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Background The most common measure of association between two continuous variables is the Pearson correlation (Maronna et al. in Safari an OMC. Robust statistics, 2019. https://login.proxy.bib.uottawa.ca/login?url=https://learning.oreilly.com/library/view/-/9781119214687/?ar&orpq&email=^u). When outliers are present, Pearson does not accurately measure association and robust measures are needed. This article introduces three new robust measures of correlation: Taba (T), TabWil (TW), and TabWil rank (TWR). The correlation estimators T and TW measure a linear association between two continuous or ordinal variables; whereas TWR measures a monotonic association. The robustness of these proposed measures in comparison with Pearson (P), Spearman (S), Quadrant (Q), Median (M), and Minimum Covariance Determinant (MCD) are examined through simulation. Taba distance is used to analyze genes, and statistical tests were used to identify those genes most significantly associated with Williams Syndrome (WS). Results Based on the root mean square error (RMSE) and bias, the three proposed correlation measures are highly competitive when compared to classical measures such as P and S as well as robust measures such as Q, M, and MCD. Our findings indicate TBL2 was the most significant gene among patients diagnosed with WS and had the most significant reduction in gene expression level when compared with control ( P value = 6.37E-05). Conclusions Overall, when the distribution is bivariate Log-Normal or bivariate Weibull, TWR performs best in terms of bias and T performs best with respect to RMSE. Under the Normal distribution, MCD performs well with respect to bias and RMSE; but TW, TWR, T, S, and P correlations were in close proximity. The identification of TBL2 may serve as a diagnostic tool for WS patients. A Taba R package has been developed and is available for use to perform all necessary computations for the proposed methods.

A re-analysis of intraclass correlation (ICC) theory is presented together with Monte Carlo simulations of ICC probability distributions. A partly revised and simplified theory of the single-score ICC is obtained, together with an alternative and simple recipe for its use in reliability studies. Our main, practical conclusion is that in the analysis of a reliability study it is neither necessary nor convenient to start from an initial choice of a specified statistical model. Rather, one may impartially use all three single-score ICC formulas. A near equality of the three ICC values indicates the absence of bias (systematic error), in which case the classical (one-way random) ICC may be used. A consistency ICC larger than absolute agreement ICC indicates the presence of non-negligible bias; if so, classical ICC is invalid and misleading. An F-test may be used to confirm whether biases are present. From the resulting model (without or with bias) variances and confidence intervals may then be calculated. In presence of bias, both absolute agreement ICC and consistency ICC should be reported, since they give different and complementary information about the reliability of the method. A clinical example with data from the literature is given.

Background To evaluate binary classifications and their confusion matrices, scientific researchers can employ several statistical rates, accordingly to the goal of the experiment they are investigating. Despite being a crucial issue in machine learning, no widespread consensus has been reached on a unified elective chosen measure yet. Accuracy and F 1 score computed on confusion matrices have been (and still are) among the most popular adopted metrics in binary classification tasks. However, these statistical measures can dangerously show overoptimistic inflated results, especially on imbalanced datasets. Results The Matthews correlation coefficient (MCC), instead, is a more reliable statistical rate which produces a high score only if the prediction obtained good results in all of the four confusion matrix categories (true positives, false negatives, true negatives, and false positives), proportionally both to the size of positive elements and the size of negative elements in the dataset. Conclusions In this article, we show how MCC produces a more informative and truthful score in evaluating binary classifications than accuracy and F 1 score, by first explaining the mathematical properties, and then the asset of MCC in six synthetic use cases and in a real genomics scenario. We believe that the Matthews correlation coefficient should be preferred to accuracy and F 1 score in evaluating binary classification tasks by all scientific communities.

Correlation implies association, but not causation. Conversely, causation implies association, but not correlation. Most studies include multiple response variables, and the dependencies among them are often of great interest. For example, we may wish to know whether the levels of mRNA and the matching protein vary together in a tissue, or whether increasing levels of one metabolite are associated with changed levels of another. This month we begin a series of columns about relationships between variables (or features of a system), beginning with how pairwise dependencies can be characterized using correlation.

In equation (1a) in function f(), the subscript for the first term within the brackets should be 1k,t, not ik,t. Please view the correct equation here: A general requirement for the stability of this equilibrium is thatd/e > a(R0 – K)/(R0 + K)\" Citation: Ruokolainen L (2013) Correction: Spatio-Temporal Environmental Correlation and Population Variability in Simple Metacommunities.

Nitrogen dioxide (NO2) is one of the main air quality pollutants of concern in many urban and industrial areas worldwide, and particularly in the European region, where in 2017 almost 20 countries exceeded the NO2 annual limit values imposed by the European Commission Directive 2008/50/EC (EEA, 2019). NO2 pollution monitoring and regulation is a necessary task to help decision makers to search for a sustainable solution for environmental quality and population health status improvement. In this study, we propose a comparative analysis of the tropospheric NO2 column spatial configuration over Europe between similar periods in 2019 and 2020, based on the ESA Copernicus Sentinel-5P products. The results highlight the NO2 pollution dynamics over the abrupt transition from a normal condition situation to the COVID-19 outbreak context, characterized by a short-time decrease of traffic intensities and industrial activities, revealing remarkable tropospheric NO2 column number density decreases even of 85% in some of the European big cities. The validation approach of the satellite-derived data, based on a cross-correlation analysis with independent data from ground-based observations, provided encouraging values of the correlation coefficients (R2), ranging between 0.5 and 0.75 in different locations. The remarkable decrease of NO2 pollution over Europe during the COVID-19 lockdown is highlighted by S-5P products and confirmed by the Industrial Production Index and air traffic volumes.

A large space still exists for improving the measurements used in orthopaedics and sports medicine, especially as we face rapid technological progress in devices used for diagnostic or patient monitoring purposes. For a specific measure to be valuable and applicable in clinical practice, its reliability must be established. Reliability refers to the extent to which measurements can be replicated, and three types of reliability can be distinguished: inter-rater, intra-rater, and test–retest. The present article aims to provide insights into reliability as one of the most important and relevant properties of measurement tools. It covers essential knowledge about the methods used in orthopaedics and sports medicine for reliability studies. From design to interpretation, this article guides readers through the reliability study process. It addresses crucial issues such as the number of raters needed, sample size calculation, and breaks between particular trials. Different statistical methods and tests are presented for determining reliability depending on the type of gathered data, with particular attention to the commonly used intraclass correlation coefficient.

To examine whether patients' trust in the health care professional is associated with health outcomes. We searched 4 major electronic databases for studies that reported quantitative data on the association between trust in the health care professional and health outcome. We screened the full-texts of 400 publications and included 47 studies in our meta-analysis. We conducted random effects meta-analyses and meta-regressions and calculated correlation coefficients with corresponding 95% confidence intervals. Two interdependent researchers assessed the quality of the included studies using the Strengthening the Reporting of Observational Studies in Epidemiology guidelines. Overall, we found a small to moderate correlation between trust and health outcomes (r = 0.24, 95% CI: 0.19-0.29). Subgroup analyses revealed a moderate correlation between trust and self-rated subjective health outcomes (r = 0.30, 0.24-0.35). Correlations between trust and objective (r = -0.02, -0.08-0.03) as well as observer-rated outcomes (r = 0.10, -0.16-0.36) were non-significant. Exploratory analyses showed a large correlation between trust and patient satisfaction and somewhat smaller correlations with health behaviours, quality of life and symptom severity. Heterogeneity was small to moderate across the analyses. From a clinical perspective, patients reported more beneficial health behaviours, less symptoms and higher quality of life and to be more satisfied with treatment when they had higher trust in their health care professional. There was evidence for upward bias in the summarized results. Prospective studies are required to deepen our understanding of the complex interplay between trust and health outcomes.

Several studies have been conducted on droughts, precipitation, and temperature, whereas none have addressed the underlying relationship between nonlinear dynamic properties and patterns of two main hydrological parameters, precipitation and temperature, and meteorological and hydrological droughts. Monthly datasets of Midlands in the UK between 1921 and 2019 were collected for analysis. Subsequent to apply a multifractal approach to attain the nonlinear features of the datasets, the relationship between two hydrological parameters and droughts was investigated through the cross-correlation technique. A similar process was performed to analyze the relationship between multifractal strength variations in time series of precipitation and temperature and droughts. The nonlinear dynamic results indicated that droughts (meteorological and hydrological) were substantially affected by precipitation than temperature. In other words, droughts were more sensitive to precipitation fluctuations than temperature fluctuations. Concerning temperature, meteorological, and hydrological droughts were dependent on the minimum and maximum temperatures (Tmin and Tmax), respectively. The correlation between precipitation and meteorological drought was more long-range persistence than precipitation and hydrological drought. Besides, the correlation between Tmax and droughts was more long-range persistence than Tmin and droughts. Analysis of nonlinear dynamic patterns proved that the multifractal strength of meteorological drought depended on the multifractal strength of precipitation and Tmax, whereas the multifractal strength of hydrological drought depended on the multifractal strength of the Tmin. The correlation between precipitation and drought indices exhibited more multifractal strength than temperature and drought indices. Finally, the pivotal role of maximum temperature on drought events was quite alerting due to global warming intensification.

We utilize train tremors as P‐wave seismic sources to investigate velocity‐strain sensitivity near the San Jacinto Fault Zone. A dense nodal array deployed at the Piñon Flat Observatory is used to detect and identify repeating train energy emitted from a railway in the Coachella valley. We construct P‐wave correlation functions across the fault zone and estimate the spatially averaged dt/t versus strain sensitivity to be 6.25 × 104. Through numerical simulations, we explore how the sensitivity decays exponentially with depth. The optimal solution reveals a subsurface sensitivity of 1.2 × 105 and a depth decay rate of 0.05 km−1. This sensitivity aligns with previous findings but is toward the higher end, likely due to the fractured fault‐zone rocks. The depth decay rate, previously unreported, is notably smaller than assumed in empirical models. This raises the necessity of further investigations of this parameter, which is crucial to study stress and velocity variations at seismogenic depth. Plain Language Summary The speed at which seismic waves travel can be affected by Earth's tidal strains. Understanding this relationship is beneficial for studying tectonic strain accumulation and earthquake nucleation. When freight trains run, they produce powerful seismic energy that can be detected tens of kilometers away. We use these signals to measure how solid Earth tides affect seismic wave speed. Our study focusing on the San Jacinto Fault Zone in southern California reveals that the velocity‐strain sensitivity is consistent, albeit at the higher end of previously reported values measured in other regions. Additionally, our numerical simulations examine how this sensitivity varies with depth. We find that the rate at which sensitivity decreases with depth is smaller than what is typically assumed. Key Points Stable P‐wave correlation functions are constructed from selected train tremors The covariance between tidal strain and P‐wave travel‐time is used to estimate the velocity‐strain sensitivity Full‐waveform simulations of correlation functions are performed to constrain the depth dependence of the velocity‐strain sensitivity