Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

Correlation between oral health perception and clinical factors in a Brazilian community

Objective: The aim of this study was to analyse associations between self-perception of oral health and relevant clinical, personal and socio-demographic factors in a Brazilian community. Material And Methods: Urban adults living in a city in southern Brazil were interviewerd and examined. Individuals with acute pain and who needed multiple extractions of teeth were excluded. Self-perception and the Oral Health Impact Profile (OHIP-14) were applied to measure the impact of oral conditions on the quality of life. Socio-demographic and clinical indicators were also analysed. Results: The clinical examination revealed a high dental caries experience (DMFT = 18.9) and a high prevalence of periodontal disease. Oral condition was considered normal by 42% of respondents. The variables associated with the OHIP-14 were: education, age, self-assessment, dental caries and the DMFT index. Conclusions: Self-perception of oral health was associated with OHIP-14 and the clinical indicators had low influence in the self-perception. Therefore, the development of educational initiatives and preventive strategies for the adult population is recommended. © BASCD 2011.

Spatial correlation between the composition of the clay fraction and contents of available phosphorus of an Oxisol at hillslope scale

Relief is regarded as the abiotic factor most strongly influencing pedogenic processes at a local scale. The spatial correlations between the composition of the clay fraction (iron - Fe and aluminum - Al oxides, kaolinite and organic matter - OM) and contents of available phosphorus (P) of an Oxisol were evaluated at hillslope scale under sugarcane cultivation. A total of 119 samples were collected at intersection points on a 100. ×. 100. m georeferenced grid of regularly spaced points 10. m apart in the 0.2-0.4. m depth in an area consisting of two landform components namely: component I (an area with a linear hillslope curvature), and component II (one with a concave-convex hillslope curvature). Soil OM and available P contents were subjected to descriptive statistics and geostatistical analyses in order to assess their variability and spatial dependence. All attributes studied were spatially dependent. Available phosphorus had positive spatial correlation with high crystalline goethite, hematite and gibbsite. Identifying small hillslope curvatures is useful with a view to better understanding their relationships with soil organic matter and available phosphorus, as well as kaolinite and Fe and Al oxide attributes. A simple correlation analysis by itself is inadequate to relate attributes, which requires a supplemental, geostatistical technique. © 2012 Elsevier B.V..

Patients' expectation and satisfaction with removable dental prosthesis therapy and correlation with patients' evaluation of the dentists

Objective. Considering that patients' satisfaction is one of the most important goals in conducting removable dental prosthesis (RDP) therapy and the fact that there are many factors which influence this parameter, the present study aims to evaluate the expectation before and satisfaction after therapy with RDP in patients who seek such therapy. As a secondary objective, other variables that may be associated with patient satisfaction are also evaluated, such as gender, age, Kennedy's classification of the arch supporting the RDP, the number of RDP adjustments after delivery and patients' evaluation of the dentists' conduct. Materials and methods. A sample of 44 patients who received RDP therapy were assigned visual analog scale scores for their expectation before and satisfaction after therapy regarding chewing, aesthetics, comfort and phonetics. They also completed a questionnaire concerning the dentists' conduct. Results. There was no statistically significant difference among scores concerning different genders, age, number of post-delivery settings and arch involved in the RDP. Regarding patients' evaluation of the dentists' conduct, there was a predominance of positive evaluations, but only different answers to the statement (i.e. 'The dentist I saw thoroughly explained the recommended treatment before it commenced') present statistically significant different scores for chewing (p = 0.040) and phonetics (p = 0.046). Conclusions. The average visual analog scale scores were high for both expectation prior to treatment and satisfaction after treatment; however, the scores for expectations were higher than those for satisfaction. © 2013 Informa Healthcare.

Report on the production of trade statistics in the Caribbean region

Includes bibliography

Cellulite: poor correlation between instrumental methods and photograph evaluation for severity classification

SynopsisBackgroundCellulite refers to skin relief alterations in womens thighs and buttocks, causing dissatisfaction and search for treatment. Its physiopathology is complex and not completely understood. Many therapeutic options have been reported with no scientific evidence about benefits. The majority of the studies are not controlled nor randomized; most efficacy endpoints are subjective, like not well-standardized photographs and investigator opinion. Objective measures could improve severity assessment. Our purpose was to correlate non-invasive instrumental measures and standardized clinical evaluation.MethodsTwenty six women presenting cellulite on buttocks, aged from 25 to 41, were evaluated by: body mass index; standardized photography analysis (10-point severity and 5-point photonumeric scales) by five dermatologists; cutometry and high-frequency ultrasonography (dermal density and dermis/hypodermis interface length). Quality of life impact was assessed. Correlations between clinical and instrumental parameters were performed.ResultsGood agreement among dermatologists and main investigator perceptions was detected. Positive correlations: body mass index and clinical scores; ultrasonographic measures. Negative correlation: cutometry and clinical scores. Quality of life score was correlated to dermal collagen density.ConclusionCellulite caused impact in quality of life. Poor correlation between objective measures and clinical evaluation was detected. Cellulite severity assessment is a challenge, and objective parameters should be optimized for clinical trials.

The canonical correlation between the biological markers of performance and physical fitness in high level judo athletes

The objective of this research was to verify the relationship between biological markers of performance of elite judo athletes and performance in different physical fitness tests. Twenty-one judo athletes were involved in the present observational and correlational study. Dermatoglyphic variables and the 2D:4D digit ratio were considered as biological markers, while the physical fitness variables analyzed were body fat, maximal strength, muscular power, the aerobic and anaerobic profile, and performance in specific tests. The statistics involved canonical correlations and a multivariate technique. A high and significant canonical correlation was observed between groups of variables, the first expressed by 1=0.999 (p<0.0001) and the second by 2=0.997 (p<0.001). It appears that, beyond height and body mass, total ridge count, pattern intensity for fingers and 2D:4D had more canonical loading. The physical fitness component of the first canonical variable incorporated, with high intensity were: the sum of skinfold thickness, the bench press onerepetition maximum (1RM), upper and lower body aerobic power. In the second canonical variable, physical fitness was composed of the squat 1RM, suspension time on the bar, the SJFT-index, and mean power during the upper body Wingate test. The data of this investigation showed the interdependence between biological markers of performance and physical fitness in high level judo athletes.

The elderly health status and its correlation with ageing biomarkers: the European Project Mark-Age

According to the latest statistics projections formulated by Eurostat, the proportion of elderly EU-27’s population aged over 65 years old is predicted to increase from 17.5 % in 2011 to 29.5 % by 2060. This "population explosion" makes extremely important to identify the different genetic and molecular mechanisms which underpin the morbidity and mortality along with new strategies able to counteract or slow down its progress. In this scenario fits the European Project MARK-AGE whose aim was to identify a robust set of biomarkers of human ageing able to discriminate between chronological and biological ageing and to derive a model for healthy ageing through the analysis of three populations from different European countries, supposed to be characterized by different ageing rate: 1. Subjects representing the “Normal” or “Physiological” aging. 2. Subjects representing the “successful” or “decelerate” aging 3. Subjects representing the “accelerated” aging. The aim of this work was to recruit and characterize volunteers, to perform an accurate analysis of the health status of elderly recruited subjects (60-79 years) verifying any possible dissimilarity in their aging trajectories, to identify a set of robust ageing biomarkers and investigate possible correlations between ageing biomarkers and health status of recruited volunteers. The model proposed by MARK-AGE Project regarding different ageing trajectories has been confirmed and several ageing biomarkers have been identified.

Hydrodynamic correlation functions of a driven granular fluid in steady state

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function Fincoh(q,t ) is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,ω), we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,ω) and the longitudinal current correlation function Cl(q,ω). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

T2 mapping in the knee after microfracture at 3.0 T: correlation of global T2 values and clinical outcome - preliminary results

OBJECTIVE: The aim of our study was to correlate global T2 values of microfracture repair tissue (RT) with clinical outcome in the knee joint. METHODS: We assessed 24 patients treated with microfracture in the knee joint. Magnetic resonance (MR) examinations were performed on a 3T MR unit, T2 relaxation times were obtained with a multi-echo spin-echo technique. T2 maps were obtained using a pixel wise, mono-exponential non-negative least squares fit analysis. Slices covering the cartilage RT were selected and region of interest analysis was done. An individual T2 index was calculated with global mean T2 of the RT and global mean T2 of normal, hyaline cartilage. The Lysholm score and the International Knee Documentation Committee (IKDC) knee evaluation forms were used for the assessment of clinical outcome. Bivariate correlation analysis and a paired, two tailed t test were used for statistics. RESULTS: Global T2 values of the RT [mean 49.8ms, standards deviation (SD) 7.5] differed significantly (P<0.001) from global T2 values of normal, hyaline cartilage (mean 58.5ms, SD 7.0). The T2 index ranged from 61.3 to 101.5. We found the T2 index to correlate with outcome of the Lysholm score (r(s)=0.641, P<0.001) and the IKDC subjective knee evaluation form (r(s)=0.549, P=0.005), whereas there was no correlation with the IKDC knee form (r(s)=-0.284, P=0.179). CONCLUSION: These findings indicate that T2 mapping is sensitive to assess RT function and provides additional information to morphologic MRI in the monitoring of microfracture.

Statistics of the received power for free space optical channels

Free space optical (FSO) communication links can experience extreme signal degradation due to atmospheric turbulence induced spatial and temporal irradiance fuctuations (scintillation) in the laser wavefront. In addition, turbulence can cause the laser beam centroid to wander resulting in power fading, and sometimes complete loss of the signal. Spreading of the laser beam and jitter are also artifacts of atmospheric turbulence. To accurately predict the signal fading that occurs in a laser communication system and to get a true picture of how this affects crucial performance parameters like bit error rate (BER) it is important to analyze the probability density function (PDF) of the integrated irradiance fuctuations at the receiver. In addition, it is desirable to find a theoretical distribution that accurately models these ?uctuations under all propagation conditions. The PDF of integrated irradiance fuctuations is calculated from numerical wave-optic simulations of a laser after propagating through atmospheric turbulence to investigate the evolution of the distribution as the aperture diameter is increased. The simulation data distribution is compared to theoretical gamma-gamma and lognormal PDF models under a variety of scintillation regimes from weak to very strong. Our results show that the gamma-gamma PDF provides a good fit to the simulated data distribution for all aperture sizes studied from weak through moderate scintillation. In strong scintillation, the gamma-gamma PDF is a better fit to the distribution for point-like apertures and the lognormal PDF is a better fit for apertures the size of the atmospheric spatial coherence radius ρ0 or larger. In addition, the PDF of received power from a Gaussian laser beam, which has been adaptively compensated at the transmitter before propagation to the receiver of a FSO link in the moderate scintillation regime is investigated. The complexity of the adaptive optics (AO) system is increased in order to investigate the changes in the distribution of the received power and how this affects the BER. For the 10 km link, due to the non-reciprocal nature of the propagation path the optimal beam to transmit is unknown. These results show that a low-order level of complexity in the AO provides a better estimate for the optimal beam to transmit than a higher order for non-reciprocal paths. For the 20 km link distance it was found that, although minimal, all AO complexity levels provided an equivalent improvement in BER and that no AO complexity provided the correction needed for the optimal beam to transmit. Finally, the temporal power spectral density of received power from a FSO communication link is investigated. Simulated and experimental results for the coherence time calculated from the temporal correlation function are presented. Results for both simulation and experimental data show that the coherence time increases as the receiving aperture diameter increases. For finite apertures the coherence time increases as the communication link distance is increased. We conjecture that this is due to the increasing speckle size within the pupil plane of the receiving aperture for an increasing link distance.

Evaluation of the accuracy of multilevel analysis parameter estimates for intra-cluster correlation in correlated binary data

Many studies in biostatistics deal with binary data. Some of these studies involve correlated observations, which can complicate the analysis of the resulting data. Studies of this kind typically arise when a high degree of commonality exists between test subjects. If there exists a natural hierarchy in the data, multilevel analysis is an appropriate tool for the analysis. Two examples are the measurements on identical twins, or the study of symmetrical organs or appendages such as in the case of ophthalmic studies. Although this type of matching appears ideal for the purposes of comparison, analysis of the resulting data while ignoring the effect of intra-cluster correlation has been shown to produce biased results.^ This paper will explore the use of multilevel modeling of simulated binary data with predetermined levels of correlation. Data will be generated using the Beta-Binomial method with varying degrees of correlation between the lower level observations. The data will be analyzed using the multilevel software package MlwiN (Woodhouse, et al, 1995). Comparisons between the specified intra-cluster correlation of these data and the estimated correlations, using multilevel analysis, will be used to examine the accuracy of this technique in analyzing this type of data. ^

Directional statistics: introduction

In many of the natural and physical sciences, measurements are directions, either in two or three dimensions. The analysis of directional data relies on specific statistical models and procedures, which differ from the usual models and methodologies of Cartesian data. This chapter briefly introduces statistical models and inference for this type of data. The basic von Mises-Fisher distribution is introduced and nonparametric methods such as goodness-of-fit tests are presented. Further references are given for exploring related topics such as correlation and regression.

AN INVESTIGATION INTO THE EFFECT OF TESTOSTERONE ON THE QUANTITATIVE MAINTENANCE OF SPERMATOGENESIS IN THE HYPOPHYSECTOMIZED ADULT RAT (PHARMACOKINETICS, MORPHOMETRY, STATISTICS)

Administration of gonadotropins or testosterone (T) will maintain qualitatively normal spermatogenesis and fertility in hypophysectomized (APX) rats. However, quantitative maintenance of the spermatogenic process in APX rats treated with T alone or in combination with follicle stimulating hormone (FSH) has not been demonstrated. Studies reported here were conducted to determine whether it would be possible to increase intratesticular testosterone (ITT) levels in APX rats to those found in normal animals by administration of appropriate amounts of testosterone propionate (TP) and if under these conditions spermatogenesis can be maintained quantitatively. Quantitative analysis of spermatogenesis was performed on stages VI and VII of the spermatogenic cycle utilizing criteria of Leblond and Clermont (1952) all cell types were enumerated. In a series of experiments designed to investigate the effects of T on spermatogenesis, TP was administered to 60 day old APX rats twice daily for 30 days in doses ranging from 0.6 to 15 mg/day or from 0.6 to 6.0 mg/day in combination with FSH. The results of this study demonstrate that the efficiency of transformation of type A to type B spermatogonia and the efficacy of the meiotic prophase are related to ITT levels, and that quantitatively normal completion of the reduction division requires normal ITT levels. The ratio of spermatids to spermatocytes in the vehicle-treated APX rats was 1:1.38; in the APX rats treated with 15 mg of TP it was 1:4.0 (the theoretically expected number). This study is probably the first to demonstrate: (1) the pharmacokinetics of TP, (2) the profile and quantity of T-immunoactivity in both serum and testicular tissue of APX and IC rats as well as APX rats treated with TP alone or in combination with FSH, (3) the direct correlation of serum T and ITT levels in treated APX rats (r = 0.9, p < 0.001) as well as in the IC rats (r = 0.9, p < 0.001), (4) the significant increase in the number of Type B spermatogonia, preleptotene and pachytene spermatocytes and round spermatids in TP-treated APX rats, (5) the correlation of the number of round spermatids formed in IC rats to ITT levels (r = 0.9, p < 0.001), and (6) the correlation of the quantitative maintenance of spermatogenesis with ITT levels (r = 0.7, p < 0.001) in the testes of TP-treated APX rats. These results provide direct experimental evidence for the key role of T in the spermatogenic process. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^