Sample Correlation Coefficient Research Articles

Psychosocial Correlates of Insomnia Severity in Primary Care

Insomnia is a substantive primary care issue that leads to adverse outcomes. These can be improved by addressing factors that accentuate insomnia severity. Accordingly, this study identifies correlates of insomnia severity and determines whether these relationships vary with sociodemographic attributes. This correlational cross-sectional study was conducted in a hospital-sponsored primary care clinic and 2 urban, academic family practice centers. Participants consisted of 236 patients 18 years old or older with clinically significant insomnia (Insomnia Severity Index scores of 7 or more). Surveys instruments included the Insomnia Severity Index, SF-8 (Medical Outcomes Study SF-8 global health status measure), CES-D (Center for Epidemiologic Studies-Depression Scale), DBAS (Dysfunctional Beliefs about Sleep scale), SE-S (Self-Efficacy for Sleep Scale), and a researcher-designed demographic survey. Analytic techniques included descriptive statistics to characterize the study sample, Pearson or Spearman Correlation Coefficients to examine individual associations with insomnia severity, and step-wise linear regression to identify net predictors. Insomnia severity was significantly correlated with health status, depression, self-efficacy, and dysfunctional beliefs (P < .001) but not with sociodemographic attributes. Linear regression demonstrated insomnia severity was best predicted by low self-efficacy and high depression scores. These findings indicate that clinicians treating insomnia should not only manage comorbid depression but also facilitate self-efficacy for sleep-inducing behavioral change.

A Goodness-of-Fit Test for Location-Scale Max-Stable Distributions

In this article, a technique based on the sample correlation coefficient to construct goodness-of-fit tests for max-stable distributions with unknown location and scale parameters and finite second moment is proposed. Specific details to test for the Gumbel distribution are given, including critical values for small sample sizes as well as approximate critical values for larger sample sizes by using normal quantiles. A comparison by Monte Carlo simulation shows that the proposed test for the Gumbel hypothesis is substantially more powerful than some other known tests against some alternative distributions with positive skewness coefficient.

Almost Sure Limit of the Smallest Eigenvalue of Some Sample Correlation Matrices

Let X(n)=(Xij) be a p×n data matrix, where the n columns form a random sample of size n from a certain p-dimensional distribution. Let R(n)=(ρij) be the p×p sample correlation coefficient matrix of X(n), and \(S^{(n)}=(1/n)X^{(n)}(X^{(n)})^{\ast}-\bar{X}\bar{X}^{\ast}\) be the sample covariance matrix of X(n), where \(\bar{X}\) is the mean vector of the n observations. Assuming that Xij are independent and identically distributed with finite fourth moment, we show that the smallest eigenvalue of R(n) converges almost surely to the limit \((1-\sqrt{c}\,)^{2}\) as n→∞ and p/n→c∈(0,∞). We accomplish this by showing that the smallest eigenvalue of S(n) converges almost surely to \((1-\sqrt{c}\,)^{2}\) .

Spectroscopic Noninvasive Measurement of Hemoglobin Compared with Capillary and Venous Values in Neonates

Background: Venepuncture-related blood loss is a common cause of neonatal anemia. Currently, this is the only way to obtain hemoglobin levels. This causes distress for the infant but can also lead to the need for blood transfusions. Recently, a new technique for measuring hemoglobin levels non-invasively has been developed to reduce iatrogenic blood loss and pain. Objective: To compare hemoglobin levels obtained using a transcutaneous spectroscopic device (Mediscan 2000, MBR Optical Systems, Wuppertal, Germany) with venous or capillary blood samples in neonates. Methods: Single-center prospective cohort study of term and preterm infants. The white light spectroscopic device was placed on the forearm for 60 s to measure hemoglobin content within 4 h of venous or capillary blood sampling. Pain reactions of the infants were assessed by using a neonatal pain assessment tool. Results were analyzed by Bland-Altman comparison and Wilcoxon signed-rank test. Results: 80 infants (mean gestational age 29.8 ± 3.8 weeks, mean birth weight 1,300 ± 690 g) were enrolled into the study. A total of 313 spectroscopic recordings within 2 h of a clinically indicated blood sample (181 capillary, 142 venous) were taken. The correlation coefficient R² was 0.96 for capillary/spectroscopic and 0.99 for venous/spectroscopic pairs. Pain scores were significantly less for the spectroscopic measurements (p < 0.01). Conclusion: The results show good correlation between the hemoglobin blood levels and spectroscopic measurements. The slightly lower correlation coefficient for the capillary samples demonstrates a naturally higher variance in these values due to the laboratory method.

Assimilation of the data of observations and adaptive prediction of the natural processes

We propose a dynamical model for the prediction of random components of natural processes. The model is based on the system concept of adaptive balance of causes (ABC-model) and contains dynamic equations for the coefficients of influence adapted to the correlations existing in the predicted processes. To improve the accuracy of predictions, we consider two possible schemes of assimilation of the data of observations in the equations of the ABC-model, namely, the Kolmogorov and Kalman schemes. Both schemes are oriented toward the application of sample correlation coefficients for the prediction of time series of measurements and, hence, take into account the nonstationarity of actual natural processes. We present some examples of prediction of the simulated time series clarifying the algorithms of assimilation of the data of observations. A conclusion is made that the methods of systems modeling and adaptive prediction of random processes by the ABC-method are quite promising.

From short to long memory: Aggregation and estimation

Contemporaneous aggregation of asymptotically stationary AR(1) processes is considered where the squared random coefficients are beta-distributed. Based on the sample correlation coefficients for the individual AR(1) processes, an estimator for the parameters of the underlying beta distribution, and thus for the long memory parameter of the aggregated process, is introduced. Consistency and asymptotic normality are derived and the new estimator is shown to be asymptotically equivalent to the maximum likelihood estimator of the beta distribution.

A Comparative Study on PSD Models for Chromite Ores Comminuted by Different Devices

AbstractThe objective of this study was to characterize the particle size distributions (PSDs) of chromite ores comminuted by different devices, i.e., subjected to different breakage modes and to compare the performances of the PSD functions selected. Different PSDs were obtained for five different mineralogical samples of chromite ores by jaw, cone and hammer crushing and ball mill grinding. The PSDs of the products were characterized to find the most suitable model by Gates–Gaudin–Schuhmann (GGS) and Rosin–Rammler (RR) functions. It was found that the PSDs of all chromite types in single‐pass devices, i.e., jaw and cone crushing were better described by the GGS model than RR model. The RR model gave the best results for all ore sample PSDs generated by retention type systems, i.e., hammer crushing and ball mill grinding. Both distribution functions gave higher R2 values as the size distribution became uniform. The results of piecewise regression were found very useful to improve the performance of GGS distribution in terms of correlation coefficients for samples from a hammer crusher and ball mill.

Testing random number generators by numerical modeling of an exactly solvable problem

Monte Carlo numerical modeling of a problem with a known exact solution is used to test linear multiplicative generators with modulus M = 231 − 1 for their applicability in parallel computing. The deviations of the calculated values of the rotational temperature from the known theoretical values are compared with the possible errors of the Monte Carlo method due to the finiteness of statistical samples. In addition, sample correlation coefficients are used to estimate true correlation coefficients between the values of the rotational temperature obtained on different processors with different multipliers, as well as in the case where additional samples were drawn at the terminal state on each processor in order to increase the size of the total sample. For this purpose, by means of special partial averaging, the random values of the rotational temperature were transformed into approximately normally distributed variables; then, for the variables obtained, true correlation coefficients were estimated by sample correlation coefficients. It was discovered that 204 different multipliers suggested by G.S. Fishman, L.R. Moore exhibit the best performance when used in a parallel implementation of the Monte Carlo method: all deviations are less than the theoretical Monte Carlo errors. Moreover, no correlations between the random variables produced by generators with different multipliers were detected. This suggests that generators with different multipliers produce independent sequences of pseudorandom numbers. However, drawing additional samples on each processor, which is frequently done to increase the size of the total sample, gives rise to correlations. Moreover, in many such cases, the theoretical errors of the Monte Carlo method for multipliers in the bottom part of the list proposed by Fishman and Moore are less than the values of temperature deviations and, therefore, should not be used in this way.

Adiponectin is positively associated with insulin resistance in subjects with type 2 diabetic nephropathy and effects of angiotensin II type 1 receptor blocker losartan

Plasma adiponectin concentration is inversely associated with renal function. There is little literature on adiponectin levels and regulation by anti-hypertensive medication with an angiotensin II type 1 receptor blocker (ARB), especially in subjects with type 2 diabetes in different stages of chronic kidney disease (CKD). Eighty subjects with type 2 diabetic nephropathy were randomly divided into two groups: losarten group (n = 41) and amlodipine group (n = 39). Fasting blood was drawn to determine HbA1c, insulin and adiponectin levels. Insulin resistance was calculated using fasting glucose and insulin, expressed as HOMA-IR. For assessment of the relationship between adiponectin and other parameters, Pearson sample correlation coefficients were used. After stratification, ARB losartan (100 mg daily) was administered for a period of 6 months. There is a positive association between adiponectin and proteinuria, fasting insulin levels and HOMA-IR in both CKD stage 1-2 and stage 3-4. Baseline adiponectin levels were not related to baseline estimated glomerular filtration rate (eGFR). At baseline, the adiponectin concentration was high in all observed subjects, and after 3 and 6 months of treatment with losartan, adiponectin levels decreased in the losartan group as compared with the amlodipine group (P < 0.01). Also fasting insulin and HOMA-IR decreased during the 6-month follow-up compared with the control group (P < 0.01). Our results demonstrate that serum adiponectin levels in type 2 diabetic nephropathy are strongly positively associated with fasting insulin levels and insulin resistance. Declines in fasting insulin and HOMA-IR by losartan are accompanied by decreased adiponectin levels, might offer potential protection in humans. The paradoxical phenomenon merits further ascertainment in future studies.

Validação laboratorial de um método automatizado de dosagem da atividade de adenosina desaminase em líquido pleural e em líquido cefalorraquidiano

The incidence of tuberculosis worldwide has emphasized the need for better assays designed to diagnose the disease, principally the extrapulmonary form. The objective of the present study was to validate the performance of an automated method for the determination of adenosine deaminase (ADA) activity in pleural fluid (PF) and cerebrospinal fluid (CSF), comparing it with a conventional method (the modified Giusti method). In total, 134 samples were selected from among those tested in our laboratory: 94 PF samples and 40 CSF samples. The ADA activity was determined using the two methods. Inter- and intra-assay precision was determined, linear regression analysis was performed, simple concordance tests were conducted, and the means of the differences were calculated. The correlation coefficients for PF and CSF samples were, respectively, 0.96 and 0.95. Inter-assay precision was determined using 21 replicates at 3 different activity levels: low, medium and high. The percentage coefficient of variation (%CV) was, respectively, 5.9, 8.1 and 5.8 for PF samples, compared with 21.9, 18.6 and 13.8 for CSF samples. Intra-assay precision in %CV was 1.3 and 11.7, respectively, for PF and CSF samples. The concordance between the methods in PF and CRF samples was, respectively, 96.8% and 100%, considering the reference values for the diagnosis of TB to be 40 U/L (conventional) and 30 U/L (automated) in PF samples, versus 9 U/L (for both methods) in CSF samples. The results validate the use of the automated method of determining ADA activity in PF and CSF samples as an alternative to the conventional method.

Ultrasound monitoring of cartilaginous matrix evolution in degradable PEG hydrogels

Ultrasound has potential as a non-destructive analytical technique to provide real-time online assessments of matrix evolution in cell-hydrogel constructs used in tissue engineering. In these studies, chondrocytes were encapsulated in poly(ethylene glycol) hydrogels, and gel degradation was manipulated to provide conditions with varying distribution of the large cartilage extracellular matrix molecule, collagen. Mechanical properties and matrix accumulations were simultaneously measured for each condition during 9.5 weeks of in vitro culture. Ultrasound data were used to construct cross-sectional B-scan images for qualitative observations of evolving constructs. Ultrasound data were also analyzed to calculate the speed of sound (SoS) and slope of attenuation (SoA) in developing constructs and a non-degrading hydrogel control without encapsulated chondrocytes. SoS and SoA were calculated from 50 and 100 MHz ultrasound data, and sample correlation coefficients were calculated to identify important relationships between these ultrasound parameters and mechanical/biochemical properties of the evolving matrix. SoA appears to be more sensitive to the density of accumulated matrix molecules than SoS, while SoS appeared to be more sensitive to mechanical modulus than SoA in measurements performed at 100 MHz. Correlation analysis revealed that ultrasound measurements at 100 MHz are more likely to be good predictors of matrix evolution and neotissue function than measurements at 50 MHz. Rigorous studies of the relationships identified in this study will lead to non-destructive real-time monitoring that will be useful in combination with bioreactors used to promote and study cartilage regeneration.

A mass function based on correlation coefficient and its application

A discrete distribution involving a product of two gamma functions has been proposed. It arises naturally in connection with the distribution of sample correlation coefficient based on a bivariate normal population. The first four factorial moments, raw moments, three corrected moments, coefficient of skewness and kurtosis have been derived. Some illustrations have been provided to show how the product moments of sample variances and correlation can be derived by exploiting the moments of the new distribution. These product moments are important for correlation analysis, covariance analysis, intra-sire regression and inference in bivariate normal population with a common mean.

비점원에 의한 중금속 원단위 부하량 - 곡간지 유역을 중심으로 -

The study was carried out to estimate runoff loads of heavy metals in the valley watershed at the middle of South Korea, during farming season. There were no other pollution sources except agricultural activity. From 27 April 2006 to 31 October 2007, water samples were collected using two methods. The first method was regular sampling wherein water samples were taken every two weeks; and the other method was through regular sampling when water were collected during each rainfall event. Results showed that heavy metals were found in the water from the regular samples, and were highest during May and June. It was presumed that this might have been contributed by farming activities. Heavy metal concentration of the irregular samples was lower than regular samples. The correlation coefficient between each heavy metal of the regular samples were as follows: Fe-Al>Cr-Al>Fe-Cr>Mn-Fe. The correlation coefficient of the irregular samples were the following: Fe-Al>Fe-Cu is positive; and Pb-Cu>Ni-Al is negative. Measured pollutant loads of heavy metals in the valley watershed were : 2.047 kg of Al, 0.008 kg of Cd, 0.034 kg of Cr, 0.311 kg of Cu, 0.601 kg of Fe, and 0.282 kg of Zn in 2006; while in 2007, the following were observed: 2.535 kg of Al, 0.026 kg of Cd, 0.055 kg of Cu, 0.727 kg of Fe, and 0.317 kg of Zn. In the analysis of data gathered, the loading rates of effluents from the valley watershed during the rainy season were : 79.8% of Al, 69.1% of Cu, 82.5% of Fe, and 69.1% of Zn in 2006; while 69.9% of Al, 67.5% of Cu, 70.4% of Fe, and 67.5% of Zn in 2007.

ORIGIN-DESTINATION ESTIMATION USING CELLULAR PHONE BS INFORMATION

Origin-Destination (O/D) is important information in route choices and trip assignments. In this study, methodology of estimating O/D based on cellular base station information is proposed. GPS coordinates and cellular base station coordinates have acquired on taxies in Cheongju. Three weeks' data were collected and used. Scatter diagram and sample correlation coefficients show that there are few significant differences of O/D pattern among weeks. However, there is a difference in O/D pattern between weekday and weekend. Besides, there is a difference between morning peak and evening peak. Two methodologies are proposed to convert cellular base station-based O/D into an administrative district-based O/D - using the distribution pattern ratio of GPS coordinates and using the coverage area ratio of the base stations. The statistical analyses through scatter diagram, MAPE and RMSE show that there is few significant difference of pattern between the estimated BS-based O/D and GPS-based O/D.

Efficiency improvements for ion chamber calculations in high energy photon beams

This article presents the implementation of several variance reduction techniques that dramatically improve the simulation efficiency of ion chamber dose and perturbation factor calculations. The cavity user code for the EGSnrc Monte Carlo code system is extended by photon cross-section enhancement (XCSE), an intermediate phase-space storage (IPSS) technique, and a correlated sampling (CS) scheme. XCSE increases the density of photon interaction sites inside and in the vicinity of the chamber and results-in combination with a Russian Roulette game for electrons that cannot reach the cavity volume-in an increased efficiency of up to a factor of 350 for calculating dose in a Farmer type chamber placed at 10 cm depth in a water phantom. In combination with the IPSS and CS techniques, the efficiency for the calculation of the central electrode perturbation factor Pcel can be increased by up to three orders of magnitude for a single chamber location and by nearly four orders of magnitude when considering the Pcel variation with depth or with distance from the central axis in a large field photon beam. The intermediate storage of the phase-space properties of particles entering a volume that contains many possible chamber locations leads to efficiency improvements by a factor larger than 500 when computing a profile of chamber doses in the field of a linear accelerator photon beam. All techniques are combined in a new EGSnrc user code egs_chamber. Optimum settings for the variance reduction parameters are investigated and are reported for a Farmer type ion chamber. A few example calculations illustrating the capabilities of the egs_chamber code are presented.

A p-value for testing the equivalence of the variances of a bivariate normal distribution

A p-value is developed for testing the equivalence of the variances of a bivariate normal distribution. The unknown correlation coefficient is a nuisance parameter in the problem. If the correlation is known, the proposed p-value provides an exact test. For large samples, the p-value can be computed by replacing the unknown correlation by the sample correlation, and the resulting test is quite satisfactory. For small samples, it is proposed to compute the p-value by replacing the unknown correlation by a scalar multiple of the sample correlation. However, a single scalar is not satisfactory, and it is proposed to use different scalars depending on the magnitude of the sample correlation coefficient. In order to implement this approach, tables are obtained providing sub-intervals for the sample correlation coefficient, and the scalars to be used if the sample correlation coefficient belongs to a particular sub-interval. Once such tables are available, the proposed p-value is quite easy to compute since it has an explicit analytic expression. Numerical results on the type I error probability and power are reported on the performance of such a test, and the proposed p-value test is also compared to another test based on a rejection region. The results are illustrated with two examples: an example dealing with the comparability of two measuring devices, and an example dealing with the assessment of bioequivalence.

Development of a chromatographic fingerprint for the chloroform extracts of Ganoderma lucidum by HPLC and LC–MS

A new high-performance liquid chromatographic (HPLC) fingerprinting method was developed for the quality control of Ganoderma lucidum. Twenty-nine batches obtained from three different origins in China were used to establish the fingerprint. The constituents of these samples were separated with a Kromasil C 18 column (250 mm × 4.6 mm, 5 μm) by linear gradient elution using water–acetic acid (100:0.1, v/v) and acetonitrile as mobile phase components at a flow rate of 0.8 ml/min and detector wavelength at 254 nm. Mean chromatograms and correlation coefficients of samples were calculated by the software “Similarity Evaluation System for Chromatographic Fingerprint of TCM”. There were 19 common peaks in this fingerprint. Eleven of these common peaks were tentatively identified with reference to literature data based on their liquid chromatography–electrospray ionization-tandem mass spectrometry (LC–ESI-MS) and UV data. This profile was then successfully used to identify and assess the differences among samples from various origins with the aid of similarity analysis. The diverse similarities among different samples indicated that the quality of G. lucidum was not stable and the products from different areas were inconsistent. All results showed that the developed fingerprint assay was specific and could further serve for quality identification and comprehensive evaluation of G. lucidum.

Revisiting adverse effects of cross-hybridization in Affymetrix gene expression data: do they matter for correlation analysis?

Background.This work was undertaken in response to a recently published paper by Okoniewski and Miller (BMC Bioinformatics 2006, 7: Article 276). The authors of that paper came to the conclusion that the process of multiple targeting in short oligonucleotide microarrays induces spurious correlations and this effect may deteriorate the inference on correlation coefficients. The design of their study and supporting simulations cast serious doubt upon the validity of this conclusion. The work by Okoniewski and Miller drove us to revisit the issue by means of experimentation with biological data and probabilistic modeling of cross-hybridization effects.Results.We have identified two serious flaws in the study by Okoniewski and Miller: (1) The data used in their paper are not amenable to correlation analysis; (2) The proposed simulation model is inadequate for studying the effects of cross-hybridization. Using two other data sets, we have shown that removing multiply targeted probe sets does not lead to a shift in the histogram of sample correlation coefficients towards smaller values. A more realistic approach to mathematical modeling of cross-hybridization demonstrates that this process is by far more complex than the simplistic model considered by the authors. A diversity of correlation effects (such as the induction of positive or negative correlations) caused by cross-hybridization can be expected in theory but there are natural limitations on the ability to provide quantitative insights into such effects due to the fact that they are not directly observable.Conclusion.The proposed stochastic model is instrumental in studying general regularities in hybridization interaction between probe sets in microarray data. As the problem stands now, there is no compelling reason to believe that multiple targeting causes a large-scale effect on the correlation structure of Affymetrix gene expression data. Our analysis suggests that the observed long-range correlations in microarray data are of a biological nature rather than a technological flaw.Reviewers:The paper was reviewed by I. K. Jordan, D. P. Gaile (nominated by E. Koonin), and W. Huber (nominated by S. Dudoit).

Comparison of Goodness-of-Fit Measures in Probit Regression Model

This article examines several goodness-of-fit measures in the binary probit regression model. Existing pseudo-R 2 measures are reviewed, two modified and one new pseudo-R 2 measure are proposed. For the probit regression model, empirical comparisons are made for different goodness-of-fit measures with the squared sample correlation coefficient of the observed response and the predicted probabilities. As an illustration, the goodness-of-fit measures are applied to a “paid labor force” data set.

Evaluating the Significance Test When the Correlation Coefficient is Different from Zero in the Test of Hypothesis

Sample size and correlation coefficient of populations are the most important factors which influence the statistical significance of the sample correlation coefficient. It is observed that for evaluating the hypothesis when the observed value of the correlation coefficient's r is different from zero, Fisher's Z transformation may be incorrect for small samples especially when population correlation coefficient ρ has big values. In this study, a simulation program has been generated for to illustrate how the bias in the Fisher transformation of the correlation coefficient affects estimate precision when sample size is small and ρ has big value. By the simulation results, 90 and 95% confidence intervals of correlation coefficients have been created and tabled. As a result, it is suggested that especially when ρ is greater than 0.2 and sample sizes of 18 or less, Tables 1 and 2 can be used for the significance test in correlations.