compared with the others; and (2) spurious negative correlation arises between successive two components. The risk of misinterpretation due to such disturbance is usually increased further if the error is concentrated on any particular developmental stages. In the tests to detect density-dependence by using regression analysis, the error consistently acts as if it were a density-dependent factor: under the effect of sampling error, the slope b for the regression of log N_i+1 on log N_i, for example, is expected to become<1 even where there is no density-dependent factor at all. A set of formulas are derived which may serve to check and correct these misleading distortions caused by the error. It is also shown that such undesirable influences can be avoided, at least to a considerable extent, if appropriate sampling plans are adopted for the study. The validity of key factor analysis is discussed in reference to this and some related problems.     

Observer error in sampling a rare plant population

Background: Estimation of abundance in vegetation sampling involving observers is almost always characterised by observer error, although such error is rarely reported.

Aims: To quantify observer error in population estimation of the rare plant species Physaria filiformis in Missouri, USA.

Methods: The abundance of P. filiformis was estimated within 25-m² plots by six trained observers with varying experience levels over 10 years. Observers assigned plots to six predefined density classes. A total of 477 plots were estimated annually, and actual counts were conducted on ca. 10% of the plots to assess per cent agreement of estimates with counts.

Results: Over a third of the estimates of plant abundance evaluated for accuracy (36.4%) deviated from exhaustive counts. The majority of the misestimates were underestimates by one density class (29.4%). The number and type of misestimates varied systematically with density class.

Conclusions: Observer error could be explained to some degree by variation in population density, but not by experience. It appears that inherent differences exist among observers that cannot be entirely compensated for by experience or training. Observer error in this system represents a systematic bias, and can be compensated for by use of correction factors, which would ideally be both density class-dependent and observer-specific.     

Evaluation of satellite retrievals of water quality parameters for Lake Victoria in East Africa

Lake Victoria in East Africa is a major ecosystem, whose size and importance has warranted the exploration of MODIS imagery to provide continuous and accurate water quality information. To this effect, two sea expeditions (in November 2014 and February 2015) were carried out to collect in situ lake surface temperature (LST), chlorophyll a (Chl) and Secchi disk depth (SDD) to compare with the corresponding satellite derived variables. Comparisons were made based on the following error matrices: coefficient of correlation (r), mean square error (MSE), root mean square error (RMSE), mean absolute deviation (MAD) and mean absolute percent error (MAPE). In general the results showed that satellite derived LST gives a good estimate of in situ LST. Conversely, the error matrices indicated that satellite derived Chl yielded more uncertainty when compared with in situ Chl. This could be because of the fact that the MODIS Chl product algorithm was designed for oceans and may not be appropriate for inland lakes. Satellite derived SDD compared fairly well with in situ SDD. From these results it is evident that with more in situ observations and improved algorithms, MODIS can be useful to improve how water quality is monitored on Lake Victoria.     

Comparison of asymptotic population growth rates with heterogeneous variances

This report explores how the heterogeneity of variances affects randomization tests used to evaluate differences in the asymptotic population growth rate, λ. The probability of Type I error was calculated in four scenarios for populations with identical λ but different variance of λ: (1) Populations have different projection matrices: the same λ may be obtained from different sets of vital rates, which gives room for different variances of λ. (2) Populations have identical projection matrices but reproductive schemes differ and fecundity in one of the populations has a larger associated variance. The two other scenarios evaluate a sampling artifact as responsible for heterogeneity of variances. The same population is sampled twice, (3) with the same sampling design, or (4) with different sampling effort for different stages. Randomization tests were done with increasing differences in sample size between the two populations. This implies additional differences in the variance of λ. The probability of Type I error keeps at the nominal significance level (α = .05) in Scenario 3 and with identical sample sizes in the others. Tests were too liberal, or conservative, under a combination of variance heterogeneity and different sample sizes. Increased differences in sample size exacerbated the difference between observed Type I error and the nominal significance level. Type I error increases or decreases depending on which population has a larger sample size, the population with the smallest or the largest variance. However, by their own, sample size is not responsible for changes in Type I errors.     

Comments on the approximate solution of the diffusion equation: II

On the basis of a previous general formulation (Bull. Math. Biophysics,15, 21–29, 1953a) a discussion is given of the error in the approximation method of N. Rashevsky. This error, inherent in the method when the metabolic rate is different at each point in the cell, is discussed in detail and numerical values are presented for two particular cases: the rate proportional to the concentration and the rate a prescribed function of the spatial coordinates. It is shown that the formulation for the first case also applies to several other cases, that the error is negligible provided the rate is sufficiently small, and that the error is fairly sensitive to the cell size. If the rate depends upon the coordinatesalone a small rate is not sufficient to insure a negligible error. The relations between the exact method, the standard approximate method, an earlier approximate method (Physics,7 260, 1936), and a more recent refinement (Bull. Math. Biophysics,10, 201, 1948) of the standard method are discussed. This work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies, assigned to the Mathematics Panel, Oak Ridge National Laboratory.     

非惩罚性报告系统在给药错误管理中的效果研究

?????? 目的 探讨非惩罚性报告系统在护士给药错误管理中的应用效果。方法 回顾性分析某三级乙等综合性医院2006—2012年给药错误报告资料,对实施非惩罚性报告系统前后给药错误的报告和管理情况进行系统的总结和分析。结果 自2008年建立了非惩罚性报告系统以来,护士给药错误报告意识增强,漏报率下降,报告及时性提高,报告人群从护士长普及到临床一线护士,同类给药错误事件发生率下降。结论 建立非惩罚性报告系统,增强护士给药错误的报告意识,护理管理人员能够获得真实数据和信息。     

Accurate kinetic parameter estimation during progress curve analysis of systems with endogenous substrate production

We have identified an error in the published integral form of the modified Michaelis–Menten equation that accounts for endogenous substrate production. The correct solution is presented and the error in both the substrate concentration, S, and the kinetic parameters V_m, K_m, and R resulting from the incorrect solution was characterized. The incorrect integral form resulted in substrate concentration errors as high as 50% resulting in 7–50% error in kinetic parameter estimates. To better reflect experimental scenarios, noise containing substrate depletion data were analyzed by both the incorrect and correct integral equations. While both equations resulted in identical fits to substrate depletion data, the final estimates of V_m, K_m, and R were different and K_m and R estimates from the incorrect integral equation deviated substantially from the actual values. Another observation was that at R = 0, the incorrect integral equation reduced to the correct form of the Michaelis–Menten equation. We believe this combination of excellent fits to experimental data, albeit with incorrect kinetic parameter estimates, and the reduction to the Michaelis–Menten equation at R = 0 is primarily responsible for the incorrectness to go unnoticed. However, the resulting error in kinetic parameter estimates will lead to incorrect biological interpretation and we urge the use of the correct integral form presented in this study. Biotechnol. Bioeng. 2011;108: 2499–2503. © 2011 Wiley Periodicals, Inc.     

A New Secondary Model Developed for the Growth Rate of <Emphasis Type="Italic">Escherichia coli</Emphasis> O157:H7 in Broth

This study was attempted to develop a new exponential sum model to describe the effect of temperature on growth rate (GR) of Escherichia coli O157:H7 in broth. The growth rates of E. coli O157:H7 at different storage temperatures (4, 10, 15, 20, 25, 30, and 35°C) estimated by fitting with the modified Gompertz model were used to develop secondary models such as square root model, Ratkowsky model and exponential sum model. Measures of coefficient of determination (R ²), root mean square error (RMSE) and the sum of squares due to error (SSE) were employed to compare the performances of these three secondary models. Based on these criteria, the developed exponential sum model showed the better goodness-of-fit and performance.     

Erratum: Octanol-Water partition of nonzwitterionic peptides: Predictive power of a molecular size-based model. Proteins 30:86–99, 1998

Buchwald, P., Bodor, N. Octanol-Water Partition of Nonzwitterionic Peptides: Predictive Power of a Molecular Size-Based Model. Proteins 30:86–99, 1998. Equation 2 should read: P = (C_in − C_fin) V_w/C_fin V_o. In the printed version, the volume ratio (Vw/Vo) incorrectly divides, and not multiplies, the concentration ratio. The publisher apologizes for this error.     

Percentage Fat in Overweight and Obese Children: Comparison of DXA and Air Displacement Plethysmography**

Objective: To compare percentage body fat (percentage fat) estimates from DXA and air displacement plethysmography (ADP) in overweight and obese children. Research Methods and Procedures: Sixty‐nine children (49 boys and 20 girls) 14.0 ± 1.65 years of age, with a BMI of 31.3 ± 5.6 kg/m² and a percentage fat (DXA) of 42.5 ± 8.4%, participated in the study. ADP body fat content was estimated from body density (D_b) using equations devised by Siri (ADP_Siri) and Lohman (ADP_Loh). Results: ADP estimates of percentage fat were highly correlated with those of DXA in both male and female subjects (r = 0.90 to 0.93, all p < 0.001; standard error of estimate = 2.50% to 3.39%). Compared with DXA estimates, ADP_Siri and ADP_Loh produced significantly (p < 0.01) lower estimates of mean body fat content in boys (?2.85% and ?4.64%, respectively) and girls (?2.95% and ?5.15%, respectively). Agreement between ADP and DXA methods was further examined using the total error and methods of Bland and Altman. Total error ranged from 4.46% to 6.38% in both male and female subjects. The 95% limits of agreement were relatively similar for all percentage fat estimates, ranging from ±6.73% to ±7.94%. Discussion: In this study, conversion of D_b using the Siri equation led to mean percentage fat estimates that agreed better with those determined by DXA compared with the Lohman equations. However, relatively high limits of agreement using either equation resulted in percentage fat estimates that were not interchangeable with percentage fat determined by DXA.     

Using a dry electrode EEG device during balance tasks in healthy young-adult males: Test–retest reliability analysis

Abstract

Background: The analysis of brain activity during balance is an important topic in different fields of science. Given that all measurements involve an error that is caused by different agents, like the instrument, the researcher, or the natural human variability, a test–retest reliability evaluation of the electroencephalographic assessment is a needed starting point. However, there is a lack of information about the reliability of electroencephalographic measurements, especially in a new wireless device with dry electrodes.

Objective: The current study aims to analyze the reliability of electroencephalographic measurements from a wireless device using dry electrodes during two different balance tests.

Method: Seventeen healthy male volunteers performed two different static balance tasks on a Biodex Balance Platform: (a) with two feet on the platform and (b) with one foot on the platform. Electroencephalographic data was recorded using Enobio (Neuroelectrics). The mean power spectrum of the alpha band of the central and frontal channels was calculated. Relative and absolute indices of reliability were also calculated.

Results: In general terms, the intraclass correlation coefficient (ICC) values of all the assessed channels can be classified as excellent (>0.90). The percentage standard error of measurement oscillated from 0.54% to 1.02% and the percentage smallest real difference ranged from 1.50% to 2.82%.

Conclusion: Electroencephalographic assessment through an Enobio device during balance tasks has an excellent reliability. However, its utility was not demonstrated because responsiveness was not assessed.     

Assessment of ATR‐NIR and ATR‐MIR spectroscopy as an analytical tool for the quantification of the total polyphenols in Dendrobium huoshanense

In this study, the potentiality of applying attenuated total reflectance near‐infrared (ATR‐NIR) and attenuated total reflectance mid‐infrared (ATR‐MIR) techniques combined with a partial least squares (PLS) regression technology to quantify the total polyphenols (TPs) in Dendrobium huoshanense (DHS) was investigated and compared. The real TP contents in the DHS samples were analysed using methods of reference. The capability of the two IR spectroscopic techniques to quantify the TPs in DHS was assessed by the root‐mean‐square error of calibration (RMSEC) and determination coefficients (R²). The results showed that both NIR and MIR might be used as a fast and simple tool to replace traditional chemical assays for the determination of the TP contents in DHS, and the best NIR model showed slightly better prediction performance [root‐mean‐square error of prediction (RMSEP): 0.307, R²: 0.9122, ratio performance deviation (RPD): 4.43] than the best MIR model (RMSEP: 0.440, R²: 0.9069, RPD: 3.09). Results from this study indicated that both the NIR and MIR models could be used to quantify the TP in DHS, and ATR‐NIR appeared to be the more predominant and more robust technique for the quantification of the TP in DHS.     

Expression of Hoxa-1 and Hoxb-7 is regulated by extracellular matrix-dependent signals in mammary epithelial cells. J Cell Biochem 69:377–391.

Srebrow A, Friedmann Y, Ravanpay A, Daniel CW, Bissell MJ (1998): Expression of Hoxa-1 and Hoxb-7 is regulated by extracellular matrix-dependent signals in mammary epithelial cells. J Cell Biochem 69:377–391. In Figure 3 on pages 384 and Figure 4 on page 385, two labels were misprinted. The top label on the right side of Figure 3B should have been Hoxb-7 instead of Hoxb-1, and the center label of Figure 4B should have been Hoxb-7 instead of Hoxa-7. The corrected figures are reprinted on the following pages. The Publisher apologizes for the error.     

A Comparison of Nonparametric Error Rate Estimation Methods in Classification Problems

Assessment of the misclassification error rate is of high practical relevance in many biomedical applications. As it is a complex problem, theoretical results on estimator performance are few. The origin of most findings are Monte Carlo simulations, which take place in the “normal setting”: The covariables of two groups have a multivariate normal distribution; The groups differ in location, but have the same covariance matrix and the linear discriminant function LDF is used for prediction. We perform a new simulation to compare existing nonparametric estimators in a more complex situation. The underlying distribution is based on a logistic model with six binary as well as continuous covariables. To study estimator performance for varying true error rates, three prediction rules including nonparametric classification trees and parametric logistic regression and sample sizes ranging from 100‐1,000 are considered. In contrast to most published papers we turn our attention to estimator performance based on simple, even inappropriate prediction rules and relatively large training sets. For the major part, results are in agreement with usual findings. The most strikingly behavior was seen in applying (simple) classification trees for prediction: Since the apparent error rate Êrr.app is biased, linear combinations incorporating Êrr.app underestimate the true error rate even for large sample sizes. The .632+ estimator, which was designed to correct for the overoptimism of Efron's .632 estimator for nonparametric prediction rules, performs best of all such linear combinations. The bootstrap estimator Êrr.B0 and the crossvalidation estimator Êrr.cv, which do not depend on Êrr.app, seem to track the true error rate. Although the disadvantages of both estimators – pessimism of Êrr.B0 and high variability of Êrr.cv – shrink with increased sample sizes, they are still visible. We conclude that for the choice of a particular estimator the asymptotic behavior of the apparent error rate is important. For the assessment of estimator performance the variance of the true error rate is crucial, where in general the stability of prediction procedures is essential for the application of estimators based on resampling methods. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Erratum to: Central European Journal of Biology, Volume 7, Issue 1

Paper by Hussein et al. “Effectiveness of the entomopathogenic nematode Steinernema feltiae in agar gel formulations against larvae of the Colarado potato beetle, Leptinotarsa decemlineata (Say.) (Coleoptera: Chrysomelidae)” in Volume 7, Issue 1, 77–82 9 / February 2012; DOI: 10.2478/s11535-011-0090-0 contains an error in the title. The correct title is presented below.     

Improving Bayesian isotope mixing models: a response to Jackson et al. (2009)

We recently described a Bayesian framework for stable isotope mixing models and provided a software tool, MixSIR, for conducting such analyses (Ecol. Lett., 2008; 11 :470). Jackson et al. (Ecol. Lett., 2009; 12:E1) criticized the performance of our software based on tests using simulated data. However, their simulation data were flawed, rendering claims of erroneous behaviour inaccurate. A re‐evaluation of the MixSIR source code did, however, uncover two minor coding errors, which we have fixed. When data are correctly simulated according to eqns  (1)–(4) in Jackson et al. (2009) , MixSIR consistently and accurately estimated the proportional contribution of prey to a predator diet, and was surprisingly robust to additional unquantified error. Jackson et al. (2009) also suggested we use a Dirichlet prior on the source proportion parameters, which we agree with. Finally, Jackson et al. (2009) propose adding additional error parameters to our mixing model framework. We caution that such increases in model complexity should be evaluated based on data support.     

Alternatives to the Chi-Square Test of Homogeneity in 2×2 Tables and to Fisher's Exact Test

In comparing two independent binomial proportions by modified X² tests: Gart's modified likelihood-ratio, Overall and Starbuck's “tailored F”, Pearson's adjusted X²[=X² multiplied by (n - 1)/n] and its skewness-corrected version proposed by Berchtold, it was found that the last two have error probabilities that in the mean are close to the significance level.     

Use and misuse of the reduced major axis for line‐fitting

Many investigators use the reduced major axis (RMA) instead of ordinary least squares (OLS) to define a line of best fit for a bivariate relationship when the variable represented on the X‐axis is measured with error. OLS frequently is described as requiring the assumption that X is measured without error while RMA incorporates an assumption that there is error in X. Although an RMA fit actually involves a very specific pattern of error variance, investigators have prioritized the presence versus the absence of error rather than the pattern of error in selecting between the two methods. Another difference between RMA and OLS is that RMA is symmetric, meaning that a single line defines the bivariate relationship, regardless of which variable is X and which is Y, while OLS is asymmetric, so that the slope and resulting interpretation of the data are changed when the variables assigned to X and Y are reversed. The concept of error is reviewed and expanded from previous discussions, and it is argued that the symmetry‐asymmetry issue should be the criterion by which investigators choose between RMA and OLS. This is a biological question about the relationship between variables. It is determined by the investigator, not dictated by the pattern of error in the data. If X is measured with error but OLS should be used because the biological question is asymmetric, there are several methods available for adjusting the OLS slope to reflect the bias due to error. RMA is being used in many analyses for which OLS would be more appropriate. Am J Phys Anthropol, 2009. © 2009 Wiley‐Liss, Inc.