Sample Correlation Coefficient Research Articles

Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling

In this article, two modified ratio estimators of the population mean are suggested provided that the first or third quartiles of the auxiliary variable can be established when the mean of the auxiliary variable is known. The double-sampling method is used to estimate the mean of the auxiliary variable if it is unknown. The suggested estimators are investigated under simple random sampling (SRS) and median ranked set sampling (MRSS) schemes. The new estimators when using MRSS are compared to their counterparts under SRS. The bias and the mean square error of the proposed estimators are derived. It turns out that the estimators are approximately unbiased and the MRSS estimators are more efficient than the SRS estimators, on the basis of the same sample size, correlation coefficient, and quartile. A real data set is used for illustration.

Adaptive extensions of a two‐stage group sequential procedure for testing primary and secondary endpoints (I): unknown correlation between the endpoints

In a previous paper we studied a two-stage group sequential procedure (GSP) for testing primary and secondary endpoints where the primary endpoint serves as a gatekeeper for the secondary endpoint. We assumed a simple setup of a bivariate normal distribution for the two endpoints with the correlation coefficient ρ between them being either an unknown nuisance parameter or a known constant. Under the former assumption, we used the least favorable value of ρ = 1 to compute the critical boundaries of a conservative GSP. Under the latter assumption, we computed the critical boundaries of an exact GSP. However, neither assumption is very practical. The ρ = 1 assumption is too conservative resulting in loss of power, whereas the known ρ assumption is never true in practice. In this part I of a two-part paper on adaptive extensions of this two-stage procedure (part II deals with sample size re-estimation), we propose an intermediate approach that uses the sample correlation coefficient r from the first-stage data to adaptively adjust the secondary boundary after accounting for the sampling error in r via an upper confidence limit on ρ by using a method due to Berger and Boos. We show via simulation that this approach achieves 5-11% absolute secondary power gain for ρ ≤0.5. The preferred boundary combination in terms of high primary as well as secondary power is that of O'Brien and Fleming for the primary and of Pocock for the secondary. The proposed approach using this boundary combination achieves 72-84% relative secondary power gain (with respect to the exact GSP that assumes known ρ). We give a clinical trial example to illustrate the proposed procedure.

Asymptotically minimax bias estimation of the correlation coefficient for bivariate independent component distributions

For bivariate independent component distributions, the asymptotic bias of the correlation coefficient estimators based on principal component variances is derived. This result allows to design an asymptotically minimax bias (in the Huber sense) estimator of the correlation coefficient, namely, the trimmed correlation coefficient, for contaminated bivariate normal distributions. The limit cases of this estimator are the sample, median and MAD correlation coefficients, the last two simultaneously being the most B- and V-robust estimators. In contaminated normal models, the proposed estimators dominate both in bias and in efficiency over the sample correlation coefficient on small and large samples.

What types of word alignment improve statistical machine translation?

In most statistical machine translation (SMT) systems, bilingual segments are extracted via word alignment. However, there is a need for systematic study as to what alignment characteristics can benefit MT under specific experimental settings such as the type of MT system, the language pair or the type or size of the corpus. In this paper we perform, in each of these experimental settings, a statistical analysis of the data and study the sample correlation coefficients between a number of alignment or phrase table characteristics and variables such as the phrase table size, the number of untranslated words or the BLEU score. We report results for two different SMT systems (a phrase-based and an n-gram-based system) on Chinese-to-English FBIS and BTEC data, and Spanish-to-English European Parliament data. We find that the alignment characteristics which help in translation greatly depend on the MT system and on the corpus size. We give alignment hints to improve BLEU score, depending on the SMT system used and the type of corpus. For example, for phrase-based SMT, dense alignments are required with larger corpora, especially on the target side, while with smaller corpora, more precise, sparser alignments are better, especially on the source side. Avoiding some long-distance crossing links may also improve BLEU score with small corpora. We take these conclusions into account to modify two types of alignment systems, and get 1 to 1.6 % relative improvements in BLEU score on two held-out corpora, although the improved system is different in each corpus.

An evaluation of the potential of linear and nonlinear skin permeation models for the prediction of experimentally measured percutaneous drug absorption

OBJECTIVES The developments in combinatorial chemistry have led to a rapid increase in drug design and discovery and, ultimately, the production of many potential molecules that require evaluation. Hence, there has been much interest in the use of mathematical models to predict dermal absorption. Therefore, the aim of this study was to test the performance of both linear and nonlinear models to predict the skin permeation of a series of 11 compounds. The modelling in this study was carried out by the application of both quantitative structure permeability relationships and Gaussian process-based machine learning methods to predict the flux and permeability coefficient of the 11 compounds. The actual permeation of these compounds across human skin was measured using Franz cells and a standard protocol with high performance liquid chromatography analysis. Statistical comparison between the predicted and experimentally-derived values was performed using mean squared error and the Pearson sample correlation coefficient. The findings of this study would suggest that the models failed to accurately predict permeation and in some cases were not within two- or three-orders of magnitude of the experimentally-derived values. However, with this set of compounds the models were able to effectively rank the permeants. Although not suitable for accurately predicting permeation the models may be suitable for determining a rank order of permeation, which may help to select candidate molecules for in-vitro screening. However, it is important to note that such predictions need to take into account actual relative drug candidate potencies.

Premenopausal serum androgens and breast cancer risk: a nested case-control study.

IntroductionProspective epidemiologic studies have consistently shown that levels of circulating androgens in postmenopausal women are positively associated with breast cancer risk. However, data in premenopausal women are limited.MethodsA case-control study nested within the New York University Women's Health Study was conducted. A total of 356 cases (276 invasive and 80 in situ) and 683 individually-matched controls were included. Matching variables included age and date, phase, and day of menstrual cycle at blood donation. Testosterone, androstenedione, dehydroandrosterone sulfate (DHEAS) and sex hormone-binding globulin (SHBG) were measured using direct immunoassays. Free testosterone was calculated.ResultsPremenopausal serum testosterone and free testosterone concentrations were positively associated with breast cancer risk. In models adjusted for known risk factors of breast cancer, the odds ratios for increasing quintiles of testosterone were 1.0 (reference), 1.5 (95% confidence interval (CI), 0.9 to 2.3), 1.2 (95% CI, 0.7 to 1.9), 1.4 (95% CI, 0.9 to 2.3) and 1.8 (95% CI, 1.1 to 2.9; Ptrend = 0.04), and for free testosterone were 1.0 (reference), 1.2 (95% CI, 0.7 to 1.8), 1.5 (95% CI, 0.9 to 2.3), 1.5 (95% CI, 0.9 to 2.3), and 1.8 (95% CI, 1.1 to 2.8, Ptrend = 0.01). A marginally significant positive association was observed with androstenedione (P = 0.07), but no association with DHEAS or SHBG. Results were consistent in analyses stratified by tumor type (invasive, in situ), estrogen receptor status, age at blood donation, and menopausal status at diagnosis. Intra-class correlation coefficients for samples collected from 0.8 to 5.3 years apart (median 2 years) in 138 cases and 268 controls were greater than 0.7 for all biomarkers except for androstenedione (0.57 in controls).ConclusionsPremenopausal concentrations of testosterone and free testosterone are associated with breast cancer risk. Testosterone and free testosterone measurements are also highly reliable (that is, a single measurement is reflective of a woman's average level over time). Results from other prospective studies are consistent with our results. The impact of including testosterone or free testosterone in breast cancer risk prediction models for women between the ages of 40 and 50 years should be assessed. Improving risk prediction models for this age group could help decision making regarding both screening and chemoprevention of breast cancer.

Estimating a bivariate linear relationship

Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and errors is unidentified without additional information. I propose a prior density that incorporates the fact that the slope and variance parameters together determine the covariance matrix of the unobserved true values but is otherwise diffuse. The marginal posterior density of the slope is invariant to interchange and scaling of the coordinates and depends on the data only through the sample correlation coefficient and ratio of standard deviations. It covers the interval between the two ordinary least squares estimates but diminishes rapidly outside of it. I introduce the R package leiv for computing the posterior density, and I apply it to examples in astronomy and method comparison.

An alternative approach for testing for linear association for two independent stationary AR(1) processes

Spurious correlations occur when two independent time series are found to be correlated according to the typical statistical procedure for testing the null hypothesis of zero correlation in the population. Using a Monte Carlo analysis, this study examines the spurious correlation phenomenon for two independent stationary AR(1) processes and it finds that if an alternative testing procedure is applied, spurious behaviour is eliminated using the variance of the sample correlation coefficient of these two series, suggested by Bartlett (1935).

What's in a jellyfish? Proximate and elemental composition and biometric relationships for use in biogeochemical studies

Many marine organisms have gelatinous bodies, but the trait is most common in the medusae (phylum Cnidaria), ctenophores (phylum Ctenophora), and the pelagic tunicates (phylum Chordata, class Thaliacea). Although there are taxonomic and trophic differences between the thaliaceans and the other two closely related phyla, the collective term has been used within the framework of this article. Because of the apparent increase in bloom events, jellyfish are receiving greater attention from the wider marine science community. Questions being posed include: (1) what is the role of jellyfish in pelagic food webs in a changing environment, and (2) what is the role of jellyfish in large-scale biogeochemical processes such as the biological carbon pump? In order to answer such questions, fundamental data on body composition and biomass are required. The purpose of this data set was to compile proximate and elemental body composition and length–mass and mass–mass regressions for jellyfish (i.e., medusae, siphonophores, ctenophores, salps, doliolids, and pyrosomes) to serve as a baseline data set informing studies on biogeochemical cycling, food web dynamics, and ecosystem modeling, and physiology. Using mainly published data from 1932 to 2010, we have assembled three data sets: (1) body composition (wet, dry, and ash-free dry mass, C, N, P as a percentage of wet and dry mass, and C:N), (2) length–mass biometric equations, and (3) mass–mass biometric equations. The data sets represent a total of 102 species from six classes (20 Thaliacea, 2 Cubozoa, 33 Hydrozoa, 26 Scyphozoa, 17 Tentaculata, 4 Nuda) in three phyla. Where it exists, we have included supplementary data on location, salinity, whole animal or tissue type, measured size range, and where appropriate, the regression type with values of sample size, correlation coefficients (r, r2), and level of significance for the relationship. In addition to the raw unpublished data, we have provided summary tables of mean (± SD) body composition for the main taxonomic groups.

A new algorithm to characterize biodegradability of biomass during anaerobic digestion: Influence of lignin concentration on methane production potential

We examined the influence of fibrous fractions of biomass on biochemical methane potential (BMP) with the objective of developing an economical and easy-to-use statistical model to predict BMP, and hence the biodegradability of organic material (BD) for biogas production. The model was developed either for energy crops (grass, maize, and straw) or for animal manures, or as a combined model for these two biomass groups. It was found that lignin concentration in volatile solids (VS) was the strongest predictor of BMP for all the biomass samples. The square of the sample correlation coefficient (R2) from the BMP versus lignin was 0.908 (p<0.0001), 0.763 (p<0.001) and 0.883 (p<0.001) for animal manure, energy crops and the combined model, respectively. Validation of the combined model was carried out using 65 datasets from the literature.

Determination of lipoprotein lipase activity using a novel fluorescent lipase assay

A novel, real-time, homogeneous fluorogenic lipoprotein lipase (LPL) assay was developed using a commercially available substrate, the EnzChek lipase substrate, which is solubilized in Zwittergent. The triglyceride analog substrate does not fluoresce, owing to apposition of fluorescent and fluorescent quenching groups at the sn-1 and sn-2 positions, respectively, fluorescence becoming unquenched upon release of the sn-1 BODIPY FA derivative following hydrolysis. Increase in fluorescence intensity at 37°C was proportional to LPL concentration. The assay was more sensitive than a similar assay using 1,2-O-dilauryl-rac-glycero-3-glutaric acid-(6-methylresorufin ester) and was validated in biological samples, including determination of LPL-specific activity in postheparin mouse plasma. The simplicity and reproducibility of the assay make it ideal for in vitro, high-throughput screening for inhibitors and activators of LPL, thus expediting discovery of drugs of potential clinical value.

2변량 정규분포의 독립성에 관한 퍼지 검정

We furnished some properties of fuzzy testing of independence for correlation in a bivariate normal distribution by agreement index. First we present some restriction of the fuzzy data, define fuzzy sample correlation coefficient and agreement index for testing hypothesis with acceptance or rejection degree. Also, we show that UMP unbiased fuzzy test and drawing conclusions the fuzzy test.

Developmental change in the relation between simple and complex spans: A meta-analysis.

In the present meta-analysis the effects of developmental level on the correlation between simple and complex span tasks were investigated. Simple span-complex span correlation coefficients presented in 52 independent samples (7,060 participants) were regressed on a variable representing mean age of sample (range: 4.96-22.80 years), using analyses adapted for meta-analytic purposes. The results showed strong positive relations between mean age of sample and simple span-complex span correlation coefficients, suggesting that the relation between simple and complex span tasks became stronger with increasing age. These results could not be accounted for by study-related differences in measurement reliability, restricted range, or sample size. A new theoretical account explaining these findings is outlined.

A Bayesian unmasking method for locating multiple gross errors based on posterior probabilities of classification variables

This paper puts forward a Bayesian method for multiple gross errors location and estimation, and studies the masking and swamping problem in multiple gross errors detection from a new point of view, further proposes the corresponding feasible solution. First, the Bayesian method for gross error location is established based on the posterior probabilities of classification variables, each of which is used to determine whether each observation contains gross error or not. When some interactions exist among observations with multiple gross errors, the above-mentioned method may lead to the failure of detection due to masking and swamping. For that, on the basis of analyzing the character of masking and swamping, starting from the eigen structure of the sample correlation coefficient matrix of the classification vector, we give the Bayesian unmasking method to locate multiple gross errors, and design the corresponding algorithm, namely the adaptive Gibbs sampling algorithm. Finally, applying the mean shift model, we raise a Bayesian approach to estimate gross errors. Significant applications of the approach show the promising results on overcoming masking and swamping.

Correlation of MAPT scores with clinical and radiographic assessment of patients awaiting THR/TKR

The Multi-attribute Arthritis Prioritisation Tool (MAPT) score is used as a tool to prioritize referrals to specialist clinics and care given to patients with hip and knee problems. Our pilot study aimed to determine the extent of any relationship between the MAPT scores and the clinician's assessment of severity of disease in terms of surgical waiting list (SWL) categories and radiological assessment. This is a retrospective study of patients with symptomatic hip or knee osteoarthritis (OA) that were referred via the orthopaedic waiting list project between January and July 2009 to the Bendigo Health's orthopaedic outpatients clinic and were waitlisted for a total hip replacement (THR)/total knee replacement (TKR). The MAPT score was calculated and the Surgical waitlist Category was obtained from the surgical booking office. The radiographs of all these patients were reviewed and graded independently according to the Kellgren and Lawrence radiographic grading for severity of arthritis. The relationships between MAPT score, SWL category and the Kellgren and Lawrence radiographic grades were examined using graphical methods and Kendall's tau correlation coefficients. There were 62 patients in the study. The Kendall-tau sample correlation coefficient between MAPT score and the radiographic grade is τ(b) = -0.091 (P = 0.330) and between MAPT score and SWL category is τ(b) = 0.007 (P = 0.951). The sample data suggests that there is no significant relationship between the MAPT score and radiographic severity of OA, or between MAPT score and surgical waitlist category of patients with OA waitlisted for a THR/TKR.

Estimation of the simple correlation coefficient

This article investigates some unfamiliar properties of the Pearson product-moment correlation coefficient for the estimation of simple correlation coefficient. Although Pearson's r is biased, except for limited situations, and the minimum variance unbiased estimator has been proposed in the literature, researchers routinely employ the sample correlation coefficient in their practical applications, because of its simplicity and popularity. In order to support such practice, this study examines the mean squared errors of r and several prominent formulas. The results reveal specific situations in which the sample correlation coefficient performs better than the unbiased and nearly unbiased estimators, facilitating recommendation of r as an effect size index for the strength of linear association between two variables. In addition, related issues of estimating the squared simple correlation coefficient are also considered.

On-line dissolution determination of Baicalin in solid dispersion based on near infrared spectroscopy and circulation dissolution system

Drug on-line circulation dissolution system with near infrared spectrophotometer for dissolution determination was reported in this paper and subsequently partial least squares (PLS) calibration model was established for concentration prediction of Baicalin in solid dispersion. When the main factor number in PLS calibration model was 6, the correlation coefficients of PLS calibration samples and prediction ones were all 0.9999 and the relative standard deviations were 0.69% and 1.10%, respectively, which showed good robustness and predictability. Combining drug circulation dissolution system with the PLS calibration model, dissolution of Baicalin in raw material drug and solid dispersion were obtained at different times. The results indicated that the dissolution property of Baicalin in solid dispersion (especially at the early time) had been significantly improved. The accumulated dissolution of Baicalin in the solid dispersion at 45 min reached nearly 40%, increasing by 15% compared with raw material drug (about 25%). The aforementioned PLS model associated with drug circulation dissolution system provided a simple, accurate and on-line support for dissolution determination of drug, especially at the early time of rapid dissolution.

Using correlation coefficients to estimate slopes in multiple linear regression

This short note takes correlation coefficients as the starting point to obtain inferential results in linear regression. Under certain conditions, the population correlation coefficient and the sampling correlation coefficient can be related via a Taylor series expansion to allow inference on the coefficients in simple and multiple regression. This general method includes nonparametric correlation coefficients and so gives a universal way to develop regression methods. This work is part of a correlation estimation system that uses correlation coefficients to perform estimation in many settings, for example, time series, nonlinear and generalized linear models, and individual distributions.

Edgeworth Expansion and Normalizing Transformation of Ratio Statistics and Their Application

Some statistics in common use take the form of a ratio of two statistics, such as sample correlation coefficient, Pearson's coefficient of variation, cumulant estimators, and so on. In this article, using an asymptotic representation of the ratio statistics, we will obtain an Edgeworth expansion and a normalizing transformation with remainder term o(n −1/2). The Edgeworth expansion is based on a Studentized ratio statistic, which is studentized by a consistent variance estimator. Applying these results to the sample correlation coefficient, we obtain the normalizing transformation and an asymptotic confidence interval of the correlation coefficient without assuming specific underlying distribution. This normalizing transformation is an extension of the Fisher's z-transformation.

On testing the skew normal hypothesis

In this work two goodness-of-fit tests are proposed for the skew normal distribution, based on properties of this family of distributions and the sample correlation coefficient. The critical values for the tests are obtained by using Monte Carlo simulation for several sample sizes and levels of significance. The power of the proposed tests are compared with that of the tests studied by Mateu et al. (2007) and the one studied by Meintanis (2007) for several sample sizes and considering diverse alternatives. The results show that the proposed tests have greater power than those studied by Mateu et al. (2007) and Meintanis (2007) against some alternative distributions.