Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis

A robust and fast two-sample test of equal correlations with an application to differential co-expression

A robust and fast two-sample test for equal Pearson correlation coefficients (PCCs) is important in solving many biological problems, including, for example, analysis of differential co-expression. However, few existing methods for this test can achieve robustness against deviation from normal distributions, accuracy under small sample sizes, and computational efficiency simultaneously. Here, we propose a new method for testing differential correlation using a saddlepoint approximation of the residual bootstrap (DICOSAR). To achieve robustness, accuracy, and efficiency, DICOSAR combines the ideas underlying the pooled residual bootstrap, the signed root of a likelihood ratio statistic, and a multivariate saddlepoint approximation. Through a comprehensive simulation study and a real data analysis of gene co-expression, we demonstrate that DICOSAR is accurate and robust in controlling the type I error rate for detecting differential correlation and provides a faster alternative to the bootstrap and permutation methods. We further show that DICOSAR can also be used for testing differential correlation matrices. These results suggest that DICOSAR provides an analytical approach to facilitate rapid testing for the equality of PCCs in large-scale analysis.

Metrics of color-difference formula improvement

Metrics of color-difference formula improvement (i.e., standardized residual sum of squares and Pearson product moment correlation) are shown to convey the same information. Furthermore, each metric has two computational forms that assume different linear data models, specifically, with or without an ordinate intercept. It is essential to choose a computational form that matches the data model. We recommend explicitly declaring whether or not the data have been centered, i.e., by subtracting the mean value from each datum, to match the intercept-free data model. Statistical testing of the metrics assumes independent, normally distributed randomness of residuals from the data model, and homogeneous variance. Procedures consistent with these assumptions include robust statistical tests, homogenizing data transformations, and meta-analysis.

Human Mitochondrial DNA: Particularities and Diseases

Mitochondria are the cell’s power site, transforming energy into a form that the cell can employ for necessary metabolic reactions. These organelles present their own DNA. Although it codes for a small number of genes, mutations in mtDNA are common. Molecular genetics diagnosis allows the analysis of DNA in several areas such as infectiology, oncology, human genetics and personalized medicine. Knowing that the mitochondrial DNA is subject to several mutations which have a direct impact on the metabolism of the mitochondrion leading to many diseases, it is therefore necessary to detect these mutations in the patients involved. To date numerous mitochondrial mutations have been described in humans, permitting confirmation of clinical diagnosis, in addition to a better management of the patients. Therefore, different techniques are employed to study the presence or absence of mitochondrial mutations. However, new mutations are discovered, and to determine if they are the cause of disease, different functional mitochondrial studies are undertaken using transmitochondrial cybrid cells that are constructed by fusion of platelets of the patient that presents the mutation, with rho osteosarcoma cell line. Moreover, the contribution of next generation sequencing allows sequencing of the entire human genome within a single day and should be considered in the diagnosis of mitochondrial mutations.

Informal versus formal judgment of statistical models: The case of normality assumptions

Researchers sometimes use informal judgment for statistical model diagnostics and assumption checking. Informal judgment might seem more desirable than formal judgment because of a paradox: Formal hypothesis tests of assumptions appear to become less useful as sample size increases. We suggest that this paradox can be resolved by evaluating both formal and informal statistical judgment via a simplified signal detection framework. In 4 studies, we used this approach to compare informal judgments of normality diagnostic graphs (histograms, Q-Q plots, and P-P plots) to the performance of several formal tests (Shapiro-Wilk test, Kolmogorov-Smirnov test, etc.). Participants judged whether or not graphs of sample data came from a normal population (Experiments 1-2) or whether or not from a population close enough to normal for a parametric test to be more powerful than a nonparametric one (Experiments 3-4). Across all experiments, participants' informal judgments showed lower discriminability than did formal hypothesis tests. This pattern occurred even after participants were given 400 training trials with feedback, a financial incentive, and ecologically valid distribution shapes. The discriminability advantage of formal normality tests led to slightly more powerful follow-up tests (parametric vs. nonparametric). Overall, the framework used here suggests that formal model diagnostics may be more desirable than informal ones.