Asymptotics of the two-stage spatial sign correlation

Acknowledgments This research was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. The authors wish to thank the editors and referees for their careful handling of the manuscript. They further acknowledge the anonymous referees of the article Spatial sign correlation (J. Multivariate Anal. 135, pages 89–105, 2015), who independently of each other suggested to further explore the properties of two-stage spatial sign correlation.Non peer reviewedPreprin

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta-analysis and group level studies

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log-odds and arcsine transformations of the estimated probability inline image, both for single-group studies and in combining results from several groups or studies in meta-analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta-analysis and result in abysmal coverage of the combined effect for large K. We also propose bias-correction for the arcsine transformation. Our simulations demonstrate that this bias-correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta-analyses of prevalence

Conducting Meta-Analyses in R with the metafor Package

The metafor package provides functions for conducting meta-analyses in R. The package includes functions for fitting the meta-analytic fixed- and random-effects models and allows for the inclusion of moderators variables (study-level covariates) in these models. Meta-regression analyses with continuous and categorical moderators can be conducted in this way. Functions for the Mantel-Haenszel and Peto's one-step method for meta-analyses of 2 x 2 table data are also available. Finally, the package provides various plot functions (for example, for forest, funnel, and radial plots) and functions for assessing the model fit, for obtaining case diagnostics, and for tests of publication bias

Impact of the spotted microarray preprocessing method on fold-change compression and variance stability

<p>Abstract</p> <p>Background</p> <p>The standard approach for preprocessing spotted microarray data is to subtract the local background intensity from the spot foreground intensity, to perform a log2 transformation and to normalize the data with a global median or a lowess normalization. Although well motivated, standard approaches for background correction and for transformation have been widely criticized because they produce high variance at low intensities. Whereas various alternatives to the standard background correction methods and to log2 transformation were proposed, impacts of both successive preprocessing steps were not compared in an objective way.</p> <p>Results</p> <p>In this study, we assessed the impact of eight preprocessing methods combining four background correction methods and two transformations (the log2 and the glog), by using data from the MAQC study. The current results indicate that most preprocessing methods produce fold-change compression at low intensities. Fold-change compression was minimized using the Standard and the Edwards background correction methods coupled with a log2 transformation. The drawback of both methods is a high variance at low intensities which consequently produced poor estimations of the p-values. On the other hand, effective stabilization of the variance as well as better estimations of the p-values were observed after the glog transformation.</p> <p>Conclusion</p> <p>As both fold-change magnitudes and p-values are important in the context of microarray class comparison studies, we therefore recommend to combine the Edwards correction with a hybrid transformation method that uses the log2 transformation to estimate fold-change magnitudes and the glog transformation to estimate p-values.</p

Approximations to non-central distributions and their applications

In testing hypotheses involving noncentral distributions percentage points are not always readily available and, if they are available, are not very well tabulated except, perhaps, for smaller degrees of freedom and noncentralities. Consequently,· for values that are not tabulated, interpolation, or, more likely, extrapolation of some kind is necessary, and the process can become tedious. In the case of calculations involving the power of the test, charts of the power of the F-test and t-test are available, but readings taken from these charts may be accurate to only one decimal place. In situations like the above, and in other cases, approximations are very useful and are sometimes as accurate, if not more so, than values obtained by interpolation (or extrapolation) or values read from charts. This thesis is chiefly concerned with applications in which approximations to the noncentral x2 , F, t and R distributions can be used. The approximations themselves, in most cases, are dealt with in a fair amount of detail to show the reader how they were obtained. Chapter 1 defines certain terms with which the reader may be unfamiliar, which are used in subsequent chapters. Chapters 2-5 deal with the approximations and their applications.· Each of these chapters is set out in the same way, section I am defining the noncentral distribution, section II dealing with the approximations, section III comparing the accuracy of the approximations with the exact values and section IV showing in which situations the approximations can be used

On a Proper Meta-Analytic Model for Correlations

Combining statistical information across studies is a standard research tool in applied psychology. The most common approach in applied psychology is the fixed effects model. The fixed-effects approach assumes that individual study characteristics such as treatment conditions, study context, or individual differences do not influence study effect sizes. That is, that the majority of the differences between the effect sizes of different studies can be explained by sampling error alone. We critique the fixed-effects methodology for correlations and propose an advancement, the random-effects model, that ameliorates problems imposed by fixed-effects models. The random-effects approach explicitly incorporates between-study differences in data analysis and provides estimates of how those study characteristics influence the relationships among constructs of interest. Because they can model the influence of study characteristics, we assert that random-effects models have advantages for psychological research. Parameter estimates of both models are compared and evidence in favor of the random-effects approach is presented

Mapping aerial metal deposition in metropolitan areas from tree bark : a case study in Sheffield, England

We investigated the use of metals accumulated on tree bark for mapping their deposition across metropolitan Sheffield by sampling 642 trees of three common species. Mean concentrations of metals were generally an order of magnitude greater than in samples from a remote uncontaminated site. We found trivially small differences among tree species with respect to metal concentrations on bark, and in subsequent statistical analyses did not discriminate between them. We mapped the concentrations of As, Cd and Ni by lognormal universal kriging using parameters estimated by residual maximum likelihood ({\sc reml}). The concentrations of Ni and Cd were greatest close to a large steel works, their probable source, and declined markedly within 500~metres of it and from there more gradually over several kilometres. Arsenic was much more evenly distributed, probably as a result of locally mined coal burned in domestic fires for many years. Tree bark seems to integrate airborne pollution over time, and our findings show that sampling and analysing it are cost-effective means of mapping and identifying sources

A Simple Statistic for Comparing Moderation of Slopes and Correlations

Given a linear relationship between two continuous random variables X and Y that may be moderated by a third, Z, the extent to which the correlation ρ is (un)moderated by Z is equivalent to the extent to which the regression coefficients β(y) and β(x) are (un)moderated by Z iff the variance ratio [Formula: see text] is constant over the range or states of Z. Otherwise, moderation of slopes and of correlations must diverge. Most of the literature on this issue focuses on tests for heterogeneity of variance in Y, and a test for this ratio has not been investigated. Given that regression coefficients are proportional to ρ via this ratio, accurate tests, and estimations of it would have several uses. This paper presents such a test for both a discrete and continuous moderator and evaluates its Type I error rate and power under unequal sample sizes and departures from normality. It also provides a unified approach to modeling moderated slopes and correlations with categorical moderators via structural equations models