The differences and similarities between two-sample t-test and paired t-test

临床研究中经常遇到比较实验组和对照组之间的结果。双样本t检验(又称为独立样本t检验)和配对t检验可能是运用于比较两个样本之间均值的最广泛的统计方法。然而,这两种方法的运用会产生混淆,从而导致使用不当。本文中,我们讨论了这两种t检验之间的异同性,并运用三个范例来阐述双样本t检验和配对t检验的计算过程。

Failure and limit energy of aircraft brake pairs

The test methods of the limit energy of aircraft brake pairs and the confirming methods for their failure were introduced. The test results of the rejected take-off (RTO) of brake pairs were analyzed. It is confirmed that the failure reality for brake pair is the destruction of the friction materials. Therefore, after the limit energy test of brake pairs, three criteria for their failure were put forword. The definition of the maximum brake pressure and the selection of the initial test energy were introduced. The products of USA and domestic substitute of brake pairs for Boeing 737 airplane were tested by these methods. The test results show that the limit energy of brake pairs can be determined by 2 or 3 experiments, thus the test cost is reduced.

New Nonparametric Rank-Based Tests for Paired Data

We propose a new nonparametric test based on the rank difference between the paired sample for testing the equality of the marginal distributions from a bivariate distribution. We also consider a modification of the novel nonparametric test based on the test proposed by Baumgartern, Weiβ, and Schindler (1998). An extensive numerical power comparison for various parametric and nonparametric tests was conducted under a wide range of bivariate distributions for small sample sizes. The two new nonparametric tests have comparable power to the paired t test for the data simulated from bivariate normal distributions, and are generally more powerful than the paired t test and other commonly used nonparametric tests in several important bivariate distributions.

Tests for paired count outcomes

Paired t-tests are widely used to compare differences in paired continuous outcomes. This test, however, does not apply to non-continuous outcomes. For binary outcomes,McNemar's test is the de facto method for comparing differences in paired binary variables. For count or frequency outcomes, there is not much discussion in the literature. The Wilcoxon signed-rank test is often used to assess differences in paired count outcomes. However, like the Mann-Whitney U test, or Wilcoxon rank-sum test for comparing two independent groups, the Wilcoxon signedrank test is generally not efficient(powerful). In this essay,we consider some alternative methods for comparing paired count outcomes and compare them with the Wilcoxon signed-rank test using Monte Carlo simulations.

Architecture and Methodology of Unit Testing Embedding Pair-Wise Mode for Small Team

In this paper, the new organization for unit testing embedding pair-wise mode is proposed with the core thought focused on the cooperation of programmer and tester by “cross-testing”. The typical content of unit testing for the new organizing mode should have three aspects, including self-checking, cross-testing and independent-testing. For cross-testing, executing “pair-wise” mode, mainly tackles data testing, function testing and state testing, which function testing must be done by details and state testing must be considered for completeness. With the specializing of independent-testing, it should be taken as more rigid testing without arbitrariness. Consequently, strategy and measure are addressed for data testing focusing on boundary testing and function/state testing. And organizing method of procedure and key points of tackling unit testing are investigated for the new organizing mode. In order to assess the validity of our study and approach, a series of actual examples are demonstrated for GUI software. The result indicates that the execution of unit testing for the new organizing mode is effective and applicable.

RESEARCH ON DISTRIBUTION PAIR OFBENT-AXIS PUMP

The oil film thickness of the distribution pair of the bent-axis pump is tested dynamically in this paper. On the basis of synthetical consideration of the leakage flow rate, the loss of power and the ability to resist contaminant of the distribution pair,the parameters used to describe the distribution state are optimized. According to theoretical analyses and experimental research, the structure of the distribution plate is improved, and the ability to resist contaminant wear of the distribution pair is increased. Thus, it is possible to prolong the service life and working reliability of the pump.

Optimal selection of tests for fault detection and isolation in multi-operating mode system

The complex systems are often in the structure of multi-operating modes, and the components implementing system functions are different under different operation modes, which results in the problems that components often fail in different operating modes, faults can be only detected in specified operating modes, tests can be available in specified operating modes,and the cost and efficiency of detecting and isolating faults are different under different operating modes and isolation levels. Aiming at these problems, an optimal test selection method for fault detection and isolation in the multi-operating mode system is proposed by using the fault pair coding and rollout algorithm. Firstly,the faults in fault-test correlation matrices under different operating modes are combined to fault-pairs, which is used to construct the fault pair-test correlation matrices under different operating modes.Secondly, the final fault pair-test correlation matrix of the multioperating mode system is obtained by operating the fault pair-test correlation matrices under different operating modes. Based on the final fault pair-test correlation matrix, the necessary tests are selected by the rollout algorithm orderly. Finally, the effectiveness of the proposed method is verified by examples of the optimal test selection in the multi-operating mode system with faults isolated to different levels. The result shows that the proposed method can effectively mine the fault detection and isolation ability of tests and it is suitable for the optimal test selection of the multi-operating mode system with faults isolated to the replacement unit and specific fault.

Constructing Test Suites for k-n Softw are System

In software testing, many troublesome faults are caused by interaction of input parameters. If automatic efficient test-case generator（AETG）, in parameter order（IPO） or orthogonal Latin square is used in the software system under test, the whole test set cannot be run completely due to time or budget constraints. In this paper, according to the number of parameter k and their values n, a software system under test can be divided into four types. As for k-2 system, an algorithm was proposed to construct test rases, based on the longitudinal binary string set and method of controlling variables. As for k-n valued parameters whose n was a prime or power of prime, a method of covering array of test sets was designed to construct test sets by taking orthogonal array and derive arrays from orthogonal array and two useful conditions. As for k parameters whose n-value was not all equal, an experience algorithm was presented in this paper. The experimental results show that the size of test sets from the proposed methods is better than that from AETG, IPO, and orthogonal Latin square.

Statistical Comparison of Eight Alternative Methods for the Analysis of Paired Sample Data with Applications

This paper presents and statistically compared eight alternative methods that could possibly be used in the analysis of matched or paired sample data, including situations in which the data being analyzed satisfy the usual assumptions of normality and continuity necessary for the use of parametric tests as well as when the data are numeric and non-numeric measurements on as low as the ordinal scale. It is shown that only the modified sign tests based on only the raw observations or their assigned ranks may be used with non numeric measurement on the ordinal scale. If the ordinary sign test, the Wilcoxon signed rank sum test and the modified sign tests can be equally used in data analysis, then it is shown that the modified sign tests are more efficient and hence more powerful than the ordinary sign tests because the two test statistics are intrinsically and structurally modified for the possible presence of tied observations between the sampled populations for both using raw and simulated data. Of all the non-parametric methods presented, the modified Wilcoxon’s signed rank sum test when applicable is the most efficient and powerful, following in this order by the modified sign test by ranks and the modified sign test based on only raw scores for raw data but simulation, modified sign test by ranks is the most efficient and powerful, following in this order by modified wilcoxon’s signed rank sum test and modified sign test. Each of the non-parametric methods presented can be easily modified and re-specified for use with one sample data by simply re-designating the observations from one of the sampled populations to correspond with a hypothesized value of some measure of central tendency. The methods are illustrated with some raw data as well as simulated data and their relative performances compared.

Selection of Minimal Test Points Set for Integer-Coded Fault Wise Table

Test points selection for integer-coded fault wise table is a discrete optimization problem. On one hand, traditional exhaustive search method is computationally expensive. On the other hand, the space complexity of traditional exhaustive is low. A tradeoff method between the high time complexity and low space complexity is proposed. At first, a new fault-pair table is constructed based on the integer-coded fault wise table. The fault-pair table consists of two columns： one column represents fault pair and the other represents test points set that can distinguish the corresponding faults. Then, the rows are arranged in ascending order according to the cardinality of corresponding test points set. Thirdly, test points in the top rows are selected one by one until all fault pair are isolated. During the test points selection process, the rows that contain selected test points are deleted and then the dimension of fault-pair table decreases gradually. The proposed test points selection algorithm is illustrated and tested using an integercoded fault wise table derived from a real analog circuit. Computational results suggest show policies are better than the exhaustive strategy.

基于配对检验的ARIMA模型在我国甲肝发病数预测中的应用

目的:探讨基于配对检验的求和自回归移动平均(autoregressive integrated moving average,ARIMA)模型在我国甲肝发病预测中的应用,提出时间序列模型预测效果评价的新思路与方法。方法:根据2004年1月—2021年12月我国甲肝传染病月发病数建立ARIMA模型,对2022年1—8月的甲肝月发病数进行预测,通过配对t检验和误差分析评估该模型的预测效果。结果:配对t检验结果显示,ARIMA(1,1,0)(0,1,1)12模型预测的甲肝月发病数与实际月发病数差异无统计学意义(P>0.05),说明模型有较好的预测能力,预测结果的相对误差平均值为3.86%,标准差为3.25%。结论:ARIMA乘积季节模型能够较准确地预测我国甲肝的发病趋势;配对检验为时间序列模型预测效果的评价提供了客观评价依据,较好地解决了时间序列模型预测效果的评价问题。

管制员个体工作负荷多维量化研究

为提高空管系统高效运行,聚焦管制员个体工作负荷建立量化模型;首先设计试验采集一线16名区域管制员的岗前与岗后各项指标数据,根据测试数据变化,选择出敏感变量,描述个体工作负荷;其次建立包含心理感知负荷、生理反应负荷与脑力工作负荷3个维度的综合评估指标体系,构建管制员个体工作负荷指数模型;然后通过熵权-客观组合法求解个体工作负荷指数最优权重,最终得出管制员个体工作负荷量化模型;最后进一步根据管制员个体工作负荷综合指数进行K-Means聚类分析,结果表明:管制员因个体不同岗后工作负荷存在差异。依据个体工作负荷指数大小,管制员可分为3类,A类管制员数量占总人数50%,岗后个体工作负荷增长最小;B类管制员数量占总人数43.75%,岗后负荷增长居中;C类管制员数量占总人数6.25%,岗后负荷增长最大,与教员对管制员能力的评分结果一致。

表面织构对径向柱塞泵滑靴副摩擦磨损性能的影响

高压大排量径向柱塞泵的承载力较大,而滑靴副是影响该类泵摩擦特性的关键因素之一。开展织构对滑靴副摩擦特性影响的研究,对提升高压大排量径向柱塞泵滑靴副润滑与摩擦特性具有重要意义。为此,以高压大排量径向柱塞泵滑靴副为研究对象,计算了不同形状、面积率、深径比织构的滑靴磨损量。首先,选取了正方形、圆形和三角形共3种形状的织构表面,对织构的深度、形状、面积率进行了定义,构建了滑靴织构形貌影响因素和正交试验样本;然后,开展了10组样本数据的试件摩擦磨损试验,分别以摩擦系数和磨损量为因变量,得到了多因素方差分析检验结果;最后,基于显著性小的因素确定了研究参数,开展了不同形状织构表面的摩擦仿真与试件试验。研究结果表明:织构的面积率对摩擦系数和磨损量影响最大;面积率为9.66%、深度为120μm的三角形织构表面的摩擦系数最小,相比无织构表面下降16%;摩擦仿真所得三种形状织构表面的磨损量排序与试验结果一致;面积率为9.66%、深度为120μm的正方形织构表面的减摩效果最好、磨损量最小,磨损量较无织构表面下降35%,摩擦系数相对无织构下降15.86%。该研究结果可以为高压大排量径向柱塞泵滑靴副设计,改善滑靴副的摩擦磨损特性,延长柱塞泵的使用寿命提供一定的参考。

2种诱饵诱蝇效果的比较研究

目的了解糖醋诱饵与腐鱼诱饵诱蝇效果的差异。方法以糖醋和腐鱼为诱饵,采用笼诱法现场诱蝇,分析蝇类发生及种群构成。采用JASP 0.11.1.0软件的贝叶斯配对样本t检验和贝叶斯相关性分析进行统计分析。结果糖醋和腐鱼诱饵共诱捕家蝇科、丽蝇科、麻蝇科和花蝇科4科10属18种,2种诱饵对该4科蝇类的诱蝇种类数差异不显著(BF_(10)=2.431)。糖醋诱饵对诱蝇优势种群家蝇科的诱捕效果显著优于腐鱼诱饵(BF_(10)=64.981)。腐鱼诱饵对诱蝇优势种群丽蝇科的诱捕效果显著优于糖醋诱饵(BF_(10)=36.277)。农贸市场、餐饮外环境、绿化带和居民区4类生境中,农贸市场为优势生境,但生境间的蝇密度统计学差异均不显著(BF_(10)<10)。腐鱼诱饵诱蝇的蝇密度显著高于糖醋诱饵(BF_(10)=204.885),2种诱饵诱蝇的蝇密度中等程度线性相关(Kendall’s tau-b=0.504,BF_(10)=26.594)。结论糖醋诱饵可作为蝇类监测笼诱法的通用诱饵。

Box-Behnken响应面法优化“五味子-吴茱萸”药对的提取工艺及含量测定

目的:优化“五味子-吴茱萸”药对提取工艺并测定其不同配伍的化学成分含量。方法:利用Box-Behnken设计在单因素考察的基础上考察“五味子-吴茱萸”药对的提取工艺,确定最佳提取工艺,并通过高效液相色谱法测定“五味子-吴茱萸”的化学含量,确定药对的最佳比例。结果:“五味子-吴茱萸”药对最优提取工艺为乙醇体积分数70%,料液比1∶15(g/mL),提取时间60 min,提取次数3次。该提取工艺科学可靠。结论:本研究方法简单可行,可为“五味子-吴茱萸”药对的开发利用及相关研究提供参考。

双对斜杆负刚度机制的恒值QZS隔振器研究

针对隔振质量偏离静态平衡位置导致准零刚度(quasi-zero stiffness,QZS)隔振器动态刚度增大而影响低频隔振性能的问题,基于双对斜杆负刚度机制,构造了恒值QZS隔振器,推导了隔振器的力和刚度表达式,通过静态平衡点处刚度及刚度二阶导数等于零的QZS条件,研究了参数影响下的力和刚度特性,获得了非线性刚度、恒值QZS和零刚度的参数条件。根据静态分析,设计了恒值QZS试验模型,通过万能试验机测得试验模型的力位移曲线,与理论值具有较好的一致性。进而采用激光测振仪和振动台开展谐波激励的动态试验,获得了恒值QZS和线性刚度隔振器的位移响应及传递率。动态试验结果表明,恒值QZS隔振器的起始隔振频率小于1.5 Hz,且传递率整体小于线性隔振器的位移传递率,而线性隔振器的起始隔振频率为4.5 Hz。综上,提出的恒值QZS隔振器不仅能实现任意恒值的QZS,并且可采用杆、弹簧方便地获得所需的恒值QZS,具有优越的低频隔振性能。

平板型电极对热离子能量转换特性的测试技术研究

为开展热离子能量转换器基础性能数据的研究,基于平板型电极热离子能量转换基础试验装置建立了针对电极对热电转换特性的测试技术,通过开展W-Mo电极对的热离子发电测试,对所建立的测试技术进行了验证及评价,并分析了热离子发电参数对输出特性的影响规律。结果表明:所建立的测试技术可准确测量发射极有效功函数值;利用热离子基础试验装置测得的W-Mo电极对的最大输出功率密度为5.6 W/cm^(2),对应的发电参数为发射极温度1800 K,铯壶温度577 K,输出电压0.7 V。

多支股票配对交易优化研究——基于中国股票市场的实证检验

随着中国股票市场的日益成熟与市场效率的持续提升,统计套利策略的应用日益增加。单支股票的配对策略盈利空间收窄,传统交易策略面临着性能优化的挑战。针对此问题,本文提出了一种多支股票配对的交易优化策略—MultiPT优化策略。首先基于最小距离法和协整检验思想构建配对选股模型,随后通过序列二次规划算法对优化模型求解,以确定两组股票的最佳配对组合。本研究选取中国A股市场中的代表性样本数据进行回测。实证结果显示,相较于传统GGR和协整策略,MultiPT优化策略在沪深300指数成分股和Wind分行业样本中分别实现了至少15.17%和14.97%的超额收益,显示出多支股票配对的显著优势。此外,配对股票数量与风险水平呈正相关关系。值得注意的是,GGR、协整以及MultiPT优化策略均在市场低迷时期表现更为突出。实证结果验证了MultiPT优化策略的可行性和有效性,为探索股票市场活力、推动中国金融市场的高质量发展提供理论支撑和实践指导。

荧光光谱法测定镀铜溶液主盐含量的误差分析

通过无标样法对荧光光谱曲线进行校准,采用校准后的曲线快速分析酸性硫酸铜和HEDP络合物铜电镀液的主盐Cu2+含量,并借助于成对二样本t检验将其与化学滴定法的测试结果进行比较。研究结果表明,两种分析方法对单盐体系镀液和络合物体系镀液的测量结果的相对误差范围分别为-3.96%~3.24%和3.01%~4.99%,均在工艺容许范围以内。相比于化学滴定法,荧光光谱法的测量结果的精密度更高,速度更快,操作更加简便,且校准后的测试结果可以进一步逼近真值。

评估原油交接过程动态计量输差的成对t检验方法研究

原油交接计量过程中由于流量计的误差、动态变化的压力与温度等不确定性因素而产生计量输差,引起交接计量纠纷。采用成对样本t检验与流量计误差分析相结合的新方法,对原油交接过程的动态计量输差进行了评估,对动态计量过程中的来油流量与回油流量两者之间的输差数据进行了正态性检验和相关性性检验。结果表明,采油厂与轻烃厂原油交接数据相关性非常的明显,输差数据服从正态分布,采油厂与轻烃厂原油交接计量的生产数据满足成对t检验的要求。通过成对样本t检验对输差数据进行了量化评估,给出了动态计量输差的合理偏差范围,分析了动态计量过程来油流量与回油流量两者之间输差的合理性。对流量计置信区间的分析表明,来油流量置信区间与回油流量置信区间的相对位置只能定性地显示输差是否明显,不像成对t检验可以定量地给出计量允差。成对t检验能够计算得到计量允差这一新量化指标,可将成对样本t检验方法与流量计的误差分析相结合,用于评估原油交接过程的动态计量输差。