Correlation ratio
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Correlation Coefficients: Appropriate Use and Interpretation Open
Correlation in the broadest sense is a measure of an association between variables. In correlated data, the change in the magnitude of 1 variable is associated with a change in the magnitude of another variable, either in the same (positiv…
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On relationships between the Pearson and the distance correlation coefficients Open
In this paper we show that for any fixed Pearson correlation coefficient strictly between −1 and 1, the distance correlation coefficient can take any value in the open unit interval (0,1).
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Sample Size Guideline for Correlation Analysis Open
Correlation analysis is a common statistical analysis in various fields. The aim is usually to determine to what extent two numerical variables are correlated with each other. One of the issues that are important to be considered before co…
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Dependent Evidence Combination Based on Shearman Coefficient and Pearson Coefficient Open
Dempster-Shafer evidence theory is efficient to deal with uncertain information. One assumption of evidence theory is that the source of information should be independent when combined by Dempster's rule for evidence combination. However, …
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Biostatistics series module 6: Correlation and linear regression Open
Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this…
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Conducting correlation analysis: important limitations and pitfalls Open
The correlation coefficient is a statistical measure often used in studies to show an association between variables or to look at the agreement between two methods. In this paper, we will discuss not only the basics of the correlation coef…
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Comparison of Objective Image Quality Metrics to Expert Radiologists’ Scoring of Diagnostic Quality of MR Images Open
Image quality metrics (IQMs) such as root mean square error (RMSE) and structural similarity index (SSIM) are commonly used in the evaluation and optimization of accelerated magnetic resonance imaging (MRI) acquisition and reconstruction s…
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An adjusted coefficient of determination (<i>R</i><sup>2</sup>) for generalized linear mixed models in one go Open
The coefficient of determination ( R 2 ) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or …
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Correlation Coefficients for a Study with Repeated Measures Open
Repeated measures are increasingly collected in a study to investigate the trajectory of measures over time. One of the first research questions is to determine the correlation between two measures. The following five methods for correlati…
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Review of sample size determination methods for the intraclass correlation coefficient in the one-way analysis of variance model Open
Reliability of measurement instruments providing quantitative outcomes is usually assessed by an intraclass correlation coefficient. When participants are repeatedly measured by a single rater or device, or, are each rated by a different g…
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A new correlation coefficient between categorical, ordinal and interval variables with Pearson characteristics Open
A prescription is presented for a new and practical correlation coefficient, $ϕ_K$, based on several refinements to Pearson's hypothesis test of independence of two variables. The combined features of $ϕ_K$ form an advantage over existing …
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Some effects of non-normal distribution shape on the magnitude of the Pearson Moment Correlation Coefficient Open
All correlational statistics must be interpreted with consideration given to certain constraints. The use of the Pearson product moment correlation coefficient as a descriptive measure of relationship necessitates the assumption that the c…
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Using Pratt's Importance Measures in Confirmatory Factor Analyses Open
When running a confirmatory factor analysis (CFA), users specify and interpret the pattern (loading) matrix. It has been recommended that the structure coefficients, indicating the factors’ correlation with the observed indicators, should …
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Comparison of Pearson’s and Spearman’s correlation coefficients for selected traits of <i>Pinus sylvestris</i> L. Open
The Spearman rank correlation coefficient is a non-parametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of the relationship between two variables. It is a measure of a monotonic relationsh…
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Nonparametric statistics. Part 3. Correlation coefficients Open
A measure of correlation or strength of association between random variables is the correlation coefficient. In scientific research, correlation analysis is most often carried out using various correlation coefficients without explaining w…
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Different Coefficients for Studying Dependence Open
Through computer simulations, we research several different measures of dependence, including Pearson’s and Spearman’s correlation coefficients, the maximal correlation, the distance correlation, a function of the mutual information called…
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ERRORS IN THE USE OF CORRELATION AND DETERMINATION COEFFICIENTS Open
Coefficients of correlation and determination are widely used in statistical analysis of data. Some of the errors attributed to their use are considered in this article. We confine ourselves to the case of two variables. The linear Pearson…
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Statistical correlation coefficients for single-valued neutrosophic sets and their applications in medical diagnosis Open
The concept of single-valued neutrosophic sets (SVNSs) is considered as an attractive tool for dealing with highly ambiguous and uncertain information. The correlation coefficient of SVNSs acts as an important measure in the single-valued…
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No-Reference Image Quality Assessment of Magnetic Resonance images with multi-level and multi-model representations based on fusion of deep architectures Open
Accurate quality assessment of Magnetic Resonance (MR) images is essential for effective medical diagnostics, as it impacts the time spent on image acquisition and image interpretation by radiologists. Therefore, this study aims to provide…
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Kendall correlation coefficient. Open
In the present paper, we first discuss the Kendall rank correlation coefficient. In continuous case, we define the Kendall rank correlation coefficient in terms of the concomitants of order statistics, find the expected value of the Kendal…
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A correlation coefficient of belief functions Open
How to manage conflict is still an open issue in Dempster-Shafer evidence theory. The correlation coefficient can be used to measure the similarity of evidence in Dempster-Shafer evidence theory. However, existing correlation coefficients …
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Comparison of Pearson’s and Spearman’s Correlation Coefficients Values for Selected Traits of <em>Pinus sylvestri</em>s L. Open
The Spearman rank correlation coefficient is a non-parametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of the relationship between two variables. It is a measure of a monotonic relationsh…
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Robust Estimators for the Correlation Measure to Resist Outliers in Data Open
The objective of this research was to propose a composite correlation coefficient to estimate the rank correlation coefficient of two variables. A simulation study was conducted using 228 situations for a bivariate normal distribution to c…
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The basics of determining the coefficients of a linear correlation Open
The aim of the paper is to present the basic measures related to the analysis of relationships between quantitative variables used in econometric modelling and their selected applications. The following measures are discussed: the Pearson …
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Modified Signed Log-Likelihood Ratio Test for Comparing the Correlation Coefficients of Two Independent Bivariate Normal Distributions Open
Modified Signed Log-Likelihood Ratio Test for Comparing the Correlation Coefficients of Two Independent Bivariate Normal Distributions
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The Performance of Different Correlation Coefficient under Contaminated Bivariate Data Open
Bivariate data consists of 2 random variables that are obtained from the same population.The relationship between 2 bivariate data can be measured by correlation coefficient.A correlation coefficient computed from the sample data is used t…
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A Multi-Way Correlation Coefficient Open
Pearson's correlation is an important summary measure of the amount of dependence between two variables. It is natural to want to generalise the concept of correlation as a single number that measures the inter-relatedness of three or more…
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Improved procedures and computer programs for equivalence assessment of correlation coefficients Open
The correlation coefficient is the most commonly used measure for summarizing the magnitude and direction of linear relationship between two response variables. Considerable literature has been devoted to the inference procedures for signi…
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The Intraclass Correlation Coefficient as a Measure of Educational Inequality: An Empirical Study with Data from PISA 2018 Open
In this study we utilized data from the Programme for International Student Assessment (PISA) to investigate differences in schools’ average mathematics scores by treating intraclass correlation coefficient (ICC) as a measure of educationa…
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Hybrid Correlation Coefficient of Spearman with MM-Estimator Open
The Spearman rho nonparametric correlation coefficient is widely used to measure the strength and degree of association between two variables.However, outliers in the data can skew the results, leading to inaccurate results as the Spearman…