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TL;DR: A new quantity is developed, I 2, which the authors believe gives a better measure of the consistency between trials in a meta-analysis, which is susceptible to the number of trials included in the meta- analysis.
Abstract: Cochrane Reviews have recently started including the quantity I 2 to help readers assess the consistency of the results of studies in meta-analyses. What does this new quantity mean, and why is assessment of heterogeneity so important to clinical practice? Systematic reviews and meta-analyses can provide convincing and reliable evidence relevant to many aspects of medicine and health care.1 Their value is especially clear when the results of the studies they include show clinically important effects of similar magnitude. However, the conclusions are less clear when the included studies have differing results. In an attempt to establish whether studies are consistent, reports of meta-analyses commonly present a statistical test of heterogeneity. The test seeks to determine whether there are genuine differences underlying the results of the studies (heterogeneity), or whether the variation in findings is compatible with chance alone (homogeneity). However, the test is susceptible to the number of trials included in the meta-analysis. We have developed a new quantity, I 2, which we believe gives a better measure of the consistency between trials in a meta-analysis. Assessment of the consistency of effects across studies is an essential part of meta-analysis. Unless we know how consistent the results of studies are, we cannot determine the generalisability of the findings of the meta-analysis. Indeed, several hierarchical systems for grading evidence state that the results of studies must be consistent or homogeneous to obtain the highest grading.2–4 Tests for heterogeneity are commonly used to decide on methods for combining studies and for concluding consistency or inconsistency of findings.5 6 But what does the test achieve in practice, and how should the resulting P values be interpreted? A test for heterogeneity examines the null hypothesis that all studies are evaluating the same effect. The usual test statistic …
TL;DR: In this article, a new statistical procedure for testing a complete sample for normality is introduced, which is obtained by dividing the square of an appropriate linear combination of the sample order statistics by the usual symmetric estimate of variance.
Abstract: The main intent of this paper is to introduce a new statistical procedure for testing a complete sample for normality. The test statistic is obtained by dividing the square of an appropriate linear combination of the sample order statistics by the usual symmetric estimate of variance. This ratio is both scale and origin invariant and hence the statistic is appropriate for a test of the composite hypothesis of normality. Testing for distributional assumptions in general and for normality in particular has been a major area of continuing statistical research-both theoretically and practically. A possible cause of such sustained interest is that many statistical procedures have been derived based on particular distributional assumptions-especially that of normality. Although in many cases the techniques are more robust than the assumptions underlying them, still a knowledge that the underlying assumption is incorrect may temper the use and application of the methods. Moreover, the study of a body of data with the stimulus of a distributional test may encourage consideration of, for example, normalizing transformations and the use of alternate methods such as distribution-free techniques, as well as detection of gross peculiarities such as outliers or errors. The test procedure developed in this paper is defined and some of its analytical properties described in ? 2. Operational information and tables useful in employing the test are detailed in ? 3 (which may be read independently of the rest of the paper). Some examples are given in ? 4. Section 5 consists of an extract from an empirical sampling study of the comparison of the effectiveness of various alternative tests. Discussion and concluding remarks are given in ?6. 2. THE W TEST FOR NORMALITY (COMPLETE SAMPLES) 2 1. Motivation and early work This study was initiated, in part, in an attempt to summarize formally certain indications of probability plots. In particular, could one condense departures from statistical linearity of probability plots into one or a few 'degrees of freedom' in the manner of the application of analysis of variance in regression analysis? In a probability plot, one can consider the regression of the ordered observations on the expected values of the order statistics from a standardized version of the hypothesized distribution-the plot tending to be linear if the hypothesis is true. Hence a possible method of testing the distributional assumptionis by means of an analysis of variance type procedure. Using generalized least squares (the ordered variates are correlated) linear and higher-order
TL;DR: In this paper, an adjusted rank correlation test is proposed as a technique for identifying publication bias in a meta-analysis, and its operating characteristics are evaluated via simulations, and the test statistic is a direct statistical analogue of the popular funnel-graph.
Abstract: An adjusted rank correlation test is proposed as a technique for identifying publication bias in a meta-analysis, and its operating characteristics are evaluated via simulations. The test statistic is a direct statistical analogue of the popular "funnel-graph." The number of component studies in the meta-analysis, the nature of the selection mechanism, the range of variances of the effect size estimates, and the true underlying effect size are all observed to be influential in determining the power of the test. The test is fairly powerful for large meta-analyses with 75 component studies, but has only moderate power for meta-analyses with 25 component studies. However, in many of the configurations in which there is low power, there is also relatively little bias in the summary effect size estimate. Nonetheless, the test must be interpreted with caution in small meta-analyses. In particular, bias cannot be ruled out if the test is not significant. The proposed technique has potential utility as an exploratory tool for meta-analysts, as a formal procedure to complement the funnel-graph.
TL;DR: In this article, a unit root test for dynamic heterogeneous panels based on the mean of individual unit root statistics is proposed, which converges in probability to a standard normal variate sequentially with T (the time series dimension) →∞, followed by N (the cross sectional dimension)→∞.
TL;DR: In this article, the authors consider pooling cross-section time series data for testing the unit root hypothesis, and they show that the power of the panel-based unit root test is dramatically higher, compared to performing a separate unit-root test for each individual time series.
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