Hypothesis Testing Procedures Research Articles

Statistical fractal analysis in testing the Hypotheses with imprecise data

A new statistical hypothesis testing procedure using fractal analysis, incorporating the concept of lacunarity for interval population parameters when the sample data are real intervals, is introduced. The decision rules for accepting or rejecting the null and alternative hypotheses are provided, along with testing procedures and numerical examples. Additionally, the proposed tests are extended to statistical hypotheses involving fuzzy data samples with lacunarity.

Modeling the output from a commercial chemical process using regression models from survival analysis

This article is concerned with the modeling of the gas output of a commercial chemical plant using the coal sources as predictor variables. We consider the use of two models to incorporate these predictors; the Cox proportional hazards and accelerated failure time regression models. These models are chosen for their simplicity and for the ease with which the effects of explanatory variables can be interpreted. The contribution of this article lies therein that these models are used in the current context for the first time. We show, using both graphical and formal hypothesis testing procedures that these models (with a Weibull baseline distribution) fit observed gas production data well. We provide a discussion of the interpretation of the estimated model parameters and we comment on how these estimates can be of substantial practical value. The large scale of production from the chemical plant in question ensures that potential cost savings and increases in production associated with more accurate models are of great practical importance.

A Bayesian flexible model for testing Granger causality

A new Bayesian hypothesis testing procedure for evaluating the Granger causality between two or more time series is proposed. The test is based on a flexible model for the joint evolution of multiple series, where a latent binary matrix indicates whether there is a Granger-causal relationship between such time series. The model is specified through a dependent Geometric stick-breaking process that generalizes the standard parametric Gaussian vector autoregression model, whereas the prior distribution of the latent matrix ensures a multiple testing correction. A Monte Carlo simulation study is provided for comparing the robustness of the proposed hypothesis test with state-of-the-art alternatives. The results show that this proposal performs better than competing approaches. Finally, the new test is applied to real economic data.

The impact of heterogeneity on the analysis of platform trials with normally distributed outcomes

BackgroundA platform trial approach allows adding arms to on-going trials to speed up intervention discovery programs. A control arm remains open for recruitment in a platform trial while intervention arms may be added after the onset of the study and could be terminated early for efficacy and/or futility when early stopping is allowed. The topic of utilising non-concurrent control data in the analysis of platform trials has been explored and discussed extensively. A less familiar issue is the presence of heterogeneity, which may exist for example due to modification of enrolment criteria and recruitment strategy.MethodWe conduct a simulation study to explore the impact of heterogeneity on the analysis of a two-stage platform trial design. We consider heterogeneity in treatment effects and heteroscedasticity in outcome data across stages for a normally distributed endpoint. We examine the performance of some hypothesis testing procedures and modelling strategies. The use of non-concurrent control data is also considered accordingly. Alongside standard regression analysis, we examine the performance of a novel method that was known as the pairwise trials analysis. It is similar to a network meta-analysis approach but adjusts for treatment comparisons instead of individual studies using fixed effects.ResultsSeveral testing strategies with concurrent control data seem to control the type I error rate at the required level when there is heteroscedasticity in outcome data across stages and/or a random cohort effect. The main parameter of treatment effects in some analysis models correspond to overall treatment effects weighted by stage wise sample sizes; while others correspond to the effect observed within a single stage. The characteristics of the estimates are not affected significantly by the presence of a random cohort effect and/ or heteroscedasticity.ConclusionIn view of heterogeneity in treatment effect across stages, the specification of null hypotheses in platform trials may need to be more subtle. We suggest employing testing procedure of adaptive design as opposed to testing the statistics from regression models; comparing the estimates from the pairwise trials analysis method and the regression model with interaction terms may indicate if heterogeneity is negligible.

Hypothesis testing and sample size considerations for the test-negative design

The test-negative design (TND) is an observational study design to evaluate vaccine effectiveness (VE) that enrolls individuals receiving diagnostic testing for a target disease as part of routine care. VE is estimated as one minus the adjusted odds ratio of testing positive versus negative comparing vaccinated and unvaccinated patients. Although the TND is related to case–control studies, it is distinct in that the ratio of test-positive cases to test-negative controls is not typically pre-specified. For both types of studies, sparse cells are common when vaccines are highly effective. We consider the implications of these features on power for the TND. We use simulation studies to explore three hypothesis-testing procedures and associated sample size calculations for case–control and TND studies. These tests, all based on a simple logistic regression model, are a standard Wald test, a continuity-corrected Wald test, and a score test. The Wald test performs poorly in both case–control and TND when VE is high because the number of vaccinated test-positive cases can be low or zero. Continuity corrections help to stabilize the variance but induce bias. We observe superior performance with the score test as the variance is pooled under the null hypothesis of no group differences. We recommend using a score-based approach to design and analyze both case–control and TND. We propose a modification to the TND score sample size to account for additional variability in the ratio of controls over cases. This work enhances our understanding of the data generating mechanism in a test-negative design (TND) and how it is distinct from that of a case-control study due to its passive recruitment of controls.

Multiple testing of interval composite null hypotheses using randomized p-values

Equivalence tests are statistical hypothesis testing procedures that aim to establish practical equivalence rather than the usual statistical significant difference. These testing procedures are frequent in “bioequivalence studies," where one would wish to show that, for example, an existing drug and a new one under development have comparable therapeutic effects. In this article, we propose a two-stage randomized (RAND2) p-value that depends on a uniformly most powerful (UMP) p-value and an arbitrary tuning parameter c∈[0,1]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c\\in [0,1]$$\\end{document} for testing an interval composite null hypothesis. We investigate the behavior of the distribution function of the two p-values under the null hypothesis and alternative hypothesis for a fixed significance level t∈(0,1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\in (0,1)$$\\end{document} and varying sample sizes. We evaluate the performance of the two p-values in estimating the proportion of true null hypotheses in multiple testing. We conduct a family-wise error rate control using an adaptive Bonferroni procedure with a plug-in estimator to account for the multiplicity that arises from our multiple hypotheses under consideration. The various claims in this research are verified using a simulation study and real-world data analysis.

Inference for Dependent Data with Learned Clusters

Abstract This paper presents and analyzes an approach to cluster-based inference for dependent data. The primary setting considered here is with spatially indexed data in which the dependence structure of observed random variables is characterized by a known, observed dissimilarity measure over spatial indices. Observations are partitioned into clusters with the use of an unsupervised clustering algorithm applied to the dissimilarity measure. Once the partition into clusters is learned, a cluster-based inference procedure is applied to a statistical hypothesis testing procedure. The procedure proposed in the paper allows the number of clusters to depend on the data, which gives researchers a principled method for choosing an appropriate clustering level. The paper gives conditions under which the proposed procedure asymptotically attains correct size. A simulation study shows that the proposed procedure attains near nominal size in finite samples in a variety of statistical testing problems with dependent data.

Design of randomized clinical trials with a binary endpoint: Conditional versus unconditional analyses of a two-by-two table.

When designing a randomized clinical trial to compare two treatments, the sample size required to have desired power with a specified type 1 error depends on the hypothesis testing procedure. With a binary endpoint (e.g., response), the trial results can be displayed in a 2 × 2 table. If one does the analysis conditional on the number of positive responses, then using Fisher's exact test has an actual type 1 error less than or equal to the specified nominal type 1 error. Alternatively, one can use one of many unconditional "exact" tests that also preserve the type 1 error and are less conservative than Fisher's exact test. In particular, the unconditional test of Boschloo is always at least as powerful as Fisher's exact test, leading to smaller required sample sizes for clinical trials. However, many statisticians have argued over the years that the conditional analysis with Fisher's exact test is the only appropriate procedure. Since having smaller clinical trials is an extremely important consideration, we review the general arguments given for the conditional analysis of a 2 × 2 table in the context of a randomized clinical trial. We find the arguments not relevant in this context, or, if relevant, not completely convincing, suggesting the sample-size advantage of the unconditional tests should lead to their recommended use. We also briefly suggest that since designers of clinical trials practically always have target null and alternative response rates, there is the possibility of using this information to improve the power of the unconditional tests.

Detecting Weak Distribution Shifts via Displacement Interpolation

Detecting weak, systematic distribution shifts and quantitatively modeling individual, heterogeneous responses to policies or incentives have found increasing empirical applications in social and economic sciences. Given two probability distributions P (null) and Q (alternative), we study the problem of detecting weak distribution shift deviating from the null P toward the alternative Q, where the level of deviation vanishes as a function of n, the sample size. We propose a model for weak distribution shifts via displacement interpolation between P and Q, drawing from the optimal transport theory. We study a hypothesis testing procedure based on the Wasserstein distance, derive sharp conditions under which detection is possible, and provide the exact characterization of the asymptotic Type I and Type II errors at the detection boundary using empirical processes. We demonstrate how the proposed testing procedure works in modeling and detecting weak distribution shifts in real datasets using two empirical examples: distribution shifts in consumer spending after COVID-19, and heterogeneity in the published p-values of statistical tests in journals across different disciplines.

A Plot is Worth a Thousand Tests: Assessing Residual Diagnostics with the Lineup Protocol

Regression experts consistently recommend plotting residuals for model diagnosis, despite the availability of many numerical hypothesis test procedures designed to use residuals to assess problems with a model fit. Here we provide evidence for why this is good advice using data from a visual inference experiment. We show how conventional tests are too sensitive, which means that too often the conclusion would be that the model fit is inadequate. The experiment uses the lineup protocol which puts a residual plot in the context of null plots. This helps generate reliable and consistent reading of residual plots for better model diagnosis. It can also help in an obverse situation where a conventional test would fail to detect a problem with a model due to contaminated data. The lineup protocol also detects a range of departures from good residuals simultaneously. Supplemental materials for the article are available online.

Efficient alternatives for Bayesian hypothesis tests in psychology.

Bayesian hypothesis testing procedures have gained increased acceptance in recent years. A key advantage that Bayesian tests have over classical testing procedures is their potential to quantify information in support of true null hypotheses. Ironically, default implementations of Bayesian tests prevent the accumulation of strong evidence in favor of true null hypotheses because associated default alternative hypotheses assign a high probability to data that are most consistent with a null effect. We propose the use of "nonlocal" alternative hypotheses to resolve this paradox. The resulting class of Bayesian hypothesis tests permits more rapid accumulation of evidence in favor of both true null hypotheses and alternative hypotheses that are compatible with standardized effect sizes of most interest in psychology. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Hypothesis Testing for Class-Conditional Noise Using Local Maximum Likelihood

In supervised learning, automatically assessing the quality of the labels before any learning takes place remains an open research question. In certain particular cases, hypothesis testing procedures have been proposed to assess whether a given instance-label dataset is contaminated with class-conditional label noise, as opposed to uniform label noise. The existing theory builds on the asymptotic properties of the Maximum Likelihood Estimate for parametric logistic regression. However, the parametric assumptions on top of which these approaches are constructed are often too strong and unrealistic in practice. To alleviate this problem, in this paper we propose an alternative path by showing how similar procedures can be followed when the underlying model is a product of Local Maximum Likelihood Estimation that leads to more flexible nonparametric logistic regression models, which in turn are less susceptible to model misspecification. This different view allows for wider applicability of the tests by offering users access to a richer model class. Similarly to existing works, we assume we have access to anchor points which are provided by the users. We introduce the necessary ingredients for the adaptation of the hypothesis tests to the case of nonparametric logistic regression and empirically compare against the parametric approach presenting both synthetic and real-world case studies and discussing the advantages and limitations of the proposed approach.

Sequential hypothesis testing for selecting the number of changepoints in segmented regression models

Segmented regression is widely used in many disciplines, especially when dealing with environmental data. This paper deals with the problem of selecting the correct number of changepoints in segmented regression models. A review of the usual selection criteria, namely information criteria and hypothesis testing, is provided. We enhance the latter method by proposing a novel sequential hypothesis testing procedure to address this problem. Our sequential procedure’s performance is compared to methods based on information-based criteria through simulation studies. The results show that our proposal performs similarly to its competitors for the Gaussian, Binomial, and Poisson cases. Finally, we present two applications to environmental datasets of crime data in Valencia and global temperature land data.

A new Bayesian discrepancy measure

The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a given hypothesis with respect to the available information (prior law and data). To summarise this information, the posterior median is employed, allowing a simple assessment of the discrepancy with a fixed hypothesis. The Bayesian Discrepancy Measure assesses the compatibility of a single hypothesis with the observed data, as opposed to the more common comparative approach where a hypothesis is rejected in favour of a competing hypothesis. The proposed measure of evidence has properties of consistency and invariance. After presenting the definition of the measure for a parameter of interest, both in the absence and in the presence of nuisance parameters, we illustrate some examples showing its conceptual and interpretative simplicity. Finally, we compare a test procedure based on the Bayesian Discrepancy Measure, with the Full Bayesian Significance Test, a well-known Bayesian testing procedure for sharp hypotheses.

Suboptimal Diets Identified Among Adults in Two Rural States During the COVID-19 Pandemic

ABSTRACT Rural communities face unique food and nutrition challenges. Analyzing population-level survey data from 2021 to 2022 in two predominantly rural U.S. states using regression and multiple hypothesis testing procedures, we examined how well diets align with national recommendations and associations between diet, age, food security, and rurality. We found dietary intake of key foods and ingredients to differ significantly from recommendations and overall diet quality to increase with age. Food secure adults had higher diet quality than food insecure adults. Neither dietary intake nor dietary quality differed by degree of rurality. Continued action is needed to address nutrition challenges among underserved populations.

Extending Buckley–James method for heteroscedastic survival data

The Buckley–James method for the classical accelerated failure time model has been extended to accommodate heteroscedastic survival data in two ways. The first is the weighted least squares method [Yu et al. Weighted least-squares method for right-censored data in accelerated failure time model. Biometrics. 2013;69:358–365], which estimates the heteroscedasticity nonparametrically, while the second is the local Buckley–James method [Pang et al. Local Buckley–James estimation for heteroscedastic accelerated failure time model. Stat Sin. 2015;25:863–877], which uses local Kaplan–Meier method to estimate the heteroscedasticity. However, no comparisons have been done for these two methods. Furthermore, there is no hypothesis testing procedure for this heteroscedastic accelerated failure time model. This paper is then aimed to fill these two gaps to compare the two methods theoretically and numerically with extensive simulation studies. In addition, we propose a class of hypothesis tests for the parameters to provide a complete procedure for analysing heteroscedastic survival data. Two real data examples are used for practical illustration of the comparison and the new proposed tests.

Factors Influencing Pet Attachment: Exploring Attachment Dimensions and Demographic Factors

This study examined the factors influencing pet attachment by investigating attachment dimensions and exploring the relationship between demographic factors and pet attachment. The study utilized the Pet Attachment Questionnaire (PAQ) to assess the level of attachment between pet owners and their animals. A demographic questionnaire was also administered to gather socio-cultural, economic, and health-related data from pet caretakers. A confirmatory factor analysis was applied to confirm the scale factor structure. Hypothesis testing procedures were used to reveal the relationship between the demographic characteristics of the participants and the attachment relationships. The study involved 304 volunteers who visited the animal hospital at Ankara University, Faculty of Veterinary Medicine. The findings revealed significant impacts of various factors on attachment dimensions, including age, household income, participant and household member anxieties and traumas, number of pets owned, pet health, and previous pet ownership. These results contributed to our understanding of the complex dynamics that shape the attachment between humans and animals. Further research is needed to delve into the underlying mechanisms and potential interactions among these factors, advancing our knowledge of human-pet attachment.

Competing Risk Modeling with Bivariate Varying Coefficients to Understand the Dynamic Impact of COVID-19

The coronavirus disease 2019 (COVID-19) pandemic has exerted a profound impact on patients with end-stage renal disease relying on kidney dialysis to sustain their lives. A preliminary analysis of dialysis patient postdischarge hospital readmissions and deaths in 2020 revealed that the COVID-19 effect has varied significantly with postdischarge time and time since the pandemic onset. However, the complex dynamics cannot be characterized by existing varying coefficient models. To address this issue, we propose a bivariate varying coefficient model for competing risks, where tensor-product B-splines are used to estimate the surface of the COVID-19 effect. An efficient proximal Newton algorithm is developed to facilitate the fitting of the new model to the massive data for Medicare beneficiaries on dialysis. Difference-based anisotropic penalization is introduced to mitigate model overfitting and effect wiggliness; a cross-validation method is derived to determine optimal tuning parameters. Hypothesis testing procedures are designed to examine whether the COVID-19 effect varies significantly with postdischarge time and the time since the pandemic onset, either jointly or separately. Applications to Medicare dialysis patients demonstrate the real-world performance of the proposed methods. Simulation experiments are conducted to evaluate the estimation accuracy, type I error rate, statistical power, and model selection procedures. Supplementary materials for this article are available online.

Variance of entropy for testing time-varying regimes with an application to meme stocks

Shannon entropy is the most common metric for assessing the degree of randomness of time series in many fields, ranging from physics and finance to medicine and biology. Real-world systems are typically non-stationary, leading to entropy values fluctuating over time. This paper proposes a hypothesis testing procedure to test the null hypothesis of constant Shannon entropy in time series data. The alternative hypothesis is a significant variation in entropy between successive periods. To this end, we derive an unbiased sample entropy variance, accurate up to the order O(n-4)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^{-4})$$\\end{document} with n the sample size. To characterize the variance of the sample entropy, we first provide explicit formulas for the central moments of both binomial and multinomial distributions describing the distribution of the sample entropy. Second, we identify the optimal rolling window length to estimate time-varying Shannon entropy. We optimize this choice using a novel self-consistent criterion based on counting significant entropy variations over time. We corroborate our findings using the novel methodology to assess time-varying regimes of entropy for stock price dynamics by presenting a comparative analysis between meme and IT stocks in 2020 and 2021. We show that low entropy values correspond to periods when profitable trading strategies can be devised starting from the symbolic dynamics used for entropy computation, namely periods of market inefficiency.

Biomarkers of Inflammation and Longitudinal Evaluation of Lung Function, Physical Activity, and Grip Strength: A Secondary Analysis in the CASCADE Study.

Physical activity, lung function, and grip strength are associated with exacerbations, hospitalizations, and mortality in people with chronic obstructive pulmonary disease (COPD). We tested whether baseline inflammatory biomarkers were associated with longitudinal outcomes of these physiologic measurements. The COPD Activity: Serotonin Transporter, Cytokines, and Depression (CASCADE) study was a prospective observational study of individuals with COPD. A total of 14 inflammatory biomarkers were measured at baseline. Participants were followed for 2 years. We analyzed associations between baseline biomarkers and forced expiratory volume in 1 second (FEV1), physical activity, and grip strength. We used a hierarchical hypothesis testing procedure to reduce type I error. We used Pearson correlations to test associations between baseline biomarkers and longitudinal changes in the outcomes of interest. We used Fisher's linear discriminant analysis to test if linear combinations of baseline biomarkers predict rapid FEV1 decline. Finally, we used linear mixed modeling to test associations between baseline biomarkers and outcomes of interest at baseline, year 1, and year 2; models were adjusted for age, smoking status, baseline biomarkers, and FEV1. A total of 302 participants (age 67.5 ± 8.5 years, 19.5% female, 28.5% currently smoking) were included. Baseline biomarkers were not associated with longitudinal changes in grip strength, physical activity, or rapid FEV1 decline. Higher interleukin-6 and C-reactive protein were associated with lower physical activity at baseline and these relationships persisted at year 1 and year 2. Baseline inflammatory biomarkers did not predict changes in lung function or physical activity, but higher inflammatory biomarkers were associated with persistently low levels of physical activity.