Search results for "II error"
showing 10 items of 19 documents
Risk tables for discrimination tests
1993
Abstract Duo-trio and triangle test are often used in the food industry for the purpose of declaring two products non-distinguishable. In that situation, it is much more important to control the power of the test rather than the type 1 error risk. This paper makes available by e-mail a SAS ® macro, called BINRISKS, for computing type 1 and type 2 risks for any one-tailed binomial test and for any level of the percentage above chance to be detected. Using this macro, two sets of tables have been compiled. The first table includes for any total number of responses below 50, for any number of correct responses and for three levels of the percentage above chance to be detected, the correspondin…
Rejection odds and rejection ratios: A proposal for statistical practice in testing hypotheses
2016
Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over 50 years. We propose, as an alternative, the use of the odds of a correct rejection of the null hypothesis to incorrect rejection. Both pre-experimental versions (involving the power and Type I error) and post-experimental versions (depending on the actual data) are considered. Implementations are provided that range from depending only on the p-value to consideration of full Bayesian analysis. A surprise is that all implementations -- even the full Baye…
Price Theory and US Antitrust: a Note on an Enduring Legal Doctrine
2013
Since the mid-1980s the post-Chicago approach to antitrust economics has produced a few game-theoretic models which have challenged many typical Chicago antitrust propositions. Yet, Chicago style antitrust has not yet lost its hold on u.s. antitrust. The paper suggests that the Chicago persistence within u.s. antitrust and, by the same token, the inhospitality of u.s. antitrust towards game-theoretical Industrial Organization theory owe much to the vitality of the legal doctrine according to which antitrust analysis should be consistent with traditional price theory. In particular, the paper analyzes two issues: i. the adoption of the equilibrium end-state notion of competition which is sti…
Adaptive trial design: a general methodology for censored time to event data.
2008
Adaptive designs allow a clinical trial design to be changed according to interim findings without inflating type I error. The Inverse Normal method can be considered as an adaptive generalization of classical group sequential designs. The use of the Inverse Normal method for censored survival data was demonstrated only for the logrank statistic. However, the logrank statistic is inefficient in the presence of nuisance covariates affecting survival. We demonstrate, how the Inverse Normal method can be applied to Cox regression analysis. The required independence between test statistics of the different stages of the trial can be obtained by two different approaches. One is using the indepen…
Liberal and Conservative Differential Item Functioning Detection Using Mantel-Haenszel and SIBTEST: Implications for Type I and Type II Error Rates
2004
The aim of this work was to determine, in terms of Type I and Type II error rates, the risks of applying various statistical procedures for evaluating differential item functioning. To this end, the authors carried out a simulation study in which the Mantel-Haenszel and SIBTEST procedures were applied in conjunction. The variables manipulated were sample size and distribution of ability between groups. Results indicated that, although there was a high rate of agreement between the procedures, the joint Type I and Type II error rate may vary substantially from that obtained when each of the procedures was applied separately. Furthermore, the authors analyzed empirical data to obtain informat…
Application of the Morris method for screening the influential parameters of fuzzy controllers applied to wastewater treatment plants
2011
In this paper,we evaluate the application of a sensitivity analysis to help fine-tuning a fuzzy controller for a biological nitrogen and phosphorus removal (BNPR) plant. TheMorris Screeningmethod is proposed and evaluated as a prior step to obtain the parameter significance ranking. First, an iterative procedure has been performed in order to find out the proper repetition number of the elementary effects (r) of the method. The optimal repetition number found in this study (r = 60) is in direct contrast to previous applications of the Morris method, which usually use low repetition number, e.g. r = 10 ~ 20. Working with a non-proper repetition number (r) could lead to Type I error (identify…
PACo: a novel procrustes application to cophylogenetic analysis.
2013
We present Procrustean Approach to Cophylogeny (PACo), a novel statistical tool to test for congruence between phylogenetic trees, or between phylogenetic distance matrices of associated taxa. Unlike previous tests, PACo evaluates the dependence of one phylogeny upon the other. This makes it especially appropriate to test the classical coevolutionary model that assumes that parasites that spend part of their life in or on their hosts track the phylogeny of their hosts. The new method does not require fully resolved phylogenies and allows for multiple host-parasite associations. PACo produces a Procrustes superimposition plot enabling a graphical assessment of the fit of the parasite phyloge…
Two-stage adaptive designs with correlated test statistics.
2005
When performing a trial using an adaptive sequential design, it is usually assumed that the data for each stage come from different units; for example, patients. However, sometimes it is not possible to satisfy this condition or to check whether it is satisfied. In these cases, the test statistics and p-values of each stage may be dependent. In this paper we investigate the type I error of two-stage adaptive designs when the test statistics from the stages are assumed to be bivariate normal. Analytical considerations are performed under the restriction that the conditional error function is constant in the continuation region. We show that the decisions can become conservative as well as an…
Indicators of Errors for Approximate Solutions of Differential Equations
2014
Error indicators play an important role in mesh-adaptive numerical algorithms, which currently dominate in mathematical and numerical modeling of various models in physics, chemistry, biology, economics, and other sciences. Their goal is to present a comparative measure of errors related to different parts of the computational domain, which could suggest a reasonable way of improving the finite dimensional space used to compute the approximate solution. An “ideal” error indicator must possess several properties: efficiency, computability, and universality. In other words, it must correctly reproduce the distribution of errors, be indeed computable, and be applicable to a wide set of approxi…