单侧假设检验中备择假设的设定依据

本文从假设检验的基本原理出发,检讨假设检验的逻辑哲学基础,指出假设检验应从备择假设入手,把希望证明的命题放在备择假设上,统计结论的正确理解只有接受备择假设,拒绝原假设;没有接受原假设,拒绝备择假设,最后指出了现行教科书中对假设检验的错误定义和结论表述的不准确,以及学生在学习过程中和一些研究文章中普遍存在的几个错误观点。     

沉默权与统计检验

生活中的许多小事,都可以通过统计检验来验证这种事发生的概率大约有多大,并通过统计来检验这种事物之间的相互关系.从统计检验上来讲,任何统计假设都有"拒真"错误与"存伪"错误."拒真"错误是指当我们在一定置信度下比较自信的拒绝虚假设时,有很少的可能犯错误,把不应该拒绝的也给拒绝了."存伪"错误是指当我们在一定的置信度下不能拒绝虚假设时,有可能会接受错眄误的虚假设,所以这时我们也不应该欣然接受虚假设.     

论数理统计中的拒真与纳伪概率

实际推断原理为我们提供了检验统计假设的方法,即做一次试验,如果小概率事件A发生了,则我们有理由怀疑假设H0,但事实上这种检验法本身,并不是从逻辑上严格论证明H0正确与否,在统计中我们不能证明任何统计假设的真伪,而是对统计假设作出拒绝或接受的判断,而这样作统计判断本身就有可能犯错误。即第一类错误a的概率与第二类错误β概率。但是这两类错误在教学中一般没有过多,过深涉及,以至于它们之间内在联系,往往给初学者带来了误解,本文将就此作进一步的讨论,仅供参考。1.β概率是统计推断本身方法产生的,在进行假设时.如果不否定原假设H0,…     

EXCEL在假设检验中的应用

一、基本原理假设检验是推断统计中的一项重要内容 ,它先对研究总体的参数作出某种假设 ,然后从所研究总体中抽取样本进行观察 ,用样本所提供的信息对假设的正确性进行判断 ,从而决定假设是否成立。若观察结果与理论不符 ,则须放弃假设 ;否则 ,认为无充分证据表明假设错误。假设检验的一般步骤是 :提出零假设和备择假设 ;确定适当的检验统计量并计算其值 ;根据显著性水平α定出拒绝区 ;作出最终结论。二、单个样本的假设检验对单个样本的假设检验 ,我们可以根据抽样推断的思路 ,用相应函数计算临界值 ,来判断是接受还是拒绝零假设。以检验均…     

实践中的假设检验

假设检验是《统计学》中很重要的内容。许多《统计学》教材都花很多笔墨详细介绍,并解释假设检验的结果如何分析。《统计学》(贾俊平编著,中国人民大学出版社2008年11月第3版)做了这样的描述:假设检验得出的结论都是根据原假设进行阐述的。我们要么拒绝原假设,要么不拒绝原假     

统计学教材中的几个问题

一、关于参数假设检验中原假设的提出假设检验是重要的统计推断内容,被广泛用于各领域、各学科,但不少教材却存在严重的错误,其错误主要是原假设的给出,特别是单边检验原假设的提出。笔者认为根据实际问题提出原假设是假设检验中最重要的一环,原假设的错误将导致结论的错误。而对一个具体的实际问题,原假设是唯一的,且不以检验者的主观意志为转移。以下给出笔者认为正确的提法。     

如何在假设检验中设立原假设

本文结合生物统计案例,对假设检验中有关单侧检验的问题,以及假设检验的两类错误、原假设与备择假设、单侧检验中原假设的设定等方面进行了探讨。     

参数检验中的错误控制及其运用

一、参数检验中的两类错误 统计参数检验是统计推断的两个主要内容之一,是用样本信息鉴定有关总体参数假设的正确性,依据的原理是小概率事件在一次试验当中不可能发生的原理。通常根据某一实际问题在假设中提供两个截然相反的关于总体参数的假设——原假设(H0)和备择假设(Ha),然后基于样本所携带的信息进行推断,在H0和Ha中挑选其一作为我们对总体参数的判断。当然期望的结果是:当H0中所作假设为真时,接受H0,拒绝Ha;反之当Ha为真时,接受Ha,拒绝H0,     

统计假设检验中小概率原理的辨析

假设检验是统计学的核心内容之一,其基本逻辑就是小概率原理,文章从观察数据与原假设的差异与相应概率的联系分析中,阐述了统计假设检验的小概率原理,揭示了假设检验的内在方法论基础。     

β值的运用

在假设检验过程中,两类错误——第一类错误、第二类错误是始终与我们的最终判断相依相随的。设定好检验假设H0、Ha,根据样本信息如果判定H0为真并接受H0假设,则结论之中包含了发生第二类错误的可能,即“以假为真”的可能;反之如果认为H0为假而拒绝H0,     

资源获得与私企成功——对广东私营企业的初步研究

改革开放以来 ,中国的私营经济发展迅速 ,已经成为国民经济的重要组成部分。据统计 ,截止 1999年 6月底 ,全国私营企业已达 12 8万户 ,比去年增加8万户 ,从业人员达 1784万人。① 因此对中国私营企业的研究具有愈来愈强的实践意义。同时 ,由于中国的私营企业是在特殊的制度转型背景下发育生长起来的 ,因而对其进行研究又具有特殊的理论意义。对研究者而言 ,当前中国私营企业对外界封闭的特点 ,决定了必须和他们有一定的“关系” ,才易于得到合作 ,获取较翔实的资料。由于特殊的环境和历史机遇 ,广东的私营企业发展较早 ,可以提供较好的研究…     

The efficient integration of abundance and demographic data

Summary. A drawback of a new method for integrating abundance and mark–recapture–recovery data is the need to combine likelihoods describing the different data sets. Often these likelihoods will be formed by using specialist computer programs, which is an obstacle to the joint analysis. This difficulty is easily circumvented by the use of a multivariate normal approximation. We show that it is only necessary to make the approximation for the parameters of interest in the joint analysis. The approximation is evaluated on data sets for two bird species and is shown to be efficient and accurate.     

An efficient numerical algorithm for exact inference in meta analysis

The performance of commonly used asymptotic inference procedures for the random-effects model used in meta analysis relies on the number of studies. When the number of studies is moderate or small, the exact inference procedure is more reliable than the asymptotic counterparts. However, the related numerical computation may be demanding and an obstacle of routine use of the exact method. In this paper, we proposed a novel numerical algorithm for constructing the exact 95% confidence interval of the location parameter in the random-effects model. The algorithm is much faster than the naive method and may greatly facilitate the use of the more appropriate exact inference procedure in meta analysis. Numerical studies and real data examples are used to illustrate the advantage of the proposed method.     

Bootstrap bias corrections for ensemble methods

This paper examines the use of a residual bootstrap for bias correction in machine learning regression methods. Accounting for bias is an important obstacle in recent efforts to develop statistical inference for machine learning. We demonstrate empirically that the proposed bootstrap bias correction can lead to substantial improvements in both bias and predictive accuracy. In the context of ensembles of trees, we show that this correction can be approximated at only double the cost of training the original ensemble. Our method is shown to improve test set accuracy over random forests by up to 70% on example problems from the UCI repository.     

The perils with the misuse of predictive power

In early drug development, especially when studying new mechanisms of action or in new disease areas, little is known about the targeted or anticipated treatment effect or variability estimates. Adaptive designs that allow for early stopping but also use interim data to adapt the sample size have been proposed as a practical way of dealing with these uncertainties. Predictive power and conditional power are two commonly mentioned techniques that allow predictions of what will happen at the end of the trial based on the interim data. Decisions about stopping or continuing the trial can then be based on these predictions. However, unless the user of these statistics has a deep understanding of their characteristics important pitfalls may be encountered, especially with the use of predictive power. The aim of this paper is to highlight these potential pitfalls. It is critical that statisticians understand the fundamental differences between predictive power and conditional power as they can have dramatic effects on decision making at the interim stage, especially if used to re-evaluate the sample size. The use of predictive power can lead to much larger sample sizes than either conditional power or standard sample size calculations. One crucial difference is that predictive power takes account of all uncertainty, parts of which are ignored by standard sample size calculations and conditional power. By comparing the characteristics of each of these statistics we highlight important characteristics of predictive power that experimenters need to be aware of when using this approach.     

A deletion/substitution/addition algorithm for classification neural networks,with applications to biomedical data

Neural networks are a popular machine learning tool, particularly in applications such as protein structure prediction; however, overfitting can pose an obstacle to their effective use. Due to the large number of parameters in a typical neural network, one may obtain a network fit that perfectly predicts the learning data, yet fails to generalize to other data sets. One way of reducing the size of the parmeter space is to alter the network topology so that some edges are removed; however it is often not immediately apparent which edges should be eliminated. We propose a data-adaptive method of selecting an optimal network architecture using a deletion/substitution/addition algorithm. Results of this approach to classification are presented on simulated data and the breast cancer data of Wolberg and Mangasarian [1990. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proc. Nat. Acad. Sci. 87, 9193–9196].     

Robust inference for group sequential trials

For ethical reasons, group sequential trials were introduced to allow trials to stop early in the event of extreme results. Endpoints in such trials are usually mortality or irreversible morbidity. For a given endpoint, the norm is to use a single test statistic and to use that same statistic for each analysis. This approach is risky because the test statistic has to be specified before the study is unblinded, and there is loss in power if the assumptions that ensure optimality for each analysis are not met. To minimize the risk of moderate to substantial loss in power due to a suboptimal choice of a statistic, a robust method was developed for nonsequential trials. The concept is analogous to diversification of financial investments to minimize risk. The method is based on combining P values from multiple test statistics for formal inference while controlling the type I error rate at its designated value.This article evaluates the performance of 2 P value combining methods for group sequential trials. The emphasis is on time to event trials although results from less complex trials are also included. The gain or loss in power with the combination method relative to a single statistic is asymmetric in its favor. Depending on the power of each individual test, the combination method can give more power than any single test or give power that is closer to the test with the most power. The versatility of the method is that it can combine P values from different test statistics for analysis at different times. The robustness of results suggests that inference from group sequential trials can be strengthened with the use of combined tests.     

Some exact tables for the squared ranks test

Since the squared ranks test was first proposed by Taha in 1964 it has been mentioned by several authors as a test that is easy to use, with good power in many situations. It is almost as easy to use as the Wilcoxon rank sum test, and has greater power when two populations differ in their scale parameters rather than in their location parameters. This paper discuss the versatility of the squared ranks test, introduces a test which uses squared ranks, and presents some exact tables     

Sample size determination and treatment screening in two‐stage phase II clinical trials via ROC curve

In pharmaceutical‐related research, we usually use clinical trials methods to identify valuable treatments and compare their efficacy with that of a standard control therapy. Although clinical trials are essential for ensuring the efficacy and postmarketing safety of a drug, conducting clinical trials is usually costly and time‐consuming. Moreover, to allocate patients to the little therapeutic effect treatments is inappropriate due to the ethical and cost imperative. Hence, there are several 2‐stage designs in the literature where, for reducing cost and shortening duration of trials, they use the conditional power obtained from interim analysis results to appraise whether we should continue the lower efficacious treatments in the next stage. However, there is a lack of discussion about the influential impacts on the conditional power of a trial at the design stage in the literature. In this article, we calculate the optimal conditional power via the receiver operating characteristic curve method to assess the impacts on the quality of a 2‐stage design with multiple treatments and propose an optimal design using the minimum expected sample size for choosing the best or promising treatment(s) among several treatments under an optimal conditional power constraint. In this paper, we provide tables of the 2‐stage design subject to optimal conditional power for various combinations of design parameters and use an example to illustrate our methods.     

Assessing and Improving the Performance of Nearly Efficient Unit Root Tests in Small Samples

Abstract

The development of unit root tests continues unabated, with many recent contributions using techniques such as generalized least squares (GLS) detrending and recursive detrending to improve the power of the test. In this article, the relation between the seemingly disparate tests is demonstrated by algebraically nesting all of them as ratios of quadratic forms in normal variables. By doing so, and using the exact sampling distribution of the ratio, it is straightforward to compute, examine, and compare the test' critical values and power functions. It is shown that use of GLS detrending parameters other than those recommended in the literature can lead to substantial power improvements. The open and important question regarding the nature of the first observation is addressed. Tests with high power are proposed irrespective of the distribution of the initial observation, which should be of great use in practical applications.