Comparison of Type I Error Rates of Siegel-Tukey and Savage Tests among Non-Parametric Tests

This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviation ratio of 1, was conducted for both small and large sample sizes. For small sample sizes, two main categories were established: equal and different sample sizes. Analyses were performed using Monte Carlo simulations with 20,000 repetitions for each scenario, and the simulations were evaluated using SAS software. For small sample sizes, the I. type error rate of the Siegel-Tukey test generally ranged from 0.045 to 0.055, while the I. type error rate of the Savage test was observed to range from 0.016 to 0.041. Similar trends were observed for Platykurtic and Skewed distributions. In scenarios with different sample sizes, the Savage test generally exhibited lower I. type error rates. For large sample sizes, two main categories were established: equal and different sample sizes. For large sample sizes, the I. type error rate of the Siegel-Tukey test ranged from 0.047 to 0.052, while the I. type error rate of the Savage test ranged from 0.043 to 0.051. In cases of equal sample sizes, both tests generally had lower error rates, with the Savage test providing more consistent results for large sample sizes. In conclusion, it was determined that the Savage test provides lower I. type error rates for small sample sizes and that both tests have similar error rates for large sample sizes. These findings suggest that the Savage test could be a more reliable option when analyzing variance differences.

Effects of Multicollinearity on Type I Error of Some Methods of Detecting Heteroscedasticity in Linear Regression Model

Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of independence between the explanatory variables of the model. With these assumption violations, Ordinary Least Square Estimator (OLS) will not give best linear unbiased, efficient and consistent estimator. In practice, there are several structures of heteroscedasticity and several methods of heteroscedasticity detection. For better estimation result, best heteroscedasticity detection methods must be determined for any structure of heteroscedasticity in the presence of multicollinearity between the explanatory variables of the model. In this paper we examine the effects of multicollinearity on type I error rates of some methods of heteroscedasticity detection in linear regression model in other to determine the best method of heteroscedasticity detection to use when both problems exist in the model. Nine heteroscedasticity detection methods were considered with seven heteroscedasticity structures. Simulation study was done via a Monte Carlo experiment on a multiple linear regression model with 3 explanatory variables. This experiment was conducted 1000 times with linear model parameters of β0 = 4 , β1 = 0.4 , β2= 1.5 and β3 = 3.6. Five (5) levels of mulicollinearity are with seven (7) different sample sizes. The method’s performances were compared with the aids of set confidence interval (C.I.) criterion. Results showed that whenever multicollinearity exists in the model with any forms of heteroscedasticity structures, Breusch-Godfrey (BG) test is the best method to determine the existence of heteroscedasticity at all chosen levels of significance.

A Simulation Based Comparison of Correlation Coefficients with Regard to Type I Error Rate and Power

In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where the underlying distributions of the variables of interest, sample sizes and correlation patterns were varied. Simulation results showed that the Type I error rate and power of Pearson correlation coefficient were negatively affected by the distribution shapes especially for small sample sizes, which was much more pronounced for Spearman Rank and Kendal Tau correlation coefficients especially when sample sizes were small. In general, Permutation-based and Winsorized correlation coefficients are more robust to distribution shapes and correlation patterns, regardless of sample size. In conclusion, when assumptions of Pearson correlation coefficient are not satisfied, Permutation-based and Winsorized correlation coefficients seem to be better alternatives.

Sensitivity and Specificity Analysis Relation to Statistical Hypothesis Testing and Its Errors: Application to Cryptosporidium Detection Techniques

The use of Statistical Hypothesis Testing procedure to determine type I and type II errors was linked to the measurement of sensitivity and specificity in clinical trial test and experimental pathogen detection techniques. A theoretical analysis of establishing these types of errors was made and compared to determination of False Positive, False Negative, True Positive and True Negative. Experimental laboratory detection methods used to detect Cryptosporidium spp. were used to highlight the relationship between hypothesis testing, sensitivity, specificity and predicted values. The study finds that, sensitivity and specificity for the two laboratory methods used for Cryptosporidium detection were low hence lowering the probability of detecting a “false null hypothesis” for the presence of cryptosporidium in the water samples using either Microscopic or PCR. Nevertheless, both procedures for cryptosporidium detection had higher “true negatives” increasing its probability of failing to reject a “true null hypothesis” with specificity of 1.00 for both Microscopic and PCR laboratory detection methods.

无删失生存数据Wilcoxon秩和检验与logrank检验的比较

目的比较Wilcoxon秩和检验与logrank检验处理无删失生存数据的统计性能。方法采用Monte-Carlo模拟方法,应用SAS9.1.3软件编程,比较两种检验方法的I型错误率和检验效能。结果小样本情形(n≤50)下,Wilcoxon秩和检验的Ⅰ型错误率较logrank检验更接近检验水准0.05,而检验效能与logrank检验相差不大,后者检验效能的提高是以扩大Ⅰ型错误率为代价的。结论对于无删失生存数据的比较,尤其是小样本情形(n≤50)下,建议采用Wilcoxon秩和检验。

Comparison of dimension reduction-based logistic regression models for case-control genome-wide association study:principal components analysis vs.partial least squares

With recent advances in biotechnology, genome-wide association study （GWAS） has been widely used to identify genetic variants that underlie human complex diseases and traits. In case-control GWAS, typical statistical strategy is traditional logistical regression （LR） based on single-locus analysis. However, such a single-locus analysis leads to the well-known multiplicity problem, with a risk of inflating type I error and reducing power. Dimension reduction-based techniques, such as principal component-based logistic regression （PC-LR）, partial least squares-based logistic regression （PLS-LR）, have recently gained much attention in the analysis of high dimensional genomic data. However, the perfor- mance of these methods is still not clear, especially in GWAS. We conducted simulations and real data application to compare the type I error and power of PC-LR, PLS-LR and LR applicable to GWAS within a defined single nucleotide polymorphism （SNP） set region. We found that PC-LR and PLS can reasonably control type I error under null hypothesis. On contrast, LR, which is corrected by Bonferroni method, was more conserved in all simulation settings. In particular, we found that PC-LR and PLS-LR had comparable power and they both outperformed LR, especially when the causal SNP was in high linkage disequilibrium with genotyped ones and with a small effective size in simulation. Based on SNP set analysis, we applied all three methods to analyze non-small cell lung cancer GWAS data.

利用SASPROC MIXED分析混合线性模型非平衡试验数据

统计软件SAS中PROCMIXED的发展使得混合线性模型非平衡试验数据的分析在技术上变得简单可行。但在小样本非平衡数据条件下,选择怎样的自由度计算方法用于固定效应统计检验,才能取得较准确的分析结果,则是一个尚未明确的问题。本文利用PROCMIXED提供的几个自由度计算方法对3个常用农业试验设计的非平衡数据进行了分析。MonteCarlo模拟研究结果表明,Kenward Roger法能够取得第一类统计错误率的最佳控制。

关于一般非参数Behrens-Fisher问题的秩和检验方法

在随机化临床试验中,针对一般非参数Behrens-Fisher问题,经常采用O'Brien秩和检验法和Huang等人的秩和检验法。为此,对O'Brien秩和检验法进行改进,讨论新检验方法的统计性质,并模拟三个检验法犯第一类错误的概率和检验功效。结果显示:新检验方法犯第一类错误的概率往往低于O'Brien秩和检验法及Huang等人的秩和检验法,而且新检验方法的功效高于其它两种检验。

A New Maximum Test via the Dependent Samples t-Test and the Wilcoxon Signed-Ranks Test

A maximum test in lieu of forcing a choice between the two dependent samples t-test and Wilcoxon signed-ranks test is proposed. The maximum test, which requires a new table of critical values, maintains nominal α while guaranteeing the maximum power of the two constituent tests. Critical values, obtained via Monte Carlo methods, are uniformly smaller than the Bonferroni-Dunn adjustment, giving it power superiority when testing for treatment alternatives of shift in location parameter when data are sampled from non-normal distributions.

An Overview of Personal Credit Scoring: Techniques and Future Work

Personal credit scoring is the application of financial risk forecasting. It becomes an even important task as financial institutions have been experiencing serious competition and challenges. In this paper, the techniques used for credit scoring are summarized and classified and the new method—ensemble learning model is introduced. This article also discusses some problems in current study. It points out that changing the focus from static credit scoring to dynamic behavioral scoring and maximizing revenue by decreasing the Type I and Type II error are two issues in current study. It also suggested that more complex models cannot always been applied to actual situation. Therefore, how to use the assessment models widely and improve the prediction accuracy is the main task for future research.

Sequential Test of Fuzzy Hypotheses

In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first give new definitions for notion of mass (density) probability function with fuzzy parameter, probability of type I and type II errors and then state and prove the sequential probability ratio test, on the basis of these new errors, for testing fuzzy hypotheses. Numerical examples are also provided to illustrate the approach.

希望区域法在临床试验适应性设计中的准确性和稳健性研究

目的评估希望区域法应用于适应性设计样本量再估计的准确性及稳健性,为该方法的适用条件提供理论参考。方法以二分类资料为例,以包含期中分析的两阶段适应性试验为框架,采用Monte Carlo方法,在相同的组间响应率率差、同合并率等参数的模拟场景下,比较固定样本量设计、成组序贯设计和希望区域法进行样本量再估计的准确性和稳健性。结果模拟研究显示希望区域法在期中检验效能落入希望区域内进行适应性样本量调整时,Ⅰ类错误与同场景下固定设计和成组序贯设计近似。初始估计样本量被低估时,希望区域法比固定设计的检验效能平均提高约5%,比成组序贯设计提高约8.8%,样本量比固定设计多耗费0.18倍,比成组序贯设计多0.38倍。高估初始估计样本量时,三种设计的检验效能相差仅在1%左右,但希望区域法比固定设计多消耗7.5%、比成组序贯设计多耗费48%的样本量。结论相比于固定样本量及成组序贯设计,希望区域法对于试验的整体检验效能提高不大,其平均样本量均大于相同设定场景下的固定设计及成组序贯设计,使用该设计方法时应谨慎权衡试验收益。

认知诊断模型中题目拟合评估的研究

有效应用认知诊断模型(cognitive diagnosis model,CDM)的一个关键步骤是检查模型和测验题目是否拟合。尽管已有研究将IRT中的题目拟合检验方法应用于CDM中,然而这些方法在CDM中的表现仍缺乏系统的比较研究。本研究通过模拟实验比较了χ2,G2,S-χ2,z(r),z(l)和Stone-Q1的一类错误率和统计检验力。实验结果显示,综合一类错误率和统计检验力而言,当用ACDM作为生成模型时,z(r)和z(l)的效果最优;当生成模型是DINA或DINO时,在高质量测验中,z(r)的表现最好,而在低质量测验中,χ2和G2的表现更好。最后通过一个实测数据分析,进一步检验了题目拟合检验方法的实证应用效果。

P值的显式表达式及其概率分布性质

针对几个常见的假设检验问题,首先给出检验P值的显式表达式,然后推导出P值作为一个随机变量的概率分布,接着证明P值在满足如下三个条件下服从均匀分布:真实参数为最接近对立假设的原假设参数值、检验统计量的相应零分布被正确指定、该零分布的分布函数可逆.

定性数据的多重比较问题

目的阐述定性数据多重比较方法,提出构成比多重比较检验水准校正方法。方法针对构成比多重比较的特殊性,应用Bonferroni法原理,并通过Monte Carlo方法在SAS9.13环境编程模拟验证,提出检验水准的调整方法。结果对于多个率或构成比资料,如果将其分解为若干四格表进行多重比较而不调整检验水准,会导致扩大I类错误的后果。对于构成比的多重比较,校正数并非一般多重比较的两两比较组合数,而是组合数减1,该结果得到了模拟结果的验证。结论应正确运用定性数据的多重比较方法,构成比的多重比较因自由度约束其校正数为组合数减1。

多阶段增长模型的方法比较

多阶段增长模型(Piecewise Growth Modeling,PGM)可以解决发展趋势中具有转折点的情形,并且相对其他复杂的曲线增长模型,解释更简单。已有的统计方法主要通过多层线性模型和潜变量增长模型对多阶段模型进行估计。通过模拟研究,用HLM6.0和Mplus6.0对上述两种模型分别进行估计,结果发现在参数估计的精度上,两种估计方法没有差异,只是在犯一类错误的概率上后者略小。进一步通过对错误模型的探讨发现,在样本量小(n=50),斜率变化小(Δb=0.2)时,用线性模型拟合数据而非PGM所犯错误概率较小,整体拟合更佳。但随着样本的增加和斜率变化的增加,错误模型的犯错概率明显增大。故在实际应用中,为了能更好拟合数据,研究者应根据数据本身的情况选择恰当的模型。

成组设计两样本率非劣效性检验方法的比较研究

目的对非劣效性检验的不同方法进行比较研究。方法通过计算正态分布法和精确检验的Ⅰ类错误与检验效能,对两种方法做出比较与评价。结果小样本或两组样本例数相差悬殊时,正态分布法的Ⅰ类错误可能会超过名义上的检验水准;多数情况下正态分布法的检验效能高于精确检验,但是在小样本或两组样本例数相差悬殊时,会出现精确检验的检验效能较高的情况。结论定性资料的非劣效性检验在大样本时应该选择正态分布法,但是在小样本或两组样本例数相差悬殊时,需要考虑采用精确检验。

研究课题与统计方法的互相促进

讨论了证实性因素分析、结构公式模型、多层线性模型与传统的探索性因素分析、方差分析的不同，分析了体育科学研究中均数比较的常见错误。指出研究课题的深入体现在：需要考虑的变量增多，变量的交互作用增多，从而导致统计技术的进步；而统计技术的进步推动人们进行更加深入的研究，两者相辅相成。科学研究的现象虽然是从简单到复杂，但理论概括却仍需具备简洁性。

水产科学研究中被忽视的Ⅱ型错误

显著性检验利用样本信息来判断对总体所做假设的合理性,检验结果可能犯2类错误,即I型错误和Ⅱ型错误(分别为弃真错误和纳伪错误)。随着水产科学研究的不断规范与深入,显著性检验方法的使用越来越频繁。在国内6个水产期刊近5年(2011年1月–2015年4月)发表的3 829篇学术文章中,使用了显著性检验方法的有2 235篇,占到58.4%。然而,这些显著性检验均只关注了I型错误,完全忽略了对Ⅱ型错误的分析。事实上,Ⅱ型错误并非不重要,犯该错误的概率也往往会大于I型错误,而且有时其带来的危害比I型错误更加严重。在水产科学研究中同样如此,对Ⅱ型错误的忽视,很可能导致管理失误,从而引起渔业资源衰退。本研究对国内外水产科学研究中Ⅱ型错误分析的应用进行了总结,阐明了国内水产科学研究中有关Ⅱ型错误分析缺失的现状;通过实例,简要介绍了犯Ⅱ型错误概率β(或检验效能power=1–β)的计算方法;分析阐述了影响检验效能的几个主要因素与β之间的关系;针对Ⅱ型错误分析,探讨今后水产科学研究与管理中需要注意的问题,并对其未来发展进行了展望。

随机化检验在内部预试验自适应设计样本量调整中的应用

目的:探讨随机化检验(Randomization test)在内部预试验IPS(Internal Pilot Study)自适应设计样本量调整中对I型错误和检验效能的影响.方法:利用蒙特-卡罗(MonteCarlo)法模拟样本量较小时的IPS样本量调整,分别采用随机化检验和t检验分析最后数据并比较二者对I型错误、检验效能值的影响.结果:重计算的第二阶段样本量波动性较大,t检验不能很好地抑制I型错误,随机化检验能较好的抑制I型错误,检验效能略有降低.结论:在临床试验样本量较小的情况下,内部预试验盲态下样本量调整后随机化检验能保护I型错误不增大,同时保证检验效能亦满足要求.