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Volume 3, Issue 1 2004 Article 32 Statistical Applications in Genetics and Molecular Biology Confidence Levels for the Comparison of Microarray Experiments Kerby Shedden, University of Michigan Recommended Citation: Shedden, Kerby (2004) "Confidence Levels for the Comparison of Microarray Experiments," Statistical Applications in Genetics and Molecular Biology: Vol. 3: Iss. 1, Article 32. DOI: 10.2202/1544-6115.1088 ©2004 by the authors. All rights reserved. Confidence Levels for the Comparison of Microarray Experiments Kerby Shedden Abstract A common

against the conventional wisdom which assumes commensurability between linguistic expression and numerical measurement. KEYWORDS: jury instructions, standard of proof, sure, beyond reasonable doubt, confidence levels Author Notes: My sincere thanks to Roger Leng for casting an acute legal eye over this work and to Craig Callen for his patient and invaluable editing. Introduction The standard for proof of guilt in criminal cases is a matter of paramount importance to the fair and effective operation of the criminal justice system – all the more so at a time when there

and numerical integration is necessary to compute it. Instead of the actual value of σ2(λ̂) we use an estimate of it in (21). In the following section the approximate expectations given by (21) are examined by means of a simulation study. Point and Interval Estimation for the Lifetime Distribution of a k-Unit Parallel System 181 5 Simulation Study A simulation study is conducted to asses the performance of the maximum likelihood estimator with respect to bias and MSE for different progressively Type-II censoring scheme. The confidence levels of the approximate

DOI 10.1515/eqc-2013-0015 | Econ. Qual. Control 2013; 28(2): 77–88 Wenhao Gui* Acceptance Sampling Plans Under Truncated Life Tests Assuming a Half Exponential Power Life Distribution Abstract: In this paper, we consider acceptance sampling plans assuming a half exponential power life dis- tribution and a life test that is truncated at a preassigned time. For various acceptance numbers, confidence levels and values of the ratio of the true mean lifetime to the specified mean life, we determine the minimum sample size necessary to ensure a certain mean lifetime

_{i=0}^{c_{1}}\binom{n_{1}}{i}p^{i}(1-p)^{n_{1}-i}+\sum_{j=c_{1}+1}^{c_{2}% }\binom{n_{1}}{i}p^{i}(1-p)^{n_{1}-i}\Bigg{[}\sum_{i=0}^{c_{2}-j}\binom{n_{2}}% {j}p^{j}(1-p)^{n_{2}-j}\Biggr{]}\geq 1-\beta.$ For the proposed acceptance sampling plan ( n 1 , n 2 , c 1 = 0 , c 2 = 2 , t / σ 0 ) $({n_{1},n_{2},c_{1}=0,c_{2}=2,t/\sigma_{0}})$ at a specified consumer’s confidence level P ∗ $P^{\ast}$ , the smallest values of σ / σ 0 $\sigma/\sigma_{0}$ satisfying inequality ( 2 ) are summarized in Table 4 . Assume that the researcher wants to ensure that the true mean

Security and Emergency Management: Vol. 7: Iss. 1, Article 42. DOI: 10.2202/1547-7355.1709 An Analysis of Texas Sheriffs' Opinions Concerning Domestic Terrorism: Training, Equipment, Funding and Perceptions Regarding Likelihood of Attack James J. Vardalis and Shannon N. Waters Abstract Domestic terrorism continues to be a major concern for the United States. Despite the fact that County Sheriffs will have a critical role in dealing with public safety during and after a terrorist event, little is known regarding their confidence levels. The three main components that were

on Tables 3 and 4 it can be noted that the OC values almost approach one, specially for large values of μ / μ 0 {\mu/\mu_{0}} based on the single and double acceptance sampling plans. Also, the probability values based on the suggested DASP are larger than their counterparts based on the single acceptance sampling plan. For the acceptance sampling plan ( n 1 , n 2 , c 1 = 0 , c 2 = 2 , t / μ 0 ) {(n_{1},n_{2},c_{1}=0,c_{2}=2,t/\mu_{0})} at a specified consumer’s confidence level P * {P^{*}} , the smallest values of μ / μ 0 {\mu/\mu_{0}} satisfying ( 3

Econ. Qual. Control 2014; 29(1): 53–62 Amer Ibrahim Al-Omari Acceptance Sampling Plan Based on Truncated Life Tests for Three Parameter Kappa Distribution Abstract: This paper considers the problem of an acceptance sampling plan for a truncated life test when the lifetime follows the three parameter Kappa distribution. For different acceptance numbers, confidence levels and values of the ratio of the fixed experiment time to the specified lower bound of themean lifetime, themin- imum sample sizes necessary to ensure a specified mean lifetime are obtained. The

of t / μ 0 ${t/\mu_{0}}$ , we want to find the minimum sample size m such that μ ≥ μ 0 ${\mu\geq\mu_{0}}$ with confidence level P ∗ ${P^{\ast}}$ if the number of failures observed up to time t does not exceed c . Therefore, the required minimum sample size m is the smallest positive integer satisfying the inequality (3) ∑ i = 0 c ( m i ) ⁢ p i ⁢ ( 1 - p ) m - i ≤ 1 - P ∗ , $\sum_{i=0}^{c}\binom{m}{i}p^{i}(1-p)^{m-i}\leq 1-P^{\ast},$ assuming that the size of the lot is large enough so to apply the binomial distribution theory, where p = F ⁢ ( t ; μ 0

inlet gas temperature has the most significant effect on the yield, with a 95% confidence level. For the outlet moisture contents, the effects of fibre, the amount of solids in the extract and the inlet gas temperature are all significant at confidence levels above 97.5%. Hence inlet conditions appeared to be more important than outlet ones, lending support to the suggestion that the performance of the equipment is more strongly influenced by the particulate drying kinetics. KEYWORDS: spray drying, biological extracts, stickiness, yield Author Notes: The laboratory