假设检验相关知识简介.pptx

,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,*,*,Hypothesis Testing,1,假设检验,2,Objectives,Explain the differences between decision making with population data and sample data,Explain the risks of sample based decision making,Explain what a hypothesis is,Explain why hypothesis testing is important to process improvement.,Define the terms“Null Hypothesis”and“Alternative Hypothesis”.,Compare Hypothesis testing to Courtroom Decision Making.,Explain the terms“,a,risk”and“,b,risk”.,Explain what a“p value,”is,3,目标,解释,由全部数据或抽样数据所作出决策的不同,解释,根据抽样资料所作出决策的风险,说明假设是什么,说明假设检验对程序优化的重要性,介定“原假设”和“备择假设”,.,比较假设检验和法庭式决策.,说明术语,“,a,风险”和“,b,风险”.,说明什么是,“p,数,值,”,4,Population:The Universe,Data or information that defines the entire set,Parameters(,m,s,)may,or may not be known.,Population,Sample,Sample:,A subset data or information that possesses the same characteristics as that of the population.We can calculate statistics(X Bar,s).,We make decisions about the population based on the sample,How many samples should be taken?,Why should we take a sample?,Should the sample be random?,Is it possible to have sampling error?,Populations and Samples,5,总体:统计总体,用以定义所有可知或不可知参数,(,m,s,),的数据或信息,Population,Sample,样品,:,总体中具有共同特征的子集。可以计算其形成的统计表（,X）.,我 们 以 样 本 为 基 础 做 出 总 体 决 策,应取多少样本？,为何要选取样本？,样本需要随机抽取吗？,可能出现取样错误吗？,总体和样本,6,Samples?Why Use Them?,Why use a sample instead of a population?,Using a sample reduces time and cost,Capturing data on the entire population may be very difficult,if not impossible.,When to use a sample,We use samples to Baseline a process,Use samples to evaluate the results of a controlled change to a process.,How should the sample be taken?,See section 5.,7,样本?为何使用样本?,为何采用样本而非总体?,采用样本可减少时间和成本消耗,即使可能，获取总体数据也是非常困难的,.,何时采用样本？,我们利用样本定流程基线,利用样本对过程的可控变化结果进行评估,.,如何获取样本?,请看第五部分,.,8,Sample A,All processes have variation.,Samples from a given process may vary.,Sample B,How can we differentiate between sample based“chance”variation and a true process difference?,How can we depend on a sample?,9,样本,A,所有的过程都有差异.,来源于给定过程的样本也可能是多样化的,.,样本,B,我们怎样区分随机变化的样本和真实总体的差别呢?,怎样使用样本？,10,Confidence Intervals and Point Estimates,Confidence intervals,identify a range of plausible values for a sample statistic of a population parameter.They can be either one-sided or two-sided.,Sample Means,Sample Standard deviation,Sample Variances and other sample statistics are known as,Point Estimators,because they are single values used to represent population parameters,11,可信区间和特征值的估计,可信区间,确定了总体参数中样本统计可能的数值范围,.,它,们可以是单边也可是双边,。,样本均值、样本标准偏差、样本方异和其它样本统计被称为特征值评估者。因为它们是用以代表总体参数的单一,数,值。,12,Hypothesis Tests help determine if an apparent difference is real or could be due to chance.,样本?为何使用样本?,不一致:用F测试 或均等差异测试,16、少年十五二十时，步行夺得胡马骑。,Defining Hypotheses,介定“原假设”和“备择假设”.,13、乍见翻疑梦，相悲各问年。,Translate the results.,2022/10/25 16:07:5116:07:5125 October 2022,用统计测试方法测验选择性假设.,25 十月 20224:07:51 下午16:07:5110月-22,13、不知香积寺，数里入云峰。,把假设以等式陈述很有用.,Explain the risks of sample based decision making,11、以我独沈久，愧君相见频。,Hypothesis Tests,Point Estimates of parameters and Confidence Interval Interpretation are both means for making inferences about sample data.,Hypothesis tests are designed to help us make an inference about the true population value at the desired level of confidence.,We will use confidence intervals and tests of sample means,variances and sample standard deviation to investigate difference and cause/effect relationships using data.,Hypothesis Tests help determine if an apparent difference is real or could be due to chance.By using data and hypothesis testing,we can quantify our level of confidence that the difference is real.,13,假设检验,对参数特征值估计和可信区间的诠释都是得出样本数据推论的路径,.,假设检验是用以帮助我们在需要的可信度上对真实的总体,数,值进行推论的。,我们将用可信区间和样本均值、,样本差异,及样本标准偏差,测验,来研究使用数据的差別和因果关系。,假设检验有助于判断一个明显的差别是否真实存在还是偶然的，而且还可以提高差异真实性的可信度,.,14,A Statistical Hypothesis,An assertion or conjecture about one or more parameters of the population,To determine whether it is true or false,we must examine the entire population.This is impossible!,Instead use a random sample to provide evidence that either supports or does not support the hypothesis.,The conclusion is then based upon statistical significance.,It is important to remember that this conclusion is an inference about the population determined from the sample data.,15,Explain why hypothesis testing is important to process improvement.,16、行动出成果，工作出财富。,The American justice system can be used to illustrate the concept of hypothesis testing.,Returning a guilty verdict corresponds to rejecting the null hypothesis and accepting the alternative hypothesis.,可以计算其形成的统计表（X）.,b 风险:通常10 20%(预设值),Type II 错误(b 错误)是当 Ho有错误时却接受 有时称作 消费者风险.,在这种情况下，决定可能是主观的.,9、杨柳散和风，青山澹吾虑。,在美国罪犯在被判有罪之前均是清白的.,样本?为何使用样本?,解释由全部数据或抽样数据所作出决策的不同,统计假设,对,于一个或多个总体,里,的参数的肯定或推断,为了判断它的正误，我们必须检查总体的全部。这是不可能的！,我们应使用随机样本，观察其是否能支持该假设,.,从而该结论是建立在统计学意义的基础之上的,.,必须记住该有关总体的结论是由样本推测出的,.,16,Why Do Hypothesis Testing?,1.,To improve processes,we need to identify factors which impact the mean or standard deviation.,2.Once we have identified these factors and made adjustments for improvement,we need to validate actual improvements in our processes.,3.Sometimes we cannot decide graphically or by using calculated statistics(sample mean and standard deviation)if there is a statistically significant difference between processes.,4.In such cases the decision will be subjective.,5.We perform a formal statistical hypothesis test to decide objectively whether there is a difference.,Data helps everyone makes the same decision,.,17,为何要做假设检验?,1.,为了改进过程，我们需要确定影响均值和标准偏差的因素,.,2.,一旦确定了这些因素并对改进措施进行了调整，我们就需要验证其在过程中的切实效果。,3.,若过程中存在统计上的重大差别，有时我们就不能利用图表或算得的统计数据（样本均值和样本标准偏差）作出决策.,4.,在这种情况下，决定可能是主观的,.,5.,我们采用,正统,假设检验以客观地判断是否存在差別。,数据帮助,每个,人作出同样的决定。,18,Nature of Hypotheses,Null Hypothesis(Ho):,Usually describes a status quo,The one you assume unless otherwise shown,Signs used in Minitab:=,Alternative Hypothesis(Ha):,Usually describes a difference,The one you accept or reject based upon evidence,Signs used in Minitab:not=or,Population,Sample,Or,Population,Sample,Its either Null(same)or Alternative(Different),19,假设的种类,虚,无,性假设,通常用以描述现状,除非其它方面有所说明，否则就是人为设想的。,在,Minitab,中用“=”表示,选择性假设(,Ha):,通常用以描述差別,以证据为基础接受或拒绝的类型,在,Minitab,中用“,not=or”,表示,Population,Sample,Or,Population,Sample,不是,全,虚,性,假设（相同）就是选择性假设（相区别的）,20,Hypothesis TestingGuilty vs.Innocent Example,The American justice system can be used to illustrate the concept of hypothesis testing.,In America we assume innocence until proven guilty.,Innocence corresponds to the null hypothesis.,It requires strong evidence,“beyond a reasonable doubt,”to convict the defendant.Returning a guilty verdict corresponds to rejecting the null hypothesis and accepting the alternative hypothesis.,More specifically,we have significant evidence to support that a difference exists.,H,o,:Person is innocent.,H,a,:Person is guilty,.,What are the possible outcomes when the truth is known?,21,假设检验有罪,vs.,无罪的案例,美国的司法体系可以用于阐述假设检验的概念,.,在美国罪犯在被判有罪之前均是清白的,.,清白对应,虚,无,性,假设,.,它需要强而有力的证据，必需“排除所有合理的怀疑”才能把被告定罪.若陪审团裁定被告有罪则相当于,拒绝,虚,无,性,假设接受选择性假设.,更具体些,我们拥有重要的证据证明差別的存在,.,H,o,:,被告是清白的.,H,a,:,被告有罪,.,当得知真相后，可能的结果是什么,?,22,Truth,Verdict,H,o,=,H,a,not=,H,o,=,H,a,not=,Innocent,Jailed,Guilty Set Free,InnocentSet Free,GuiltyJailed,Set Free,Jail,Innocent,Guilty,The Type I Error(,a,error),is rejecting H,o,when it is true sometimes called the,producers risk,.,The Type II Error,(,b,error),is failing to reject H,o,when it is false sometimes called the,consumers risk,.,Decision,Type 1,Error,Type 2,Error,Correct,Decision,Correct,Decision,Truth,H,o,=,H,a,not=,H,o,=,H,a,not=,Risk Decision Making in our Courts and in Business,23,真相,裁决,H,o,=,H,a,not=,H,o,=,H,a,not=,清白,监禁,有罪,释放,清白,释放,有罪,监禁,释放,监禁,清白,有罪,Type I,错误(,a,错误),当,H,o,是,无,误时而,拒绝,有时称作,生产者风险,Type II,错误,(,b,错误),是当,H,o,有错误时却,接受,有时称作,消费者风险,.,Decision,Type 1,错误,Type 2,错误,正确,决定,正确,决定,真相,H,o,=,H,a,not=,H,o,=,H,a,not=,法庭和商业上的决策风险,24,The p Value,Another way to measure the risk in the decision is through the p Value.,The p-value is known as the,Observed Level of Significance,for a factor.,It is the chance of observing this amount of difference if the sample is consistent with the population.,The p-value is also the probability of being wrong if we reject the Null Hypothesis(Type I Error.),Unless there is an exception based on engineering judgment,we will set an acceptance level of a Type I error at,a,=0.05.,Thus,any p-value less than 0.05 means we reject the Null hypothesis.,25,p,值,衡量决策风险的另一种方法是通过,P,值,.,P,值是指一个因素可测的重要性水平,.,当样本和总体相,对,时，,P,值是指观测到其中差別的,机会,率.,P,值也指如果拒绝,虚,无,性假设可能发生错误的概率（错误,I）,除非在基于工程判断上的例外，我们将错误,I,的可接受水平定在,a,=0.05.,从而，任何小于0.05的,P,值就表示,虚,无,性假设被拒绝。,26,Defining Hypotheses,Null Hypotheses,H,O,:X,1,=Target,H,O,:X,1,=,m,H,O,:X,1,-X,2,=0,H,O,:,m,1-,m,2,=0,H,O,:X,1,=X,2,=X,3,=.X,n,HO:,s,1,=s,2,H,O,:S,1,=S,2,H,O,:S,1,=S,2,=S,3,=.S,n,Alternative Hypotheses,H,A,:,m,1,m,2,Inequalities are two sided tests,H,A,:X,1,X,2,H,A,:,m,1,m,2,H,A,:X,1,m2,H,A,:X,1,X,2,H,A,:X,1,-,X,2,0 _,H,A,:X,1,-,X,2,0 _,HA:,s1s2,_,HA:s1S2 _,Scripting Hypotheses as equations is useful when stating.,27,定义假设,虚,无,性假设,H,O,:X,1,=Target,H,O,:X,1,=,m,H,O,:X,1,-X,2,=0,H,O,:,m,1-,m,2,=0,H,O,:X,1,=X,2,=X,3,=.X,n,HO:,s,1,=s,2,H,O,:S,1,=S,2,H,O,:S,1,=S,2,=S,3,=.S,n,选择性假设,H,A,:,m,1,m,2,不等式是针对两边的测试,H,A,:X,1,X,2,H,A,:,m,1,m,2,H,A,:X,1,m2,H,A,:X,1,X,2,H,A,:X,1,-,X,2,0 _,H,A,:X,1,-,X,2,0 _,HA:,s1s2,_,HA:s1S2 _,把假设以等式陈述很有用,.,28,Hypothesis Testing Protocol,The hypotheses are always statements about the population parameters.,State your null hypothesis(H,o,),H,O,:The height of citizens in country A is equal to the height of citizens in country B,(,m,A=,m,B).,State your Alternative Hypothesis(H,a,),H,A,:The height of citizens in country A is less than the height of citizens in country B,(,m,A,m,B).,Determine the appropriate statistical test based on the Hypothesis being tested.,Determine the level of acceptable risk.,a,Risk:usually 5%(Default),b,Risk:Usually 10 20%(Default),29,假设检验协议,假设总是关于总体参数的,陈述,.,定明,虚,无,性,假设,(H,o,),H,O,:A,国与,B,国居民身高相等,(,m,A=,m,B).,规定选择性假设,(,H,a,),H,A,:A,国居民身高低于,B,国居民的身高,(,m,A,m,B).,基于在需被测试的假设上，决定适合的统计测试,.,决定可接受的风险程度.,a,风险:通常 5%(,预设,值,),b,风险:通常10 20%(,预设,值,),30,Hypothesis Testing Protocol(Cont),Determine the proper sample size for the test(Section 5),C,ollect a sample of observations from the population.,Calculate statistics based on the sample.,Use a statistical test to test alternative hypothesis.,Based on the test result,we accept or reject Ho based on the previously determined criterion.,Translate the results.Translate the statistical conclusion to a practical one.,Statistical Conclusion:Can we prove difference statistically.,Practical Conclusion:Do we care about the difference?,31,假设检验协议,(,续),决定适合测试的样本数量(第五部分),从总体中选取需观察的样本群,.,计算样本的统计,.,用统计测试方法测验选择性假设,.,在测试结果的基础上，根据先前确定的标准，做出选择或拒绝,Ho,的决定.,转化结果.将统计的结论转换为现实的结果,.,统计结论:我们能从统计的角度证明差別吗？,现实结果:我们需注意这些差別吗?,32,Well be using hypothesis testing as a method to prove change,Target or desired value,One Sample t,Are multiple samples the same,Mean:two sample t or ANOVA,Variation:F test or Test for Equal Variance,Proportion of Occurrence,:,Chi Square,C,2,33,我们将假设检验作为证明差异的一种方法,目标,数,值,一个样本,t,若干样本是否一致,一致:两个,t,样本 或,ANOVA,不一致:用,F,测试 或均等,差异,测试,事情发生的概率,:,Chi Square,C,2,34,9,、静夜四无邻，荒居旧业贫。,10月-26,10月-26,Sunday,October 4,2026,10,、雨中黄叶树，灯下白头人。,10:47:22,10:47:22,10:47,10/4/2026 10:47:22 AM,11,、以我独沈久，愧君相见频。,10月-26,10:47:22,10:47,Oct-26,04-Oct-26,12,、故人江海别，几度隔山川。,10:47:22,10:47:22,10:47,Sunday,October 4,2026,13,、乍见翻疑梦，相悲各问年。,10月-26,10月-26,10:47:22,10:47:22,October 4,2026,14,、他乡生白发，旧国见青山。,04 十月 2026,10:47:22 上午,10:47:22,10月-26,15,、比不了得就不比，得不到的就不要。,。,十月 26,10:47 上午,10月-26,10:47,October 4,2026,16,、行动出成果，工作出财富。,2026/10/4 10:47:22,10:47:22,04 October 2026,17,、做前，能够环视四周；做时，你只能或者最好沿着以脚为起点的射线向前。,10:47:22 上午,10:47 上午,10:47:22,10月-26,9,、没有失败，只有暂时停止成功！。,10月-26,10月-26,Sunday,October 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