Empirical Bayes confidence intervals shrinking both means and variances

Summary.  We construct empirical Bayes intervals for a large number p of means. The existing intervals in the literature assume that variances     are either equal or unequal but known. When the variances are unequal and unknown, the suggestion is typically to replace them by unbiased estimators     . However, when p is large, there would be advantage in 'borrowing strength' from each other. We derive double-shrinkage intervals for means on the basis of our empirical Bayes estimators that shrink both the means and the variances. Analytical and simulation studies and application to a real data set show that, compared with the t -intervals, our intervals have higher coverage probabilities while yielding shorter lengths on average. The double-shrinkage intervals are on average shorter than the intervals from shrinking the means alone and are always no longer than the intervals from shrinking the variances alone. Also, the intervals are explicitly defined and can be computed immediately.     

Guarded Weights Of Evidence And Acceptability Profiles Based On Signs: I. Permutation Arguments (With Discussion)

A test for a hypothesized parameter is generalized by replacing the indicator function of the test critical region with a function ('weight of evidence for the alternative') having values in [0,1] and estimating the value 1 when the alternative is true and 0 otherwise. It is a 'guarded' weight of evidence if a bound is placed on the Type I risk. The focus of this paper is on a guarded weight of evidence which is a function of the likelihood ratio of the sign statistic for a two-sided alternative to a point hypothesis regarding the centre of a symmetric distribution. Inversion of a family of such guarded weights of evidence yields an 'acceptability profile' for the median which is more informative than the traditional confidence interval for the median. The main results, with the exception of the comparison of the Type II risks with an envelope risk, are based entirely on permutation arguments.     

What is your research question? A mixed methods evaluation of an academic statistical consulting center

Academic consulting centers on research and statistics are the bridge between applied researchers and statisticians and thus at the core of university-wide research. The client-centered evaluation focused on investigating the perspective of the clients in university research and statistical consulting center. A mixed-methods methodology was used in this study, specifically a concurrent triangulation design was implemented to have multiple data sources collected and analyzed simultaneously in order to identify areas of overlapping information. The Research Consulting Scale (RCS) instrument was developed and analyzed using an exploratory factor analysis with 129 participants and resulted in two factors: consulting experience, and consulting facilities. The internal consistency reliability of the scores for these two factors was 0.89 and .86 respectively. These results support the RCS has strong internal consistency. Additionally, client interviews were conducted sampling from those who had responded to the survey in order to gather additional data. Thematic analysis was performed to interview data and resulted in two major themes: consultant expertise and consultancy skills. The results provide a survey instrument and key themes for university consulting centers to focus and assess their efficiency through client’s perspectives.     

Replication with MTurk of the experimental design by Gangadharan,Grossman, Jones & Leister (2018): Charitable giving across donor types

Understanding the motivations behind charitable giving and the identification of donor types have aroused growing interest among researchers. The economic literature has highlighted the model of pure altruist and subsequently the more realistic model of impure altruist or warm-glow giver. The need to distinguish and empirically identify these types of donors has given rise to some economic experiments. This paper - using the platform by Amazon's Mechanical Turk with a large sample of participants (N = 1062) - shows the findings of a near replication of the experimental design by Gangadharan et al. (2018). Results are consistent with the original study and confirm the validity of the procedure and the ability to replicate a critical feature of the original design.     

Estimating Listeria monocytogenes Growth in Ready-to-Eat Chicken Salad Using a Challenge Test for Quantitative Microbial Risk Assessment

Currently, there is a growing preference for convenience food products, such as ready-to-eat (RTE) foods, associated with long refrigerated shelf-lives, not requiring a heat treatment prior to consumption. Because Listeria monocytogenes is able to grow at refrigeration temperatures, inconsistent temperatures during production, distribution, and at consumer's household may allow for the pathogen to thrive, reaching unsafe limits. L. monocytogenes is the causative agent of listeriosis, a rare but severe human illness, with high fatality rates, transmitted almost exclusively by food consumption. With the aim of assessing the quantitative microbial risk of L. monocytogenes in RTE chicken salads, a challenge test was performed. Salads were inoculated with a three-strain mixture of cold-adapted L. monocytogenes and stored at 4, 12, and 16 °C for eight days. Results revealed that the salad was able to support L. monocytogenes’ growth, even at refrigeration temperatures. The Baranyi primary model was fitted to microbiological data to estimate the pathogen's growth kinetic parameters. Temperature effect on the maximum specific growth rate (μ_max) was modeled using a square-root-type model. Storage temperature significantly influenced μ_max of L. monocytogenes (p < 0.05). These predicted growth models for L. monocytogenes were subsequently used to develop a quantitative microbial risk assessment, estimating a median number of 0.00008726 listeriosis cases per year linked to the consumption of these RTE salads. Sensitivity analysis considering different time–temperature scenarios indicated a very low median risk per portion (<−7 log), even if the assessed RTE chicken salad was kept in abuse storage conditions.     

"应试教育"旗偃鼓不息,素质教育举步维艰--也谈目前的中学教育现状

应试教育的模式已被否定 ,素质教育正被倡导推行 ,但由于片面追求升学率的影响和利益的驱动 ,应试教育的现象仍然存在 ,素质教育举步维艰。改革应试教育 ,推进素质教育要从三个方面努力 :改革考试制度 ,改革教材和教学内容 ,明确考试主体观念     

英语WISH型虚拟语气的习得研究

以"注意假设"理论为载体,从认知语言学和心理语言学的角度来研究显性的形式加工输入和隐性的形式强化输入在中国语境下,对中国英语学习者习得Wish型虚拟语气的作用.借助统计学原理和方法,对所收集到的语料进行定性和定量分析.结果表明:显性的形式加工输入能促使中国英语学习者习得WISH型虚拟语气;而隐性的形武强化输入在这点上没有显示出优势.     

四川绿豆地方品种群体主要农艺性状的因子分析

利用因子分析法,把70个四川绿豆地方品种的13个主要农艺性状分成受7个独立公因子制约的7个性状群。这7个公因子是;f_1,荚粒数因子,它是由单株英数和单株粒数构成的;f_2,粒重因子,由百粒重、英长和英宽构成;f_3,节、枝数因子,由主茎节数,单株分枝数构成;f_4、f_5和f_6均由一个性状组成,分别称之为单荚粒数因子、株高因子和生育期因子;f_7,产量因子,由单株粒重,播种至开花日数和小区产量构成。受同一因子制约的所有性状称为因子群,文中建议在育种过程中按因子群进行性状选择。试验结果的分析表明,因子分析法是处理多种性状,确定数目较少的起主导作用的因子的一种有用方法,文中介绍了因子分析法的统计学原理和具体计算步骤。     

ON TESTING AGAINST RESTRICTED ALTERNATIVES FOR THE VARIANCES OF GAUSSIAN MODELS

Let π₁,…,π_p be p independent normal populations with means μ₁…, μ_p and variances σ²₁,…, σ²_p respectively. Let X(n_i) be a simple random sample of size n_i from π_i, i = 1,…,p. Given the simple random samples X(n₁),…, X(n_p) from π₁,…,π_p respectively, a test has been proposed for testing the homogeneity of variances H₀: σ²₁=…σ²_p, against the restricted alternative, H₁: σ²₁≥…≥σ²_p, with at least one strict inequality. Some properties of the test are discussed and critical values are tabulated.     

An application of a multi‐stage strategy involving confidence intervals to evaluate whether a response rate is favourable or not

In early clinical development of new medicines, a single‐arm study with a limited number of patients is often used to provide a preliminary assessment of a response rate. A multi‐stage design may be indicated, especially when the first stage should only include very few patients so as to enable rapid identification of an ineffective drug. We used decision rules based on several types of nominal confidence intervals to evaluate a three‐stage design for a study that includes at most 30 patients. For each decision rule, we used exact binomial calculations to determine the probability of continuing to further stages as well as to evaluate Type I and Type II error rates. Examples are provided to illustrate the methods for evaluating alternative decision rules and to provide guidance on how to extend the methods to situations with modifications to the number of stages or number of patients per stage in the study design. Copyright © 2004 John Wiley & Sons, Ltd.