scholarly journals Testing for equality of distributions using the concept of (niche) overlap

2021 ◽  
Author(s):  
Judith H. Parkinson-Schwarz ◽  
Arne C. Bathke
Keyword(s):  
Basic Assumption ◽  
Type I Error ◽  
Test Procedure ◽  
Niche Overlap ◽  
Relative Effect ◽  
Type I ◽  
Underlying Distribution ◽  
Parametric Test ◽  
Higher Power ◽  
Non Parametric

AbstractIn this paper, we propose a new non-parametric test for equality of distributions. The test is based on the recently introduced measure of (niche) overlap and its rank-based estimator. As the estimator makes only one basic assumption on the underlying distribution, namely continuity, the test is universal applicable in contrast to many tests that are restricted to only specific scenarios. By construction, the new test is capable of detecting differences in location and scale. It thus complements the large class of rank-based tests that are constructed based on the non-parametric relative effect. In simulations this new test procedure obtained higher power and lower type I error compared to two common tests in several settings. The new procedure shows overall good performance. Together with its simplicity, this test can be used broadly.

scholarly journals Comparison of Type I Error of some Non-Parametric Tests on Multiple Regression Models Coefficients

2015 ◽  
Vol 11 (7) ◽  
pp. 5426-5443
Author(s):  
Ali Shadrokh
Keyword(s):  
Multiple Regression ◽  
Regression Models ◽  
Type I Error ◽  
Hypothesis Test ◽  
Type I ◽  
Lower Type ◽  
Modified Method ◽  
Higher Power ◽  
Multiple Regression Models ◽  
Non Parametric

Various non-parametric methods have been used to perform hypothesis test on multiple regression coefficients. In this article, at first the most important methods which has been introduced from other statisticians as proper methods, such as Kennedy, Freedman and Lane, and modified Kennedy, are explained and then, Freedman and Lane (Huh-John) method will be modified in the form of Kennedy method; finally, all aforementioned methods will be compared as simulating. At last, we look for a method that done best. So, Huh-John (2001) modify the method of Kennedy which was proposed in 1995 and showed by simulation that is called modified Huh-John method; and it has less type I error. On the other hand, Anderson as simulation (1991) and Schadrekh as theory (2011) had shown that Freedman& Lane method has lower type I error in comparison with Kennedy method. We did some modification on Freedman and Lane method that Huh-John had done on Kennedy method and compared this modified method with Freedman and Lane and Huh-John method. We conclude that Freedman and Lane modified method often has lower type I error estimation and higher power than Freedman& Lane and Huh-John method.

Location Tests for Biomarker Studies: A Comparison Using Simulations for the Two-sample Case

2013 ◽  
Vol 52 (04) ◽  
pp. 351-359 ◽  
Author(s):  
M. O. Scheinhardt ◽  
A. Ziegler
Keyword(s):  
Heavy Tails ◽  
Type I Error ◽  
Adaptive Methods ◽  
Type I ◽  
Skewed Data ◽  
Error Level ◽  
Adaptive Tests ◽  
Wide Range ◽  
Heavy Tailed ◽  
Non Parametric

Summary Background: Gene, protein, or metabolite expression levels are often non-normally distributed, heavy tailed and contain outliers. Standard statistical approaches may fail as location tests in this situation. Objectives: In three Monte-Carlo simulation studies, we aimed at comparing the type I error levels and empirical power of standard location tests and three adaptive tests [O’Gorman, Can J Stat 1997; 25: 269 –279; Keselman et al., Brit J Math Stat Psychol 2007; 60: 267– 293; Szymczak et al., Stat Med 2013; 32: 524 – 537] for a wide range of distributions. Methods: We simulated two-sample scena -rios using the g-and-k-distribution family to systematically vary tail length and skewness with identical and varying variability between groups. Results: All tests kept the type I error level when groups did not vary in their variability. The standard non-parametric U-test per -formed well in all simulated scenarios. It was outperformed by the two non-parametric adaptive methods in case of heavy tails or large skewness. Most tests did not keep the type I error level for skewed data in the case of heterogeneous variances. Conclusions: The standard U-test was a powerful and robust location test for most of the simulated scenarios except for very heavy tailed or heavy skewed data, and it is thus to be recommended except for these cases. The non-parametric adaptive tests were powerful for both normal and non-normal distributions under sample variance homogeneity. But when sample variances differed, they did not keep the type I error level. The parametric adaptive test lacks power for skewed and heavy tailed distributions.

scholarly journals Effective Analysis of Interactive Effects with Non-Normal Data Using the Aligned Rank Transform, ARTool and SAS® University Edition

Horticulturae ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 57 ◽  
Author(s):  
Edward Durner
Keyword(s):  
Type I Error ◽  
Interactive Effects ◽  
Type I ◽  
Rank Transform ◽  
Parametric Testing ◽  
Aligned Rank ◽  
Departure From Normality ◽  
Main Effects ◽  
Horticultural Research ◽  
Non Parametric

Most statistical techniques commonly used in horticultural research are parametric tests that are valid only for normal data with homogeneous variances. While parametric tests are robust when the data ‘slightly’ deviate from normality, a significant departure from normality leads to reduced power and the probability of a type I error increases. Transformations often used to normalize non-normal data can be time consuming, cumbersome and confusing and common non-parametric tests are not appropriate for evaluating interactive effects common in horticultural research. The aligned rank transformation allows non-parametric testing for interactions and main effects using standard ANOVA techniques. This has not been widely adapted due to its rigorous mathematical nature, however, a downloadable (ARTool) is now available, which performs the math needed for the transformation. This study provides step-by-step instructions for integrating ARTool with the free edition of SAS (SAS University Edition) in an easily employed method for testing normality, transforming data with aligned ranks, and analysing data using standard ANOVAs.

scholarly journals Probability of Type I Error and Power of Some Parametric Test: Comparative Approach

2019 ◽  
Vol 13 (1) ◽  
pp. 7-13
Author(s):  
Enegesele Dennis ◽  
Biu O. Emmanuel ◽  
Otaru O.A. Paul
Keyword(s):  
Type I Error ◽  
Comparative Approach ◽  
Type I ◽  
Parametric Test

scholarly journals A Monte Carlo Study of an Iterative Wald Test Procedure for DIF Analysis

2016 ◽  
Vol 77 (1) ◽  
pp. 104-118 ◽  
Author(s):  
Mengyang Cao ◽  
Louis Tay ◽  
Yaowu Liu
Keyword(s):  
Monte Carlo ◽  
Type I Error ◽  
Test Procedure ◽  
Monte Carlo Study ◽  
Error Rates ◽  
Type I ◽  
Iterative Approach ◽  
Response Options ◽  
Type I Error Rates ◽  
Dichotomous Data

This study examined the performance of a proposed iterative Wald approach for detecting differential item functioning (DIF) between two groups when preknowledge of anchor items is absent. The iterative approach utilizes the Wald-2 approach to identify anchor items and then iteratively tests for DIF items with the Wald-1 approach. Monte Carlo simulation was conducted across several conditions including the number of response options, test length, sample size, percentage of DIF items, DIF effect size, and type of cumulative DIF. Results indicated that the iterative approach performed well for polytomous data in all conditions, with well-controlled Type I error rates and high power. For dichotomous data, the iterative approach also exhibited better control over Type I error rates than the Wald-2 approach without sacrificing the power in detecting DIF. However, inflated Type I error rates were found for the iterative approach in conditions with dichotomous data, noncompensatory DIF, large percentage of DIF items, and medium to large DIF effect sizes. Nevertheless, the Type I error rates were substantially less inflated in those conditions compared with the Wald-2 approach.

A Practical Method for Analyzing Factorial Designs with Heteroscedastic Data

2008 ◽  
Vol 102 (3) ◽  
pp. 643-656
Author(s):  
Guiillermo Vallejo ◽  
M. Paula Fernández ◽  
Manuel Ato ◽  
Pablo E. Livacic-Rojas
Keyword(s):  
Mixed Model ◽  
Type I Error ◽  
Practical Method ◽  
Error Rates ◽  
Type I ◽  
Factorial Designs ◽  
Symmetric Distributions ◽  
Higher Power ◽  
Asymmetric Distributions ◽  
Heteroscedastic Data

The Type I error rates and powers of three recent tests for analyzing nonorthogonal factorial designs under departures from the assumptions of homogeneity and normality were evaluated using Monte Carlo simulation. Specifically, this work compared the performance of the modified Brown-Forsythe procedure, the generalization of Box's method proposed by Brunner, Dette, and Munk, and the mixed-model procedure adjusted by the Kenward-Roger solution available in the SAS statistical package. With regard to robustness, the three approaches adequately controlled Type I error when the data were generated from symmetric distributions; however, this study's results indicate that, when the data were extracted from asymmetric distributions, the modified Brown-Forsythe approach controlled the Type I error slightly better than the other procedures. With regard to sensitivity, the higher power rates were obtained when the analyses were done with the MIXED procedure of the SAS program. Furthermore, results also identified that, when the data were generated from symmetric distributions, little power was sacrificed by using the generalization of Box's method in place of the modified Brown-Forsythe procedure.

An adaptive seamless Phase 2-3 design with multiple endpoints

2021 ◽  
pp. 096228022098693 ◽  
Author(s):  
Man Jin ◽  
Pingye Zhang
Keyword(s):  
Type I Error ◽  
Test Procedure ◽  
Type I ◽  
Phase 2 ◽  
Phase 3 ◽  
Multiple Endpoints ◽  
Multiple Test ◽  
Phase 2 Trial ◽  
Multiple Test Procedure ◽  
Ongoing Phase

Adaptive seamless Phase 2-3 design has been considered as one possible way to expedite development time for a drug program by allowing the expansion from an ongoing Phase 2 trial into a Phase 3 trial. Multiple endpoints are often tested when a regulatory approval is pursued. Here we propose an adaptive seamless Phase 2-3 design with multiple endpoints which can expand an ongoing Phase 2 trial into a Phase 3 trial based on an intermediate endpoint for adaptive decision and test the endpoints with a powerful multiple test procedure. It is proved that the proposed design can preserve the familywise Type I error under a mild assumption that is expected to hold in practical considerations. We illustrate our proposed design with an example trial design for oncology. Simulations are conducted to confirm the control of the familywise Type I error and the adaptive seamless Phase 2-3 design is illustrated with an example.

scholarly journals An Improved Two Independent-Samples Randomization Test for Single-Case AB-Type Intervention Designs: A 20-Year Journey

2020 ◽  
Vol 18 (1) ◽  
pp. 2-20
Author(s):  
Joel R. Levin ◽  
John M. Ferron ◽  
Boris S. Gafurov
Keyword(s):  
Error Control ◽  
Type I Error ◽  
Single Case ◽  
Test Procedure ◽  
Randomization Test ◽  
Multiple Baseline ◽  
Type I ◽  
Two Phase ◽  
Sample Test ◽  
Adequate Power

Detailed is a 20-year arduous journey to develop a statistically viable two-phase (AB) single-case two independent-samples randomization test procedure. The test is designed to compare the effectiveness of two different interventions that are randomly assigned to cases. In contrast to the unsatisfactory simulation results produced by an earlier proposed randomization test, the present test consistently exhibited acceptable Type I error control under various design and effect-type configurations, while at the same time possessing adequate power to detect moderately sized intervention-difference effects. Selected issues, applications, and a multiple-baseline extension of the two-sample test are discussed.

Combined 5 × 2 cv F Test for Comparing Supervised Classification Learning Algorithms

1999 ◽  
Vol 11 (8) ◽  
pp. 1885-1892 ◽  
Author(s):  
Ethem Alpaydm
Keyword(s):  
Type I Error ◽  
Statistical Tests ◽  
Error Rates ◽  
Type I ◽  
Classification Learning ◽  
F Test ◽  
Robust Test ◽  
Significant Difference ◽  
Higher Power ◽  
Test Result

Dietterich (1998) reviews five statistical tests and proposes the 5 × 2 cvt test for determining whether there is a significant difference between the error rates of two classifiers. In our experiments, we noticed that the 5 × 2 cvt test result may vary depending on factors that should not affect the test, and we propose a variant, the combined 5 × 2 cv F test, that combines multiple statistics to get a more robust test. Simulation results show that this combined version of the test has lower type I error and higher power than 5 × 2 cv proper.

scholarly journals SPARK-X: non-parametric modeling enables scalable and robust detection of spatial expression patterns for large spatial transcriptomic studies

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Jiaqiang Zhu ◽  
Shiquan Sun ◽  
Xiang Zhou
Keyword(s):  
Error Control ◽  
Type I Error ◽  
Expression Patterns ◽  
Parametric Method ◽  
Parametric Modeling ◽  
Type I ◽  
Cell Type ◽  
Robust Detection ◽  
Transcriptomic Studies ◽  
Non Parametric

AbstractSpatial transcriptomic studies are becoming increasingly common and large, posing important statistical and computational challenges for many analytic tasks. Here, we present SPARK-X, a non-parametric method for rapid and effective detection of spatially expressed genes in large spatial transcriptomic studies. SPARK-X not only produces effective type I error control and high power but also brings orders of magnitude computational savings. We apply SPARK-X to analyze three large datasets, one of which is only analyzable by SPARK-X. In these data, SPARK-X identifies many spatially expressed genes including those that are spatially expressed within the same cell type, revealing new biological insights.

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