Resampling Permutation Probability Values for Six Measures of Qualitative Variation

2007 ◽  
Vol 104 (3) ◽  
pp. 773-776 ◽  
Author(s):  
Janis E. Johnston ◽  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Tail Probability ◽  
Fortran Program ◽  
Test Statistics ◽  
Test Statistic ◽  
Lower Tail ◽  
Qualitative Variation ◽  
Data Table ◽  
Kendall’S Τ ◽  
Lower Tail Probability

An algorithm and associated FORTRAN program are provided for six common measures of ordinal association: Kendall's τ a and τ b, Stuart's τ c, Goodman and Kruskal's γ, and Somers' dyx and dxy. Program ROMA reports the observed data table, the values for the six test statistics, and the resampling upper- and lower-tail probability values associated with each test statistic.

scholarly journals On the Lower Tail Variational Problem for Random Graphs

2016 ◽  
Vol 26 (2) ◽  
pp. 301-320 ◽  
Author(s):  
YUFEI ZHAO
Keyword(s):  
Variational Problem ◽  
Random Graph ◽  
Random Graphs ◽  
Large Deviation ◽  
Tail Probability ◽  
Edge Density ◽  
Lower Tail ◽  
Lower Tail Probability ◽  
Large Deviation Problem ◽  
Deviation Problem

We study the lower tail large deviation problem for subgraph counts in a random graph. Let XH denote the number of copies of H in an Erdős–Rényi random graph $\mathcal{G}(n,p)$. We are interested in estimating the lower tail probability $\mathbb{P}(X_H \le (1-\delta) \mathbb{E} X_H)$ for fixed 0 < δ < 1.Thanks to the results of Chatterjee, Dembo and Varadhan, this large deviation problem has been reduced to a natural variational problem over graphons, at least for p ≥ n−αH (and conjecturally for a larger range of p). We study this variational problem and provide a partial characterization of the so-called ‘replica symmetric’ phase. Informally, our main result says that for every H, and 0 < δ < δH for some δH > 0, as p → 0 slowly, the main contribution to the lower tail probability comes from Erdős–Rényi random graphs with a uniformly tilted edge density. On the other hand, this is false for non-bipartite H and δ close to 1.

Exact Permutation Probability Values for Weighted Kappa

2008 ◽  
Vol 102 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Kenneth J. Berry ◽  
Janis E. Johnston ◽  
Paul W. Mielke
Keyword(s):  
Weighted Kappa ◽  
Tail Probability ◽  
Fortran Program ◽  
Test Statistic ◽  
Kappa Test

A permutation algorithm and associated FORTRAN program are provided for weighted kappa. Program EWK provides the weighted kappa test statistic and the exact one-sided upper-tail probability values.

Resampling Permutation Probability Values for Weighted Kappa

2008 ◽  
Vol 103 (2) ◽  
pp. 467-475 ◽  
Author(s):  
Janis E. Johnston ◽  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Weighted Kappa ◽  
Tail Probability ◽  
Fortran Program ◽  
Test Statistic ◽  
Kappa Test

A permutation algorithm and associated FORTRAN program are provided for resampling weighted kappa. Program RWK provides the weighted kappa test statistic and the resampling one-sided upper-tail probability value.

scholarly journals Effects of kinship correction on inflation of genetic interaction statistics in commonly used mouse populations

2021 ◽  
Author(s):  
Anna L Tyler ◽  
Baha El Kassaby ◽  
Georgi Kolishovski ◽  
Jake Emerson ◽  
Ann E Wells ◽  
...  
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Genetic Interaction ◽  
Recombinant Inbred Lines ◽  
Test Statistics ◽  
Test Statistic ◽  
Kinship Matrix ◽  
Main Effect ◽  
Main Effects ◽  
Interaction Test

Abstract It is well understood that variation in relatedness among individuals, or kinship, can lead to false genetic associations. Multiple methods have been developed to adjust for kinship while maintaining power to detect true associations. However, relatively unstudied, are the effects of kinship on genetic interaction test statistics. Here we performed a survey of kinship effects on studies of six commonly used mouse populations. We measured inflation of main effect test statistics, genetic interaction test statistics, and interaction test statistics reparametrized by the Combined Analysis of Pleiotropy and Epistasis (CAPE). We also performed linear mixed model (LMM) kinship corrections using two types of kinship matrix: an overall kinship matrix calculated from the full set of genotyped markers, and a reduced kinship matrix, which left out markers on the chromosome(s) being tested. We found that test statistic inflation varied across populations and was driven largely by linkage disequilibrium. In contrast, there was no observable inflation in the genetic interaction test statistics. CAPE statistics were inflated at a level in between that of the main effects and the interaction effects. The overall kinship matrix overcorrected the inflation of main effect statistics relative to the reduced kinship matrix. The two types of kinship matrices had similar effects on the interaction statistics and CAPE statistics, although the overall kinship matrix trended toward a more severe correction. In conclusion, we recommend using a LMM kinship correction for both main effects and genetic interactions and further recommend that the kinship matrix be calculated from a reduced set of markers in which the chromosomes being tested are omitted from the calculation. This is particularly important in populations with substantial population structure, such as recombinant inbred lines in which genomic replicates are used.

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

scholarly journals An approach to gene-based testing accounting for dependence of tests among nearby genes

2021 ◽  
Author(s):  
Ronald J Yurko ◽  
Kathryn Roeder ◽  
Bernie Devlin ◽  
Max G'Sell
Keyword(s):  
Multiple Testing ◽  
Association Studies ◽  
Autism Spectrum ◽  
P Value ◽  
Genome Wide Association Studies ◽  
Strongly Correlated ◽  
Test Statistics ◽  
Test Statistic ◽  
Genome Wide ◽  
Insight Into

In genome-wide association studies (GWAS), it has become commonplace to test millions of SNPs for phenotypic association. Gene-based testing can improve power to detect weak signal by reducing multiple testing and pooling signal strength. While such tests account for linkage disequilibrium (LD) structure of SNP alleles within each gene, current approaches do not capture LD of SNPs falling in different nearby genes, which can induce correlation of gene-based test statistics. We introduce an algorithm to account for this correlation. When a gene's test statistic is independent of others, it is assessed separately; when test statistics for nearby genes are strongly correlated, their SNPs are agglomerated and tested as a locus. To provide insight into SNPs and genes driving association within loci, we develop an interactive visualization tool to explore localized signal. We demonstrate our approach in the context of weakly powered GWAS for autism spectrum disorder, which is contrasted to more highly powered GWAS for schizophrenia and educational attainment. To increase power for these analyses, especially those for autism, we use adaptive p-value thresholding (AdaPT), guided by high-dimensional metadata modeled with gradient boosted trees, highlighting when and how it can be most useful. Notably our workflow is based on summary statistics.

Testing for equality of means with equal and unequal variances

2021 ◽  
Vol 20 (2) ◽  
pp. 51-60
Author(s):  
A.O. Abidoye ◽  
W.A. Lamidi ◽  
M.O. Alabi ◽  
J. Popoola
Keyword(s):  
Agricultural Development ◽  
Secondary Data ◽  
Development Project ◽  
T Test ◽  
Harmonic Mean ◽  
Test Statistics ◽  
Test Statistic ◽  
Unequal Variances ◽  
Equality Of Means ◽  
Pooled Sample

In this paper, we are interested in comparing the conventional t –test with the proposed t – test for testing equality of means with unequal and equal variances. Here, we proposed harmonic mean of variances as an alternative to the pooled sample variance when there is heterogeneity of variances. Two sets of secondary data were obtained from Agricultural Development Project (KWADP) and the Ministry of Agriculture in Ilorin, Kwara State to demonstrate the two test statistics used and the results show that the proposed t – test statistic is found to be appropriate than the conventional t – test statistic when we have unequal variances but the conventional t – test perform better when we have equal variances.

A Bounds Approach to Inference Using the Long Run Multiplier

2019 ◽  
Vol 27 (3) ◽  
pp. 281-301 ◽  
Author(s):  
Clayton Webb ◽  
Suzanna Linn ◽  
Matthew Lebo
Keyword(s):  
Unit Root ◽  
Unit Roots ◽  
Small Sample ◽  
Stochastic Simulations ◽  
Upper And Lower Bounds ◽  
Test Statistics ◽  
Test Statistic ◽  
Independent Variables ◽  
Long Run ◽  
Presidential Success

Pesaran, Shin, and Smith (2001) (PSS) proposed a bounds procedure for testing for the existence of long run cointegrating relationships between a unit root dependent variable ($y_{t}$) and a set of weakly exogenous regressors $\boldsymbol{x}_{t}$ when the analyst does not know whether the independent variables are stationary, unit root, or mutually cointegrated processes. This procedure recognizes the analyst’s uncertainty over the nature of the regressors but not the dependent variable. When the analyst is uncertain whether $y_{t}$ is a stationary or unit root process, the test statistics proposed by PSS are uninformative for inference on the existence of a long run relationship (LRR) between $y_{t}$ and $\boldsymbol{x}_{t}$. We propose the long run multiplier (LRM) test statistic as a means of testing for LRRs without knowing whether the series are stationary or unit roots. Using stochastic simulations, we demonstrate the behavior of the test statistic given uncertainty about the univariate dynamics of both $y_{t}$ and $\boldsymbol{x}_{t}$, illustrate the bounds of the test statistic, and generate small sample and approximate asymptotic critical values for the upper and lower bounds for a range of sample sizes and model specifications. We demonstrate the utility of the bounds framework for testing for LRRs in models of public policy mood and presidential success.

scholarly journals Genes differentially expressed in medulloblastoma and fetal brain

1999 ◽  
Vol 1 (2) ◽  
pp. 83-91 ◽  
Author(s):  
E. M. C. MICHIELS ◽  
E. OUSSOREN ◽  
M. VAN GROENIGEN ◽  
E. PAUWS ◽  
P. M. M. BOSSUYT ◽  
...  
Keyword(s):  
Gene Expression ◽  
Brain Tumor ◽  
Northern Blot ◽  
Fetal Brain ◽  
Differentially Expressed ◽  
P Value ◽  
Test Statistics ◽  
Childhood Brain Tumor ◽  
Germinal Layer ◽  
Test Statistic

Michiels, E. M. C., E. Oussoren, M. van Groenigen, E. Pauws, P. M. M. Bossuyt, P. A. Voûte, and F. Baas. Genes differentially expressed in medulloblastoma and fetal brain. Physiol. Genomics 1: 83–91, 1999.—Serial analysis of gene expression (SAGE) was used to identify genes that might be involved in the development or growth of medulloblastoma, a childhood brain tumor. Sequence tags from medulloblastoma (10229) and fetal brain (10692) were determined. The distributions of sequence tags in each population were compared, and for each sequence tag, pairwise χ2 test statistics were calculated. Northern blot was used to confirm some of the results obtained by SAGE. For 16 tags, the χ2 test statistic was associated with a P value < 10−4. Among those transcripts with a higher expression in medulloblastoma were the genes for ZIC1 protein and the OTX2 gene, both of which are expressed in the cerebellar germinal layers. The high expression of these two genes strongly supports the hypothesis that medulloblastoma arises from the germinal layer of the cerebellum. This analysis shows that SAGE can be used as a rapid differential screening procedure.

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