Hypothesis-Testing假設(shè)檢驗(yàn)講義(中英文版)(ppt-34頁(yè))課件

1、Hypothesis Testing1假設(shè)檢驗(yàn)2ObjectivesExplain the differences between decision making with population data and sample dataExplain the risks of sample based decision makingExplain what a hypothesis isExplain why hypothesis testing is important to process improvement.Define the terms “Null Hypothesis” and

2、 “Alternative Hypothesis”.Compare Hypothesis testing to Courtroom Decision Making.Explain the terms “a risk” and “b risk”. Explain what a “p value” is3目標(biāo)解釋由全部數(shù)據(jù)或抽樣數(shù)據(jù)所作出決策的不同解釋根據(jù)抽樣資料所作出決策的風(fēng)險(xiǎn)說(shuō)明假設(shè)是什么說(shuō)明假設(shè)檢驗(yàn)對(duì)程序優(yōu)化的重要性介定 “原假設(shè)”和“備擇假設(shè)”.比較假設(shè)檢驗(yàn)和法庭式?jīng)Q策.說(shuō)明術(shù)語(yǔ)“a 風(fēng)險(xiǎn)” 和 “b 風(fēng)險(xiǎn)”. 說(shuō)明什么是 “p數(shù)值” 4Population: The UniverseDa

3、ta or information that defines the entire setParameters(m, s) may, or may not be known.PopulationSampleSample: 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 sa

4、mpleHow 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 Samples5總體: 統(tǒng)計(jì)總體用以定義所有可知或不可知參數(shù)(m, s)的數(shù)據(jù)或信息PopulationSample樣品: 總體中具有共同特征的子集?？梢杂?jì)算其形成的統(tǒng)計(jì)表（X）.我 們 以 樣 本 為 基 礎(chǔ) 做 出 總 體 決 策應(yīng)取多少樣本？為何要選取樣本？樣本需要隨機(jī)抽取嗎？可能出現(xiàn)取樣錯(cuò)誤嗎？總

5、體和樣本6Samples? Why Use Them?Why use a sample instead of a population?Using a sample reduces time and costCapturing data on the entire population may be very difficult, if not impossible.When to use a sampleWe use samples to Baseline a processUse samples to evaluate the results of a controlled change

6、to a process.How should the sample be taken?See section 5.7樣本? 為何使用樣本?為何采用樣本而非總體?采用樣本可減少時(shí)間和成本消耗即使可能，獲取總體數(shù)據(jù)也是非常困難的.何時(shí)采用樣本？我們利用樣本定流程基線(xiàn)利用樣本對(duì)過(guò)程的可控變化結(jié)果進(jìn)行評(píng)估.如何獲取樣本?請(qǐng)看第五部分.8Sample AAll processes have variation.Samples from a given process may vary.Sample BHow can we differentiate between sample based “chan

7、ce” variation and a true process difference?How can we depend on a sample?9樣本 A所有的過(guò)程都有差異.來(lái)源于給定過(guò)程的樣本也可能是多樣化的.樣本 B我們?cè)鯓訁^(qū)分隨機(jī)變化的樣本和真實(shí)總體的差別呢?怎樣使用樣本？10Confidence Intervals and Point EstimatesConfidence intervals identify a range of plausible values for a sample statistic of a population parameter. They can

8、 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 parameters11可信區(qū)間和特征值的估計(jì)可信區(qū)間 確定了總體參數(shù)中樣本統(tǒng)計(jì)可能的數(shù)值范圍. 它們可以是單邊也可是雙邊。樣本均值、樣本標(biāo)準(zhǔn)偏差、樣本方異和其它樣本統(tǒng)計(jì)被稱(chēng)為特征

9、值評(píng)估者。因?yàn)樗鼈兪怯靡源砜傮w參數(shù)的單一數(shù)值。12Hypothesis TestsPoint 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 wil

10、l 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

11、 quantify our level of confidence that the difference is real. 13假設(shè)檢驗(yàn)對(duì)參數(shù)特征值估計(jì)和可信區(qū)間的詮釋都是得出樣本數(shù)據(jù)推論的路徑. 假設(shè)檢驗(yàn)是用以幫助我們?cè)谛枰目尚哦壬蠈?duì)真實(shí)的總體數(shù)值進(jìn)行推論的。 我們將用可信區(qū)間和樣本均值、樣本差異及樣本標(biāo)準(zhǔn)偏差測(cè)驗(yàn)來(lái)研究使用數(shù)據(jù)的差別和因果關(guān)系。假設(shè)檢驗(yàn)有助于判斷一個(gè)明顯的差別是否真實(shí)存在還是偶然的，而且還可以提高差異真實(shí)性的可信度. 14A Statistical HypothesisAn assertion or conjecture about one or more parame

12、ters of the populationTo 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

13、 to remember that this conclusion is an inference about the population determined from the sample data.15統(tǒng)計(jì)假設(shè)對(duì)于一個(gè)或多個(gè)總體里的參數(shù)的肯定或推斷為了判斷它的正誤，我們必須檢查總體的全部。這是不可能的！我們應(yīng)使用隨機(jī)樣本，觀(guān)察其是否能支持該假設(shè).從而該結(jié)論是建立在統(tǒng)計(jì)學(xué)意義的基礎(chǔ)之上的.必須記住該有關(guān)總體的結(jié)論是由樣本推測(cè)出的.16Why Do Hypothesis Testing?1. To improve processes, we need to identify factors

14、 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 the

15、re 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為何要做假設(shè)檢驗(yàn)?1. 為了改進(jìn)過(guò)程，我們需要確定影響均值和標(biāo)準(zhǔn)偏差的因素.2

16、. 一旦確定了這些因素并對(duì)改進(jìn)措施進(jìn)行了調(diào)整，我們就需要驗(yàn)證其在過(guò)程中的切實(shí)效果。3. 若過(guò)程中存在統(tǒng)計(jì)上的重大差別，有時(shí)我們就不能利用圖表或算得的統(tǒng)計(jì)數(shù)據(jù)（樣本均值和樣本標(biāo)準(zhǔn)偏差）作出決策.4. 在這種情況下，決定可能是主觀(guān)的.5. 我們采用正統(tǒng)假設(shè)檢驗(yàn)以客觀(guān)地判斷是否存在差別。數(shù)據(jù)幫助每個(gè)人作出同樣的決定。18Nature of HypothesesNull Hypothesis (Ho):Usually describes a status quoThe one you assume unless otherwise shownSigns used in Minitab: =Altern

17、ative Hypothesis (Ha ):Usually describes a differenceThe one you accept or reject based upon evidenceSigns used in Minitab: not =or PopulationSampleOr PopulationSampleIts either Null (same) or Alternative (Different)19假設(shè)的種類(lèi)虛無(wú)性假設(shè)通常用以描述現(xiàn)狀除非其它方面有所說(shuō)明，否則就是人為設(shè)想的。在Minitab中用“=”表示選擇性假設(shè) (Ha ):通常用以描述差別以證據(jù)為基礎(chǔ)接受

18、或拒絕的類(lèi)型在Minitab中用“not =or ”表示PopulationSampleOr PopulationSample不是全虛性假設(shè)（相同）就是選擇性假設(shè)（相區(qū)別的）20Hypothesis TestingGuilty vs. Innocent ExampleThe American justice system can be used to illustrate the concept of hypothesis testing.In America we assume innocence until proven guilty.Innocence corresponds to th

19、e 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.

20、Ho : Person is innocent.Ha : Person is guilty.What are the possible outcomes when the truth is known?21假設(shè)檢驗(yàn)有罪 vs. 無(wú)罪的案例美國(guó)的司法體系可以用于闡述假設(shè)檢驗(yàn)的概念.在美國(guó)罪犯在被判有罪之前均是清白的.清白對(duì)應(yīng)虛無(wú)性假設(shè).它需要強(qiáng)而有力的證據(jù)，必需“排除所有合理的懷疑”才能把被告定罪. 若陪審團(tuán)裁定被告有罪則相當(dāng)于拒絕虛無(wú)性假設(shè)接受選擇性假設(shè). 更具體些,我們擁有重要的證據(jù)證明差別的存在.Ho : 被告是清白的.Ha : 被告有罪.當(dāng)?shù)弥嫦嗪?，可能的結(jié)果是什么?22TruthVe

21、rdictHo, =Ha, not =Ho, =Ha, not =InnocentJailedGuilty Set FreeInnocentSet FreeGuiltyJailedSet FreeJailInnocentGuiltyThe Type I Error (a error) is rejecting Ho when it is true sometimes called the producers risk.The Type II Error (b error) is failing to reject Ho when it is false sometimes called the

22、 consumers risk.DecisionType 1ErrorType 2ErrorCorrectDecisionCorrectDecisionTruthHo, =Ha, not =Ho, =Ha, not =Risk Decision Making in our Courts and in Business23真相裁決Ho, =Ha, not =Ho, =Ha, not =清白監(jiān)禁有罪釋放清白釋放有罪監(jiān)禁釋放監(jiān)禁清白有罪Type I 錯(cuò)誤 (a 錯(cuò)誤) 當(dāng) Ho 是無(wú)誤時(shí)而拒絕 有時(shí)稱(chēng)作 生產(chǎn)者風(fēng)險(xiǎn)Type II 錯(cuò)誤 (b 錯(cuò)誤) 是當(dāng) Ho有錯(cuò)誤時(shí)卻接受 有時(shí)稱(chēng)作 消費(fèi)者風(fēng)險(xiǎn).D

23、ecisionType 1錯(cuò)誤Type 2錯(cuò)誤正確決定正確決定真相Ho, =Ha, not =Ho, =Ha, not =法庭和商業(yè)上的決策風(fēng)險(xiǎn)24The p ValueAnother 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 i

24、s 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 reje

25、ct the Null hypothesis.25p 值衡量決策風(fēng)險(xiǎn)的另一種方法是通過(guò)P值.P值是指一個(gè)因素可測(cè)的重要性水平. 當(dāng)樣本和總體相對(duì)時(shí)，P值是指觀(guān)測(cè)到其中差別的機(jī)會(huì)率.P值也指如果拒絕虛無(wú)性假設(shè)可能發(fā)生錯(cuò)誤的概率（錯(cuò)誤I）除非在基于工程判斷上的例外，我們將錯(cuò)誤I 的可接受水平定在a = 0.05.從而，任何小于0.05的P值就表示虛無(wú)性假設(shè)被拒絕。26Defining HypothesesNull HypothesesHO: X1=TargetHO: X1=mHO: X1-X2=0HO:m1-m2=0HO: X1=X2=X3=.XnHO: s1=s2HO: S1=S2HO: S1=

26、S2=S3=.SnAlternative HypothesesHA:m1m2 Inequalities are two sided testsHA:X1X2HA:m1m2HA:X1X2 One Sided test are used for hypotheses.HA: m1m2HA:X1X2HA: X1-X20 _HA: X1-X20 _HA: s1s2 _HA: s1S2 _Scripting Hypotheses as equations is useful when stating. 27定義假設(shè)虛無(wú)性假設(shè)HO: X1=TargetHO: X1=mHO: X1-X2=0HO:m1-m2

27、=0HO: X1=X2=X3=.XnHO: s1=s2HO: S1=S2HO: S1=S2=S3=.Sn選擇性假設(shè)HA:m1m2 不等式是針對(duì)兩邊的測(cè)試HA:X1X2HA:m1m2HA:X1X2 單邊測(cè)試用于 假設(shè).HA: m1m2HA:X1X2HA: X1-X20 _HA: X1-X20 _HA: s1s2 _HA: s1S2 _把假設(shè)以等式陳述很有用. 28Hypothesis Testing ProtocolThe hypotheses are always statements about the population parameters.State your null hypoth

28、esis (Ho ) HO : 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 (Ha )HA : 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 base

29、d on the Hypothesis being tested.Determine the level of acceptable risk.a Risk: usually 5% (Default)b Risk: Usually 10 20% (Default)29假設(shè)檢驗(yàn)協(xié)議假設(shè)總是關(guān)于總體參數(shù)的陳述.定明虛無(wú)性假設(shè) (Ho ) HO : A國(guó)與B國(guó)居民身高相等 (m A = m B ).規(guī)定選擇性假設(shè) (Ha )HA : A國(guó)居民身高低于B國(guó)居民的身高 (m A m B ).基于在需被測(cè)試的假設(shè)上，決定適合的統(tǒng)計(jì)測(cè)試.決定可接受的風(fēng)險(xiǎn)程度.a 風(fēng)險(xiǎn): 通常 5% (預(yù)設(shè)值)b 風(fēng)險(xiǎn): 通常10 20% (預(yù)設(shè)值)30Hypothesis Testing Protocol (Cont)Determine the