略谈假设检验中零假设的确定

假设检验是统计推断的重要内容,而假设检验问题首先便面临零假设的确定。本文中笔者试图通过对假设检验的统计逻辑分析,认识零假设与被择假设的非对称性,探索针对具体统计问题零假设的确定方法,并尝试以双向检验的办法解决零假设与被择假设地位有争议情况下的假设检验问题。     

解析显著性水平及应用

文章从正态分布“3σ”准则出发,结合中心极限定理,从概率与统计的角度,对基本概念显著性水平a进行了简明剖析,对与此概念密切相关的参数估计和假设检验问题进行了详细解读,并利用风险决策中有关原理,结合实际问题进行合理的统计推断与科学决策.     

决策规则均值检验时的样本容量确定

开展抽样调查,观察样本的抽取规模是需要慎重对待的问题,因为它不仅决定着样本推断的统计效果,同时也关系到决策分析的经济性。均值是一个十分常用的统计特征数字。文章根据统计决策的基本原理,对均值假设检验时所需要的样本量进行了讨论,并给出了具体的计算公式。     

多重假设检验及其在经济计量中的应用

 基于错误发现率(FDR: False Discovery Rate)的多重假设检验（MHT：Multiple Hypothesis Testing），已成为一种有效解决大规模统计推断问题的新方法。本文以错误控制为主线，对多重假设检验问题的错误控制理论、方法、过程和最新进展进行综述，并对多重假设检验方法在经济计量中的应用进行展望。     

含方程误差的重复测量误差模型参数的假设检验

含方程误差的重复测量误差模型解决了协变量真值与响应变量真值之间存在的不完全匹配问题.为使中小型样本量下的假设检验结果更为准确,文章基于多元正态分布推导改进形式的Skovgaard似然比检验统计量,提高其在原假设下收敛到卡方分布的渐近速度,并应用该检验统计量对重复测量误差模型中回归参数的显著性进行假设检验.模拟研究的结果表明改进的似然比检验统计量在有限样本检验下的优越性;实例分析中通过检验气温与气压之间回归参数的显著性来说明该方法的实用性.     

贝叶斯假设检验与经典假设检验的对比研究

文章基于对经典假设检验和贝叶斯检验的对比研究,指出了经典假设检验在使用中存在的一些问题,给出了贝叶斯统计对这些问题的处理方法。     

巧用SPSS做均值向量检验

文章基于两总体均值比较的特殊情形(样本容量n2=1),推导出其统计量F2与单总体均值向量检验中的统计量F1之间的关系表达式。这样,为了实现用SPSS做单总体均值向量的假设检验,可以将均值μ0视作随机样本Y来做两总体均值比较的假设检验,可以得到F2的值,进而通过关系表达式求得F1的值,然后,用F检验法完成这个的假设检验问题。最后,文章通过一个实例验证了该方法的快捷。     

假设检验在质量管理中的运用

假设检验是推断统计的重要内容,本文运用这一统计分析方法对某独资企业中国生产的助听器和总部生产的助听器进行显著性检验,从而分析和解决产品生产中存在的问题,收到了较好的效果。     

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。     

灰色统计相关系数探讨

文章在灰色系统理论的基础上,建立了在随机样本信息下,相关分析的相关系数灰色统计假设检验方法,应用于实例与经典的N-P假设检验方法进行比较,从而说明灰色统计估计和假设检验方法能够提供更多的有效信息,以便解决更多带有灰色的数据系统研究.     

A Five-Decision Testing Procedure to Infer the Value of a Unidimensional Parameter

ABSTRACT

A statistical test can be seen as a procedure to produce a decision based on observed data, where some decisions consist of rejecting a hypothesis (yielding a significant result) and some do not, and where one controls the probability to make a wrong rejection at some prespecified significance level. Whereas traditional hypothesis testing involves only two possible decisions (to reject or not a null hypothesis), Kaiser’s directional two-sided test as well as the more recently introduced testing procedure of Jones and Tukey, each equivalent to running two one-sided tests, involve three possible decisions to infer the value of a unidimensional parameter. The latter procedure assumes that a point null hypothesis is impossible (e.g., that two treatments cannot have exactly the same effect), allowing a gain of statistical power. There are, however, situations where a point hypothesis is indeed plausible, for example, when considering hypotheses derived from Einstein’s theories. In this article, we introduce a five-decision rule testing procedure, equivalent to running a traditional two-sided test in addition to two one-sided tests, which combines the advantages of the testing procedures of Kaiser (no assumption on a point hypothesis being impossible) and Jones and Tukey (higher power), allowing for a nonnegligible (typically 20%) reduction of the sample size needed to reach a given statistical power to get a significant result, compared to the traditional approach.     

Abandon Statistical Significance

ABSTRACT

We discuss problems the null hypothesis significance testing (NHST) paradigm poses for replication and more broadly in the biomedical and social sciences as well as how these problems remain unresolved by proposals involving modified p-value thresholds, confidence intervals, and Bayes factors. We then discuss our own proposal, which is to abandon statistical significance. We recommend dropping the NHST paradigm—and the p-value thresholds intrinsic to it—as the default statistical paradigm for research, publication, and discovery in the biomedical and social sciences. Specifically, we propose that the p-value be demoted from its threshold screening role and instead, treated continuously, be considered along with currently subordinate factors (e.g., related prior evidence, plausibility of mechanism, study design and data quality, real world costs and benefits, novelty of finding, and other factors that vary by research domain) as just one among many pieces of evidence. We have no desire to “ban” p-values or other purely statistical measures. Rather, we believe that such measures should not be thresholded and that, thresholded or not, they should not take priority over the currently subordinate factors. We also argue that it seldom makes sense to calibrate evidence as a function of p-values or other purely statistical measures. We offer recommendations for how our proposal can be implemented in the scientific publication process as well as in statistical decision making more broadly.     

Non parametric hypothesis tests for comparing reliability functions

In reliability and related disciplines, comparing reliability functions of two (or more) aging processes is a crucial step in the process of determining reliability and understanding an aging process. The aim of this paper is to propose a non parametric statistical methodology to compare two populations based on their mean residual life function and expected inactivity time function. We introduce some novel hypothesis testing procedures that involve both Cramér–von Mises- and Kolmogorov–Smirnov-type test statistics and their decision rules are constructed based on the asymptotic distributions of these test statistics and bootstrapping method. We study the practical behavior of the proposed testing procedures extensively through simulations. The results reveal that the proposed hypothesis testing procedures perform efficiently in identifying small and large differences. Two real-life examples are discussed to demonstrate the practical utility of the tests.     

Bayesian optimal phase II designs with dual-criterion decision making

The conventional phase II trial design paradigm is to make the go/no-go decision based on the hypothesis testing framework. Statistical significance itself alone, however, may not be sufficient to establish that the drug is clinically effective enough to warrant confirmatory phase III trials. We propose the Bayesian optimal phase II trial design with dual-criterion decision making (BOP2-DC), which incorporates both statistical significance and clinical relevance into decision making. Based on the posterior probability that the treatment effect reaches the lower reference value (statistical significance) and the clinically meaningful value (clinical significance), BOP2-DC allows for go/consider/no-go decisions, rather than a binary go/no-go decision. BOP2-DC is highly flexible and accommodates various types of endpoints, including binary, continuous, time-to-event, multiple, and coprimary endpoints, in single-arm and randomized trials. The decision rule of BOP2-DC is optimized to maximize the probability of a go decision when the treatment is effective or minimize the expected sample size when the treatment is futile. Simulation studies show that the BOP2-DC design yields desirable operating characteristics. The software to implement BOP2-DC is freely available at www.trialdesign.org .     

Fitting DNA sequences through log-linear modelling with linear constraints

For some discrete state series, such as DNA sequences, it can often be postulated that its probabilistic behaviour is given by a Markov chain. For making the decision on whether or not an uncharacterized piece of DNA is part of the coding region of a gene, under the Markovian assumption, there are two statistical tools that are essential to be considered: the hypothesis testing of the order in a Markov chain and the estimators of transition probabilities. In order to improve the traditional statistical procedures for both of them when stationarity assumption can be considered, a new version for understanding the homogeneity hypothesis is proposed so that log-linear modelling is applied for conditional independence jointly with homogeneity restrictions on the expected means of transition counts in the sequence. In addition we can consider a variety of test-statistics and estimators by using φ-divergence measures. As special case of them the well-known likelihood ratio test-statistics and maximum-likelihood estimators are obtained.     

Bayesian inference method for model validation and confidence extrapolation

This paper presents a Bayesian-hypothesis-testing-based methodology for model validation and confidence extrapolation under uncertainty, using limited test data. An explicit expression of the Bayes factor is derived for the interval hypothesis testing. The interval method is compared with the Bayesian point null hypothesis testing approach. The Bayesian network with Markov Chain Monte Carlo simulation and Gibbs sampling is explored for extrapolating the inference from the validated domain at the component level to the untested domain at the system level. The effect of the number of experiments on the confidence in the model validation decision is investigated. The probabilities of Type I and Type II errors in decision-making during the model validation and confidence extrapolation are quantified. The proposed methodologies are applied to a structural mechanics problem. Numerical results demonstrate that the Bayesian methodology provides a quantitative approach to facilitate rational decisions in model validation and confidence extrapolation under uncertainty.     

假设检验的一个常见误区

文章通过对假设检验的一个常见错误进行了理论分析,指出假设检验的方法只能在一定情况下否定原假设而不能肯定原假设,并提出了设定原假设和备择假设的正确而简明的方法。     

Some Remarks on Statistical Education

A definition of the subject of statistics is given, and the difference between the chalkboard world of the teacher of statistics and the real world of the experimenter is stressed. An overemphasis on significance testing, hypothesis testing, and decision procedures has led to a de-emphasis of statistical design. The teaching of statistical design theory, statistics teaching in a changing world, the importance of model building, and different approaches to teaching statistics are discussed. Some published materials developed to meet teaching needs and a new type of statistics course are described. Information about special issues in statistical education (teaching and consulting) is presented.     

Improved bonferroni procedures for testing overall and pairwise homogeneity hypotheses

Simes' (1986) improved Bonferroni test is verified by simulations ^?to control the α-level when testing the overall homogeneity hypothesis with all pairwise t statistics in a balanced parallel group design. Similarly, this result was found to hold (for practical purposes) in various underlying distributions other than the normal and in some unbalanced designs. To allow the use of step-up procedures based on pairwise t statistics, simulations were used to verify that Simes' test, when applied to testing multiple subset homogeneity hypotheses with pairwise t statistics also keeps the level ? α. Some robustness as above was found here too. Tables of the simulation results are provided and an example of a step-up Hommel-Shaffer type procedure with pairwise comparisons is given.     

Uniformly most powerful unbiased test in univariate linear calibration

In this paper, we deal with the hypothesis testing problems for the univariate linear calibration, where a normally distributed response variable and an explanatory variable are involved, and the observations of the response variable corresponding to known values of the explanatory variable are used for making inferences concerning a single unknown value of the explanatory variable. The uniformly most powerful unbiased tests for both one-sided and two-sided hypotheses are constructed and verified. The power behaviour of the proposed tests is numerically compared with that of the existing method, and simulations show that the proposed tests make the powers improved.