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An introduction to new robust linear and monotonic correlation coefficients
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.
Journal Article
Intraclass correlation – A discussion and demonstration of basic features
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.
Journal Article
Integration of theory and practice in CLIL
Content and Language Integrated Learning (CLIL) has now become a feature of education in Europe from primary school to university level. CLIL programmes are intended to integrate language and content learning in a process of mutual enrichment. Yet there is little consensus as to how this is to be achieved, or how the outcomes of such programmes should be measured. It is evident that a further type of integration is required: that of bringing the practice of CLIL into closer contact with the theory. In this, it is necessary to establish the role played by other fundamental aspects of the learning process, including learner and teacher perspectives, learning strategies, task design and general pedagogical approaches. The first part of this book provides a variety of theoretical approaches to the question of what integration means in CLIL, addressing key skills and competences that are taught and learned in CLIL classrooms, and exploring the role of content and language teachers in achieving an integrated syllabus. The second part takes specific cases and experimental studies conducted at different educational levels and analyses them in the light of theoretical considerations.
Book
The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation
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.
Journal Article
Reading reconsidered : a practical guide to rigorous literacy instruction
\"This book takes you into the trenches with actionable guidance from real-life educators and instructional champions. The authors address the anxiety-inducing world of Common Core State Standards, distilling from those standards four key ideas that help hone teaching practices both generally and in preparation for assessments. This \"Core of the Core\" shows how to teach students to: read harder texts, closely read texts rigorously and intentionally, read nonfiction more effectively, and write more effectively in direct response to texts\"-- Provided by publisher.
Book
Points of Significance: Association, correlation and causation
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.
Journal Article
Correction: Spatio-Temporal Environmental Correlation and Population Variability in Simple Metacommunities
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.
Journal Article