Statistical guidelines for the analysis of data obtained from one or both eyes

Purpose - Measurements obtained from the right and left eye of a subject are often correlated whereas many statistical tests assume observations in a sample are independent. Hence, data collected from both eyes cannot be combined without taking this correlation into account. Current practice is reviewed with reference to articles published in three optometry journals, viz., Ophthalmic and Physiological Optics (OPO), Optometry and Vision Science (OVS), Clinical and Experimental Optometry (CEO) during the period 2009–2012. Recent findings - Of the 230 articles reviewed, 148/230 (64%) obtained data from one eye and 82/230 (36%) from both eyes. Of the 148 one-eye articles, the right eye, left eye, a randomly selected eye, the better eye, the worse or diseased eye, or the dominant eye were all used as selection criteria. Of the 82 two-eye articles, the analysis utilized data from: (1) one eye only rejecting data from the adjacent eye, (2) both eyes separately, (3) both eyes taking into account the correlation between eyes, or (4) both eyes using one eye as a treated or diseased eye, the other acting as a control. In a proportion of studies, data were combined from both eyes without correction. Summary - It is suggested that: (1) investigators should consider whether it is advantageous to collect data from both eyes, (2) if one eye is studied and both are eligible, then it should be chosen at random, and (3) two-eye data can be analysed incorporating eyes as a ‘within subjects’ factor.

Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers [Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013)1751-811310.1088/1751-8113/46/3/035501; Nath, Phys. Rev. E 88, 013010 (2013)PLEEE81539-375510.1103/PhysRevE.88.013010] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a "cold" accretion flow at 3000 K is too "hot" in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

High-throughput manufacturing of size-tuned liposomes by a new microfluidics method using enhanced statistical tools for characterization

Microfluidics has recently emerged as a new method of manufacturing liposomes, which allows for reproducible mixing in miliseconds on the nanoliter scale. Here we investigate microfluidics-based manufacturing of liposomes. The aim of these studies was to assess the parameters in a microfluidic process by varying the total flow rate (TFR) and the flow rate ratio (FRR) of the solvent and aqueous phases. Design of experiment and multivariate data analysis were used for increased process understanding and development of predictive and correlative models. High FRR lead to the bottom-up synthesis of liposomes, with a strong correlation with vesicle size, demonstrating the ability to in-process control liposomes size; the resulting liposome size correlated with the FRR in the microfluidics process, with liposomes of 50 nm being reproducibly manufactured. Furthermore, we demonstrate the potential of a high throughput manufacturing of liposomes using microfluidics with a four-fold increase in the volumetric flow rate, maintaining liposome characteristics. The efficacy of these liposomes was demonstrated in transfection studies and was modelled using predictive modeling. Mathematical modelling identified FRR as the key variable in the microfluidic process, with the highest impact on liposome size, polydispersity and transfection efficiency. This study demonstrates microfluidics as a robust and high-throughput method for the scalable and highly reproducible manufacture of size-controlled liposomes. Furthermore, the application of statistically based process control increases understanding and allows for the generation of a design-space for controlled particle characteristics.

Revealing statistical properties of quasi-CW fibre lasers in bandwidth-limited measurements

We introduce a general technique how to reveal in experiments of limited electrical bandwidth which is lower than the optical bandwidth of the optical signal under study, whether the statistical properties of the light source obey Gaussian distribution or mode correlations do exist. To do that one needs to perform measurements by decreasing the measurement bandwidth. We develop a simple model of bandwidth-limited measurements and predict universal laws how intensity probability density function and intensity auto-correlation function of ideal completely stochastic source of Gaussian statistics depend on limited measurement bandwidth and measurement noise level. Results of experimental investigation are in good agreement with model predictions. In particular, we reveal partial mode correlations in the radiation of quasi-CW Raman fibre laser.

A Statistical Convergence Aplication for the Hopfield Networks

When Recurrent Neural Networks (RNN) are going to be used as Pattern Recognition systems, the problem to be considered is how to impose prescribed prototype vectors ξ^1,ξ^2,...,ξ^p as fixed points. The synaptic matrix W should be interpreted as a sort of sign correlation matrix of the prototypes, In the classical approach. The weak point in this approach, comes from the fact that it does not have the appropriate tools to deal efficiently with the correlation between the state vectors and the prototype vectors The capacity of the net is very poor because one can only know if one given vector is adequately correlated with the prototypes or not and we are not able to know what its exact correlation degree. The interest of our approach lies precisely in the fact that it provides these tools. In this paper, a geometrical vision of the dynamic of states is explained. A fixed point is viewed as a point in the Euclidean plane R2. The retrieving procedure is analyzed trough statistical frequency distribution of the prototypes. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented

Modeling of Effective Process of Network Maintaining Based on Statistical Data

This paper is dedicated to modelling of network maintaining based on live example – maintaining ATM banking network, where any problems are mean money loss. A full analysis is made in order to estimate valuable and not-valuable parameters based on complex analysis of available data. Correlation analysis helps to estimate provided data and to produce a complex solution of increasing network maintaining effectiveness.

An investigation of the strategies used by organizations participating in the welfare-to-work network program and correlation of the strategies with the retention data to determine best practices for job retention among former welfare recipients

This ex post facto study (N = 209) examined the relationships between employer job strategies and job retention among organizations participating in Florida welfare-to-work network programs and associated the strategies with job retention data to determine best practices. ^ An internet-based self-report survey battery was administered to a heterogeneous sampling of organizations participating in the Florida welfare-to-work network program. Hypotheses were tested through correlational and hierarchical regression analytic procedures. The partial correlation results linked each of the job retention strategies to job retention. Wages, benefits, training and supervision, communication, job growth, work/life balance, fairness and respect were all significantly related to job retention. Hierarchical regression results indicated that the training and supervision variable was the best predictor of job retention in the regression equation. ^ The size of the organization was also a significant predictor of job retention. Large organizations reported higher job retention rates than small organizations. There was no statistical difference between the types of organizations (profit-making and non-profit) and job retention. The standardized betas ranged from to .26 to .41 in the regression equation. Twenty percent of the variance in job retention was explained by the combination of demographic and job retention strategy predictors, supporting the theoretical, empirical, and practical relevance of understanding the association between employer job strategies and job retention outcomes. Implications for adult education and human resource development theory, research, and practice are highlighted as possible strategic leverage points for creating conditions that facilitate the development of job strategies as a means for improving former welfare workers’ job retention.^

Statistical Analysis of Wind Power Generation in Europe

Studies have shown that large geographical spreading can reduce the wind power variability and smooth production. It is frequently assumed that storage and interconnection can manage wind power variability and are totally flexible. However, constraints do exist. In the future more and more electricity will be provided by renewable energy sources and more electricity interconnectors will be built between European Union (EU) countries, as outlines in many of the Projects of Common Interests. It is essential to understand the correlation of wind generation throughout Europe considering power system constraints. In this study the spatial and temporal correlation of wind power production across several countries is examined in order to understand how “the wind ‘travels’ across Europe”. Three years of historical hourly wind power generation from ten EU countries is analysed to investigate the geographic diversity and time scales influence on correlation of wind power variations. Results are then compared with two other studies and show similar general characteristics of correlation between EU country pairs to identify opportunities for storage optimisation, power system operations, and trading.

Statistical Analysis of Sea Surface Temperature and Chlorophyll-a Concentration Patterns in the Gulf of Tadjourah (Djibouti)

The sea surface temperature (SST) and chlorophyll-a concentration (CHL-a) were analysed in the Gulf of Tadjourah from two set of 8-day composite satellite data, respectively from 2008 to 2012 and from 2005 to 2011. A singular spectrum analysis (SSA) shows that the annual cycle of SST is strong (74.3% of variance) and consists of warming (April-October) and cooling (November-March) of about 2.5C than the long-term average. The semi-annual cycle captures only 14.6% of temperature variance and emphasises the drop of SST during July-August. Similarly, the annual cycle of CHL-a (29.7% of variance) depicts high CHL-a from June to October and low concentration from November to May. In addition, the first spatial empirical orthogonal function (EOF) of SST (93% of variance) shows that the seasonal warming/cooling is in phase across the whole study area but the southeastern part always remaining warmer or cooler. In contrast to the SST, the first EOF of CHL-a (54.1% of variance) indicates the continental shelf in phase opposition with the offshore area in winter during which the CHL-a remains sequestrated in the coastal area particularly in the south-east and in the Ghoubet Al-Kharab Bay. Inversely during summer, higher CHL-a quantities appear in the offshore waters. In order to investigate processes generating these patterns, a multichannel spectrum analysis was applied to a set of oceanic (SST, CHL-a) and atmospheric parameters (wind speed, air temperature and air specific humidity). This analysis shows that the SST is well correlated to the atmospheric parameters at an annual scale. The windowed cross correlation indicates that this correlation is significant only from October to May. During this period, the warming was related to the solar heating of the surface water when the wind is low (April-May and October) while the cooling (November-March) was linked to the strong and cold North-East winds and to convective mixing. The summer drop in SST followed by a peak of CHL-a, seems strongly correlated to the upwelling. The second EOF modes of SST and CHL-a explain respectively 1.3% and 5% of the variance and show an east-west gradient during winter that is reversed during summer. This work showed that the seasonal signals have a wide spatial influence and dominate the variability of the SST and CHL-a while the east-west gradient are specific for the Gulf of Tadjourah and seem induced by the local wind modulated by the topography.

A Study on the Correlation of Bivariate And Trivariate Normal Models

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.

Comparison Of Postoperative Stability Of Three Rigid Internal Fixation Techniques After Sagittal Split Ramus Osteotomy For Mandibular Advancement.

The aim of this investigation was to compare the skeletal stability of three different rigid fixation methods after mandibular advancement. Fifty-five class II malocclusion patients treated with the use of bilateral sagittal split ramus osteotomy and mandibular advancement were selected for this retrospective study. Group 1 (n = 17) had miniplates with monocortical screws, Group 2 (n = 16) had bicortical screws and Group 3 (n = 22) had the osteotomy fixed by means of the hybrid technique. Cephalograms were taken preoperatively, 1 week within the postoperative care period, and 6 months after the orthognathic surgery. Linear and angular changes of the cephalometric landmarks of the chin region were measured at each period, and the changes at each cephalometric landmark were determined for the time gaps. Postoperative changes in the mandibular shape were analyzed to determine the stability of fixation methods. There was minimum difference in the relapse of the mandibular advancement among the three groups. Statistical analysis showed no significant difference in postoperative stability. However, a positive correlation between the amount of advancement and the amount of postoperative relapse was demonstrated by the linear multiple regression test (p < 0.05). It can be concluded that all techniques can be used to obtain stable postoperative results in mandibular advancement after 6 months.

Core-valence Correlation Effects On Ir Calculations: The Bf3 And Bcl3 Cases.

The first theoretical results of core-valence correlation effects are presented for the infrared wavenumbers and intensities of the BF3 and BCl3 molecules, using (double- and triple-zeta) Dunning core-valence basis sets at the CCSD(T) level. The results are compared with those calculated in the frozen core approximation with standard Dunning basis sets at the same correlation level and with the experimental values. The general conclusion is that the effect of core-valence correlation is, for infrared wavenumbers and intensities, smaller than the effect of adding augmented diffuse functions to the basis set, e.g., cc-pVTZ to aug-cc-pVTZ. Moreover, the trends observed in the data are mainly related to the augmented functions rather than the core-valence functions added to the basis set. The results obtained here confirm previous studies pointing out the large descrepancy between the theoretical and experimental intensities of the stretching mode for BCl3.

Measuring The Hydrodynamic Radius Of Quantum Dots By Fluorescence Correlation Spectroscopy.

Fluorescence Correlation Spectroscopy (FCS) is an optical technique that allows the measurement of the diffusion coefficient of molecules in a diluted sample. From the diffusion coefficient it is possible to calculate the hydrodynamic radius of the molecules. For colloidal quantum dots (QDs) the hydrodynamic radius is valuable information to study interactions with other molecules or other QDs. In this chapter we describe the main aspects of the technique and how to use it to calculate the hydrodynamic radius of quantum dots (QDs).

Correlation Between Cephalometric Data And Severity Of Sleep Apnea.

Obstructive sleep apnea syndrome has a high prevalence among adults. Cephalometric variables can be a valuable method for evaluating patients with this syndrome. To correlate cephalometric data with the apnea-hypopnea sleep index. We performed a retrospective and cross-sectional study that analyzed the cephalometric data of patients followed in the Sleep Disorders Outpatient Clinic of the Discipline of Otorhinolaryngology of a university hospital, from June 2007 to May 2012. Ninety-six patients were included, 45 men, and 51 women, with a mean age of 50.3 years. A total of 11 patients had snoring, 20 had mild apnea, 26 had moderate apnea, and 39 had severe apnea. The distance from the hyoid bone to the mandibular plane was the only variable that showed a statistically significant correlation with the apnea-hypopnea index. Cephalometric variables are useful tools for the understanding of obstructive sleep apnea syndrome. The distance from the hyoid bone to the mandibular plane showed a statistically significant correlation with the apnea-hypopnea index.

Histologic Correlation Of Expression Of Ki-67 In Squamous Cell Carcinoma Of The Glottis According To The Degree Of Cell Differentiation.

Squamous cell carcinoma is the most common neoplasm of the larynx and glottis, and its prognosis depends on the size of the lesion, level of local invasion, cervical lymphatic spread, and presence of distant metastases. Ki-67 (MKI67) is a protein present in the core, whose function is related to cell proliferation. To evaluate the expression of marker Ki-67 in squamous cell carcinoma of the larynx and glottis and its correlation to pathological findings. Experimental study with immunohistochemistry analysis of Ki-67, calculating the percentage of the cell proliferation index in glottic squamous cell carcinomas. Sixteen cases were analyzed, with six well-differentiated and 10 poorly/moderately differentiated tumors. There was a correlation between cell proliferation index and degree of cell differentiation, with higher proliferation in poorly/moderately differentiated tumors. The cell proliferation index, as measured by Ki-67, may be useful in the characterization of histological degree in glottic squamous cell tumors.