The asymptotic non-null distribution of theF-static for testing a partial null-hypothesis in a randomized PBIB design withm associate classes under the Neyman model

1973 ◽  
Vol 25 (1) ◽  
pp. 239-259
Author(s):  
Junjiro Ogawa ◽  
Sadao Ikeda
Keyword(s):  
Null Hypothesis ◽  
Null Distribution ◽  
Pbib Design

Indeterminacy

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Regression Model ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Hypothesis Test ◽  
Null Distribution ◽  
Elementary Approach ◽  
Test Statistic ◽  
Exponential Regression ◽  
Lack Of Fit ◽  
Exponential Regression Model

This chapter discusses models like the exponential regression model y = a[1− exp(− bx)] where if a = 0 then b is an indeterminate, non-identifiable parameter, as it vanishes from the model. The hypothesis test that H0 : a = 0 versus H1 : a ≠ 0 is then non-standard. The well-known Davies test is explained. This uses a portmanteau test statistic T that is a functional of Sn(b), L< b< U, where Sn(b) is a regular test statistic of the null hypothesis a = 0 versus the alternative a ≠ 0 with b fixed. The null distribution of T is not usually easy to obtain. One can instead just test if a = 0 using a GoF test or a lack-of-fit test with an alternative hypothesis not specified. In the exponential regression example, this means simply testing if the observations are solely pure error. This elementary approach is compared with the Davies approach.

A Cusum Test for Symmetry Against Positive Biasedness

1994 ◽  
Vol 44 (3-4) ◽  
pp. 157-164
Author(s):  
Emad-Eldin A. A. Aly ◽  
Subhash C. Kochar
Keyword(s):  
Null Hypothesis ◽  
Continuous Distribution ◽  
Null Distribution ◽  
Random Variable ◽  
Cusum Test ◽  
Monte Carlo Simulation Study ◽  
Absolutely Continuous ◽  
Test For Symmetry ◽  
The One ◽  
Tests For Symmetry

Let X be a random variable with an absolutely continuous distribution function F(.) and density function f(.). We propose and study a cusum test for testing the symmetry of X around zero against the one-side alternative H1 : f( x ) ⩾ f(- x ) for all x ⩾ 0 with strict inequality for some x. The proposed test is distribution-free under the null hypothesis. The null distribution of the proposed test is given. A Monte Carlo simulation study to compare the power of the proposed test with other one-sided tests for symmetry is reported.

scholarly journals A powerful method for pleiotropic analysis under composite null hypothesis identifies novel shared loci between Type 2 Diabetes and Prostate Cancer

PLoS Genetics ◽  
2020 ◽  
Vol 16 (12) ◽  
pp. e1009218
Author(s):  
Debashree Ray ◽  
Nilanjan Chatterjee
Keyword(s):  
Prostate Cancer ◽  
Type 2 Diabetes ◽  
Genetic Variants ◽  
Null Hypothesis ◽  
Null Distribution ◽  
Type I ◽  
Multiple Traits ◽  
Major Power ◽  
A Genome

There is increasing evidence that pleiotropy, the association of multiple traits with the same genetic variants/loci, is a very common phenomenon. Cross-phenotype association tests are often used to jointly analyze multiple traits from a genome-wide association study (GWAS). The underlying methods, however, are often designed to test the global null hypothesis that there is no association of a genetic variant with any of the traits, the rejection of which does not implicate pleiotropy. In this article, we propose a new statistical approach, PLACO, for specifically detecting pleiotropic loci between two traits by considering an underlying composite null hypothesis that a variant is associated with none or only one of the traits. We propose testing the null hypothesis based on the product of the Z-statistics of the genetic variants across two studies and derive a null distribution of the test statistic in the form of a mixture distribution that allows for fractions of variants to be associated with none or only one of the traits. We borrow approaches from the statistical literature on mediation analysis that allow asymptotic approximation of the null distribution avoiding estimation of nuisance parameters related to mixture proportions and variance components. Simulation studies demonstrate that the proposed method can maintain type I error and can achieve major power gain over alternative simpler methods that are typically used for testing pleiotropy. PLACO allows correlation in summary statistics between studies that may arise due to sharing of controls between disease traits. Application of PLACO to publicly available summary data from two large case-control GWAS of Type 2 Diabetes and of Prostate Cancer implicated a number of novel shared genetic regions: 3q23 (ZBTB38), 6q25.3 (RGS17), 9p22.1 (HAUS6), 9p13.3 (UBAP2), 11p11.2 (RAPSN), 14q12 (AKAP6), 15q15 (KNL1) and 18q23 (ZNF236).

scholarly journals A simple permutation-based test of intermodal correspondence

2020 ◽  
Author(s):  
Sarah M Weinstein ◽  
Simon N Vandekar ◽  
Azeez Adebimpe ◽  
Tinashe M Tapera ◽  
Timothy Robert-Fitzgerald ◽  
...  
Keyword(s):  
Cortical Thickness ◽  
Null Hypothesis ◽  
Memory Task ◽  
Null Distribution ◽  
Simulated Data ◽  
Testing Procedure ◽  
Type I ◽  
Imaging Data ◽  
Statistical Assumptions ◽  
The Brain

Many key findings in neuroimaging studies involve similarities between brain maps. While several statistical procedures have been proposed to test correspondence between maps, there remains no consensus on the correct framing of a null hypothesis or a suitable testing approach. We propose a simple yet powerful permutation-based testing procedure for assessing similarities between two modalities using subject-level data. Our proposed method is similar to traditional permutation procedures in that it involves randomly permuting subjects to generate a null distribution. However, it differs from other recently proposed methods that have involved spherical rotations of the cortical surface or spatial autocorrelation-preserving ''surrogate'' maps of the brain, which depend on strong and potentially unrealistic statistical assumptions. To address these issues, we first demonstrate in simulated data that our method is conservative in terms of type I error and has high power. Next, we illustrate that our method performs well for assessing intermodal relationships from multimodal magnetic resonance imaging data from the Philadelphia Neurodevelopmental Cohort. The proposed test rejects the null hypothesis for modalities for which there is known interdependence in structure (cortical thickness and sulcal depth) but not in cases where an association would not be predicted biologically (cortical thickness and activation on the n-back working memory task). In contrast to previous methods, our approach does not depend on strong statistical assumptions other than the independence of subjects. Notably, our method is the most flexible for analyzing intermodal correspondence within subregions of the brain and has the greatest potential to be used for generalizable statistical inference.

scholarly journals A Powerful Method for Pleiotropic Analysis under Composite Null Hypothesis Identifies Novel Shared Loci Between Type 2 Diabetes and Prostate Cancer

2020 ◽  
Author(s):  
Debashree Ray ◽  
Nilanjan Chatterjee
Keyword(s):  
Prostate Cancer ◽  
Type 2 Diabetes ◽  
Null Hypothesis ◽  
Null Distribution ◽  
Mixture Distribution ◽  
Type I ◽  
Multiple Traits ◽  
Test Statistic ◽  
Major Power

SummaryThere is increasing evidence that pleiotropy, the association of multiple traits with the same genetic variants/loci, is a very common phenomenon. Cross-phenotype association tests are often used to jointly analyze multiple traits from a GWAS. The underlying methods, however, are often designed to test the global null hypothesis that there is no association of a genetic variant with any of the traits, the rejection of which does not implicate pleiotropy. In this article, we propose a new statistical approach, PLACO, for specifically detecting pleiotropic loci between two traits by considering an underlying composite null hypothesis that a variant is associated with none or only one of the traits. We propose testing the null hypothesis based on the product of the Z-statistics of the SNPs across two studies and derive a null distribution of the test statistic in the form of a mixture distribution that allows for fractions of SNPs to be associated with none or only one of the traits. We borrow approaches from the statistical literature on mediation analysis that allow asymptotic approximation of the null distribution avoiding estimation of nuisance parameters related to mixture proportions and variance components. Simulation studies demonstrate that the proposed method can maintain type I error and can achieve major power gain over alternative simpler methods that are typically used for testing pleiotropy. PLACO allows correlation in summary statistics between studies that may arise due to sharing of controls between disease traits. Application of PLACO to publicly available summary data from two large case-control GWAS of Type 2 Diabetes and of Prostate Cancer implicated a number of novel shared genetic regions near ZBTB38 (3q23), RGS17 (6q25.3), HAUS6 (9p22.1), UBAP2 (9p13.3), RAPSN (11p11.2), AKAP6 (14q12), KNL1 (15q15) and ZNF236 (18q23).

A Robust Null Hypothesis for the Potential Causes of Megadrought in Western North America

2017 ◽  
Vol 31 (1) ◽  
pp. 3-24 ◽  
Author(s):  
Toby R. Ault ◽  
Scott St. George ◽  
Jason E. Smerdon ◽  
Sloan Coats ◽  
Justin S. Mankin ◽  
...  
Keyword(s):  
Twentieth Century ◽  
North America ◽  
Climate Variability ◽  
Null Hypothesis ◽  
Null Distribution ◽  
Severity Index ◽  
Drought Severity ◽  
Internal Climate Variability ◽  
Out Of Sample ◽  
Change In Mean

Abstract The western United States was affected by several megadroughts during the last 1200 years, most prominently during the Medieval Climate Anomaly (MCA; 800 to 1300 CE). A null hypothesis is developed to test the possibility that, given a sufficiently long period of time, these events are inevitable and occur purely as a consequence of internal climate variability. The null distribution of this hypothesis is populated by a linear inverse model (LIM) constructed from global sea surface temperature anomalies and self-calibrated Palmer drought severity index data for North America. Despite being trained only on seasonal data from the late twentieth century, the LIM produces megadroughts that are comparable in their duration, spatial scale, and magnitude to the most severe events of the last 12 centuries. The null hypothesis therefore cannot be rejected with much confidence when considering these features of megadrought, meaning that similar events are possible today, even without any changes to boundary conditions. In contrast, the observed clustering of megadroughts in the MCA, as well as the change in mean hydroclimate between the MCA and the 1500–2000 period, are more likely to have been caused by either external forcing or by internal climate variability not well sampled during the latter half of the twentieth century. Finally, the results demonstrate that the LIM is a viable tool for determining whether paleoclimate reconstructions events should be ascribed to external forcings or to “out of sample” climate mechanisms, or if they are consistent with the variability observed during the recent period.

An Alternative to Cohen's κ

2006 ◽  
Vol 11 (1) ◽  
pp. 12-24 ◽  
Author(s):  
Alexander von Eye
Keyword(s):  
Simulation Study ◽  
Null Hypothesis ◽  
Categorical Variables ◽  
Alternative Measure ◽  
Rater Agreement ◽  
Verbal Processing ◽  
Heavy Tailed ◽  
Applicant Selection

At the level of manifest categorical variables, a large number of coefficients and models for the examination of rater agreement has been proposed and used. The most popular of these is Cohen's κ. In this article, a new coefficient, κ s , is proposed as an alternative measure of rater agreement. Both κ and κ s allow researchers to determine whether agreement in groups of two or more raters is significantly beyond chance. Stouffer's z is used to test the null hypothesis that κ s = 0. The coefficient κ s allows one, in addition to evaluating rater agreement in a fashion parallel to κ, to (1) examine subsets of cells in agreement tables, (2) examine cells that indicate disagreement, (3) consider alternative chance models, (4) take covariates into account, and (5) compare independent samples. Results from a simulation study are reported, which suggest that (a) the four measures of rater agreement, Cohen's κ, Brennan and Prediger's κ n , raw agreement, and κ s are sensitive to the same data characteristics when evaluating rater agreement and (b) both the z-statistic for Cohen's κ and Stouffer's z for κ s are unimodally and symmetrically distributed, but slightly heavy-tailed. Examples use data from verbal processing and applicant selection.

Proving the null hypothesis.

1991 ◽  
Vol 46 (10) ◽  
pp. 1089-1089 ◽  
Author(s):  
John J. Bartko
Keyword(s):  
Null Hypothesis
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