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"Hypothesis testing"
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E-VALUES
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper, we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors and likelihood ratios. We demonstrate that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e-values can be merged simply by averaging them. This allows us to develop efficient procedures using e-values for testing multiple hypotheses.
Journal Article
Sequential selection procedures and false discovery rate control
We consider a multiple‐hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,…,Hk of hypotheses. A rejection rule in this setting amounts to a procedure for choosing the stopping point k. This setting is inspired by the sequential nature of many model selection problems, where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter. We propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting. We also show how the methods can be applied to model selection by using recent results on p‐values in sequential model selection settings.
Journal Article
Basic and advanced statistical tests : writing results sections and creating tables and figures
\"This book focuses on extraction of pertinent information from statistical test outputs, in order to write result sections and/or accompanying tables and/or figures. Each chapter provides the name of a basic or advanced statistical test, a brief description, examples of when to use each, a sample scenario, and a sample results section write-up. Depending on the test and need, most chapters provide a table and/or figure to accompany the write-up.\"--Provided by publisher.
Book
Multiple hypothesis testing in experimental economics
The analysis of data from experiments in economics routinely involves testing multiple null hypotheses simultaneously. These different null hypotheses arise naturally in this setting for at least three different reasons: when there are multiple outcomes of interest and it is desired to determine on which of these outcomes a treatment has an effect; when the effect of a treatment may be heterogeneous in that it varies across subgroups defined by observed characteristics and it is desired to determine for which of these subgroups a treatment has an effect; and finally when there are multiple treatments of interest and it is desired to determine which treatments have an effect relative to either the control or relative to each of the other treatments. In this paper, we provide a bootstrap-based procedure for testing these null hypotheses simultaneously using experimental data in which simple random sampling is used to assign treatment status to units. Using the general results in Romano and Wolf (Ann Stat 38:598–633,
2010
), we show under weak assumptions that our procedure (1) asymptotically controls the familywise error rate—the probability of one or more false rejections—and (2) is asymptotically balanced in that the marginal probability of rejecting any true null hypothesis is approximately equal in large samples. Importantly, by incorporating information about dependence ignored in classical multiple testing procedures, such as the Bonferroni and Holm corrections, our procedure has much greater ability to detect truly false null hypotheses. In the presence of multiple treatments, we additionally show how to exploit logical restrictions across null hypotheses to further improve power. We illustrate our methodology by revisiting the study by Karlan and List (Am Econ Rev 97(5):1774–1793,
2007
) of why people give to charitable causes.
Journal Article
Accumulation Tests for FDR Control in Ordered Hypothesis Testing
Multiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses, with relatively few true signals. In this article, we consider the multiple testing problem where prior information is available (for instance, from an earlier study under different experimental conditions), that can allow us to test the hypotheses as a ranked list to increase the number of discoveries. Given an ordered list of n hypotheses, the aim is to select a data-dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate (FDR). Generalizing several existing methods, we develop a family of \"accumulation tests\" to choose a cutoff k that adapts to the amount of signal at the top of the ranked list. We introduce a new method in this family, the HingeExp method, which offers higher power to detect true signals compared to existing techniques. Our theoretical results prove that these methods control a modified FDR on finite samples, and characterize the power of the methods in the family. We apply the tests to simulated data, including a high-dimensional model selection problem for linear regression. We also compare accumulation tests to existing methods for multiple testing on a real data problem of identifying differential gene expression over a dosage gradient. Supplementary materials for this article are available online.
Journal Article
CONTROLLING THE FALSE DISCOVERY RATE VIA KNOCKOFFS
In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR)—the expected fraction of false discoveries among all discoveries—is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. This paper introduces the knockoff filter, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables. This method achieves exact FDR control in finite sample settings no matter the design or covariates, the number of variables in the model, or the amplitudes of the unknown regression coefficients, and does not require any knowledge of the noise level. As the name suggests, the method operates by manufacturing knockoff variables that are cheap—their construction does not require any new data—and are designed to mimic the correlation structure found within the existing variables, in a way that allows for accurate FDR control, beyond what is possible with permutation-based methods. The method of knockoffs is very general and flexible, and can work with a broad class of test statistics. We test the method in combination with statistics from the Lasso for sparse regression, and obtain empirical results showing that the resulting method has far more power than existing selection rules when the proportion of null variables is high.
Journal Article
Methods Matter
The credibility revolution in economics has promoted causal identification using randomized control trials (RCT), difference-in-differences (DID), instrumental variables (IV) and regression discontinuity design (RDD). Applying multiple approaches to over 21,000 hypothesis tests published in 25 leading economics journals, we find that the extent of p-hacking and publication bias varies greatly by method. IV (and to a lesser extent DID) are particularly problematic. We find no evidence that (i) papers published in the Top 5 journals are different to others; (ii) the journal “revise and resubmit” process mitigates the problem; (iii) things are improving through time.
Journal Article
Bayesian alternatives to null hypothesis significance testing in biomedical research: a non-technical introduction to Bayesian inference with JASP
Background
Although null hypothesis significance testing (NHST) is the agreed gold standard in medical decision making and the most widespread inferential framework used in medical research, it has several drawbacks. Bayesian methods can complement or even replace frequentist NHST, but these methods have been underutilised mainly due to a lack of easy-to-use software. JASP is an open-source software for common operating systems, which has recently been developed to make Bayesian inference more accessible to researchers, including the most common tests, an intuitive graphical user interface and publication-ready output plots. This article provides a non-technical introduction to Bayesian hypothesis testing in JASP by comparing traditional tests and statistical methods with their Bayesian counterparts.
Results
The comparison shows the strengths and limitations of JASP for frequentist NHST and Bayesian inference. Specifically, Bayesian hypothesis testing via Bayes factors can complement and even replace NHST in most situations in JASP. While
p
-values can only reject the null hypothesis, the Bayes factor can state evidence for both the null and the alternative hypothesis, making confirmation of hypotheses possible. Also, effect sizes can be precisely estimated in the Bayesian paradigm via JASP.
Conclusions
Bayesian inference has not been widely used by now due to the dearth of accessible software. Medical decision making can be complemented by Bayesian hypothesis testing in JASP, providing richer information than single
p
-values and thus strengthening the credibility of an analysis. Through an easy point-and-click interface researchers used to other graphical statistical packages like SPSS can seemlessly transition to JASP and benefit from the listed advantages with only few limitations.
Journal Article