Minitab簡易教學(xué)

1、Statistical Analysis with Minitab 15 分析簡易清楚版11、Minitab的基本操作2Minitab有五個標(biāo)準(zhǔn)窗口:SessionProject ManagerGraphData WorksheetMinitab Basics - Layout1、Basics3Open a project (worksheet): project (open worksheet) minitab project (worksheet)Keyboard shortcutsShow worksheets folder: Ctrl+Alt+DShow graphs folder:

2、Ctrl+Alt+GShow session folder: Ctrl+Alt+MEdit last dialog: Ctrl+EOpen a project and shortcut key 1、Basics42、基本圖形分析5Graph 常見圖形ScatterplotHistogramBoxplotTime series plotGraph2、Graph 6GraphScatterplot Batteries.MTW1打開 BATTERIES.MTW.2選擇 Graph Scatterplot.3 選擇 With Regression and Groups, 然后 OK.4在Y varia

3、bles, 輸入FlashRecov. 在Xvariables, 輸入VoltsAfter.5 在Categorical variables for grouping (0-3), 輸入 Formulation.6 單擊Scale, 然后選擇 Reference Lines.7 在Show reference lines at Y values,輸入5.25. 單擊各對話框OK.2、Graph 7GraphScatterplot Batteries.MTW2、Graph 8用CAP .MTW中的數(shù)據(jù)，創(chuàng)建柱形圖以描述頻率分布的形狀)In Minitab:GraphHistogramGraphH

4、istogramCAP .MTW2、Graph 9Histogram Another Option1打開 PULSE.MTW.2選擇 Stat Basic Statistics Graphical Summary.3在Variables, 輸入Pulse1. 選擇OK.選擇“Graphical Summary”PULSE .MTW2、Graph 10GraphBoxplot(Box Plot 是一種將所有的數(shù)值排序后的圖形表示) （Box Plot 包含有箱子, 胡須 (whiskers), 飛點(diǎn) (outliers)Whisker-(胡須)上下胡須是從四分位線延伸到上下限范圍內(nèi)的最高、最低值

5、Outliers (飛點(diǎn)) 超出上或下限的點(diǎn))Upper Limit = Q3 + 1.5(Q3-Q1)Lower Limit = Q1 - 1.5(Q3-Q1)WhiskerWhiskerMedianFirst QuartileThird QuartileOutlier2、Graph 11Boxplot ExampleCARPET .MTW1 打開CARPET.MTW.2選擇Graph Boxplot 3 選擇One Y下的With Groups. 單擊OK.4在Graph variables, 輸入Durability. 5 在Categorical variables for group

6、ing (1-4, outermost first), 輸入Carpet. 6 單擊Labels, 然后選中 Data Labels.7 在Label標(biāo)簽里, 選擇Medians. 選中 Use y-value labels. 單擊OK.8 選中Data View.9 在Categorical variables for attribute assignment, 輸入Carpet. 在各對話框單擊OK.2、Graph 12Boxplot Example CARPET .MTW2、Graph 13Boxplot Another OptionCARPET .MTW2、Graph 14Graph

7、Time Series Plot 1打開 ABCSALES.MTW.2選擇Graph Time Series Plot 或者Stat Time Series Time Series Plot. 3 選擇With Groups, 單擊 OK.4 在Series,輸入sales.5 在Categorical variables for grouping (1-3), 輸入AdAgency.6 單擊Time/Scale.7 在Time Scale選Calendar 然后選擇 Month Year.8 在Month的開始值下輸入1 在Year下輸入2000.9 在各對話框單擊OK.ABCSALES.M

8、TW2、Graph 15ABCSALES.MTWGraph Time Series Plot 2、Graph 16StatBasic Statistics Normality Test 2、Graph 1打開 CRANKSH.MTW.2選擇 Stat Basic Statistics Normality Test.3在Variable, 輸入 AtoBDist. 單擊OK.17StatBasic Statistics Normality Test 2、Graph 183.1、基本統(tǒng)計量分析19StatBasic Statistics Display Descriptive Statistics

9、 3.1、StatBasic Statistics1打開 PULSE.MTW.2選擇Stat Basic Statistics Display Descriptive Statistics.3在 Variables, 輸入Height. 4 在By variable, 輸入Sex.5單擊Graphs 選中Boxplot of data and Individual value plot. 6 在各對話框單擊OK.PULSE.MTW203.1、StatBasic StatisticsStatBasic Statistics Display Descriptive Statistics 213.1

10、、StatBasic StatisticsStatBasic Statistics Display Descriptive Statistics Session 窗口Descriptive Statistics: Height Variable Sex N N* Mean SE Mean StDev Minimum Q1 Median Q3Height 1 57 0 70.754 0.342 2.583 66.000 69.000 71.000 73.000 2 35 0 65.400 0.433 2.563 61.000 63.000 65.500 68.000Variable Sex Ma

11、ximum Height 1 75.000 2 70.000 平均的標(biāo)準(zhǔn)誤差 = / n223.1、StatBasic StatisticsStatBasic Statistics Store Descriptive Statistics 將所需要的分析性數(shù)據(jù)存儲在worksheet中233.2、相關(guān)與回歸24Correlation3.2、Stat Correlation and Regression打開文件 DM Correlation Regression.mpj, worksheet Correlation Example.mtw - Measurement data我們先逐個分析 X

12、和Y, 及X2 和 Y2之間的關(guān)系.Correlations (Pearson)Correlation of Y and X = 0.878Correlations (Pearson)Correlation of Y2 and X2 = 0.391相關(guān)系數(shù) r25相關(guān)系數(shù)(r) 為 -1 和+1之間的某個數(shù)值。-1 表示有很強(qiáng)的負(fù)相關(guān)0 表示完全不相關(guān)+1 表示有很強(qiáng)的正相關(guān) 判定規(guī)則: 相關(guān)系數(shù) (r) .80 或者 Correlation and RegressionCorrelation26為更加明顯的表示 X (Predictor) 與 Y (Response)的關(guān)系，我們用Fitte

13、d Line Plot進(jìn)行分析 打開 DMCorrelation Regression.mpjRegressionR-Square回歸式3.2、Stat Correlation and Regression27From the Fitted Line Plot, we can see that as the age of the propellant increases the Shear Strength decreases.This is an example of an inverse relationship.We also see a linear equation and an R

14、-Sq value. What are these? Lets explore!3.2、Stat Correlation and RegressionRegression28Session窗口Regression Analysis: Shear Strength (psi) versus Age of Propellant (weeks) The regression equation isShear Strength (psi) = 2628 - 37.15 Age of Propellant (weeks)S = 96.1061 R-Sq = 90.2% R-Sq(adj) = 89.6%

15、Analysis of VarianceSource DF SS MS F PRegression 1 1527483 1527483 165.38 0.000Error 18 166255 9236Total 19 1693738 R-Square (決定系數(shù)) 全體變動中根據(jù)回歸直線能說明的變動. R-Square = 90.2%,即是說Shear Strength (psi) 的變化有90.2%的變動可由versus Age of Propellant (weeks)變動來說明. 而9.8%的變動是由其它的原因引起的變動. 回歸式 0 : 截距 X是0的時候,預(yù)測的Y值 上例中, Age

16、 of Propellant (weeks)變動率是0的時候, Shear Strength (psi)是2628. 1 : 偏差 X增加1時, Y值的增加幅度 上例中, Age of Propellant (weeks)增加1, Shear Strength (psi)增加1,即, 預(yù)想增加-37.15.3.2、Stat Correlation and RegressionRegression293.3、假設(shè)檢驗30假設(shè)檢驗?zāi)軒椭阃ㄟ^數(shù)據(jù)作出決斷，確定什么才是真正影響過程的因素介紹假設(shè)檢驗介紹假設(shè)檢驗程序?qū)W習(xí)以下假設(shè)檢驗方法VARIANCE TESTING (方差檢驗)Test for e

17、qual variancesMEAN TESTING (均值檢驗)2 sample t-testPROPORTIONS TESTING(比例檢驗)2 proportions testHypothesis Testing3.3、StatBasic Statistics31Global Warming ExampleWashington, DC - (AP)Global warming continues to increase at alarming rates. The EPA continues to develop plans to curb C02 output at all U.S.

18、manufacturing facilities.Avg Change In Temp1960s 70s 80sCO2 Output1960s 70s 80s3.3、StatBasic Statistics32假設(shè)檢驗的基本概念正確處理一些有疑惑的事情 減少主觀判斷提出設(shè)想篩選并丟棄冗長的信息有效的防止錯誤性結(jié)論的風(fēng)險3.3、StatBasic StatisticsHo = Null Hypothesis Ha = Alternative HypothesisP-Value = Probability Value 它能 關(guān)鍵術(shù)語33假設(shè)檢驗的基本概念3.3、StatBasic Statisti

19、cs假設(shè)檢驗是簡單比較真實結(jié)果與假設(shè)的差異，通過詢問:它們的結(jié)論相一致嗎?假設(shè)檢驗步驟： 通過表述零假設(shè)開始, (即兩個總體的特征是相等的) Ho 然后闡述備擇假設(shè) (即兩個總體的特征是不相同的，具有顯著差異) Ha 假設(shè)檢驗將通過樣本數(shù)據(jù)決定零假設(shè)不為假的可能性 PValue假設(shè)檢驗的結(jié)論是針對總體參數(shù)的(而不是樣本)34無處不在的P值!One-way ANOVA: Clarity versus Region Source DF SS MS F PRegion 2 0.0383 0.0192 1.27 0.295Error 35 0.5303 0.0152Total 37 0.5687S =

20、 0.1231 R-Sq = 6.74% R-Sq(adj) = 1.41% Pooled StDev = 0.12313.3、StatBasic Statistics35兩種類型的錯誤 3.3、StatBasic Statistics在假設(shè)檢驗過程中，我們可能會犯兩類錯誤 Type I Error ( Risk, Producers Risk) 從同一個總體取出的兩組數(shù)據(jù)，結(jié)論卻是存在差異 的可能性。 Type II Error ( Risk, Consumers Risk) 從兩個不同的總體中取出的兩組數(shù)據(jù)，結(jié)論卻是沒有差異的可能性 Your DecisionAccept HoThe Tr

21、uthHo TrueHo FalseType IError -Risk)Type II Error -Risk)CorrectCorrectReject Ho36假設(shè)檢驗的判定P Value Is Extremely Important Remember This Key Saying.If P is Low , Ho Must Go!p a fail to reject the Null Hypothesis (不能拒絕零假設(shè))p Basic Statistics37如何設(shè)定 P值 ?We would like there to be less than a 10% chance that

22、these observations could have occurred randomly ( = .10)Five percent is much more comfortable ( = .05)One percent feels very good ( = .01)The selection of the alpha level is based on the consequences of an incorrect decision to reject the null hypothesis and accept the alternative hypothesis.For mos

23、t cases we will use .05 It depends3.3、StatBasic Statistics381-Sample Z2-Sample t1-Sample tPaired tt-test的選擇 1-Sample Z 在當(dāng)我們想評價樣本Data的平均和母集團(tuán)(全體集團(tuán))的平均是否相同的時候. 且當(dāng)母集團(tuán)的平均和標(biāo)準(zhǔn)偏差已知的時候適用. 為了觀察從D電子購買的部品的平均重量,隨機(jī)抽取10個樣本并對其重量進(jìn)行測量. 我們希望部品的重量為40g, 到目前為止生產(chǎn)的部品的母標(biāo)準(zhǔn)偏差為3g. 1-Sample t 在當(dāng)我們想評價樣本Data的平均和母集團(tuán)(全體集團(tuán))的平均是否相同的時

24、候. 且當(dāng)母集團(tuán)的平均已知而標(biāo)準(zhǔn)偏差未知的時候適用. 為了觀察從D電子購買的部品的平均重量,隨機(jī)抽取10個樣本并對其重量進(jìn)行測量. 我們希望部品的重量為40g, 而部品的母標(biāo)準(zhǔn)偏差未知. 2-Sample t 在當(dāng)我們想評價從兩個相互不同的集團(tuán)中取出的樣本Data的平均是否相同的時候適用. 為了評價從D公司和E公司購買的部品的平均重量是相同還是不同,從各公司購買的部品中各隨機(jī)抽取10個并測量其重量. Paired t 在當(dāng)我們想評價兩個互相成對的樣本Data的平均是否的時候適用. 為了評價從D公司購買的部品的左側(cè)厚度和右側(cè)厚度的平均是相同還是不同,隨機(jī)抽取 10個并測量其左側(cè)和右側(cè)厚度.Sta

25、tBasic Statistics t-test3.3、StatBasic Statistics393.3、StatBasic StatisticsStatBasic Statistics 2 Sample tFURNACE.MTW 1打開 FURNACE.MTW. 2選擇Stat Basic Statistics 2-Sample T.3選擇 Samples in one column. 4在 Samples, 輸入BTU.In.5 在Subscripts, 輸入Damper.6選中Assume equal variances. 單擊OK.403.3、StatBasic Statistics

26、Session 窗口Two-Sample T-Test and CI: BTU.In, Damper Two-sample T for BTU.InDamper N Mean StDev SE Mean 1 40 9.91 3.02 0.48 2 50 10.14 2.77 0.39Difference = mu (1) - mu (2)Estimate for difference: -0.23595% CI for difference: (-1.450, 0.980)T-Test of difference = 0 (vs not =): T-Value = -0.38 P-Value

27、= 0.701 DF =88Both use Pooled StDev = 2.8818 P-Value P-Value 0.05 的時候 可以推斷出兩個設(shè)備的Data 平均相同. P-Value 0.05 的時候 可以推斷出兩個設(shè)備的Data 平均不相同. 上例中的P-Value=0.701, 比0.05大,可說明 從BTU.In平均效率和Damper的平均效率相同. 95.0% CI : 兩個設(shè)備平均差異的95%信賴區(qū)間 - 上例中兩個設(shè)備平均差異的95% 信賴區(qū)間 (-1.450, 0.980) , 0在這個95% 信賴區(qū)間以內(nèi). 即,(BTU.In平均效率 Damper平均效率 = 0

28、 ) 可以成立. 從這兩個設(shè)備中分別收集的Data的平均可以相等的意思. 所以, 安裝的BTU.In和Damper平均效率是相等的.StatBasic Statistics 2 Sample tFURNACE.MTW 411-Proportion2-Proportionp-test的選擇 1-Proportion 在當(dāng)我們想評價樣本Data的比例和母集團(tuán) (全體集團(tuán))的比例是否相同的時候.且當(dāng) 母集團(tuán)的比例已知的時候適用. 2-Proportion 在當(dāng)我們想評價互不相同的集團(tuán)中取出的 樣品的比例是否相同的時候. StatBasic Statistics p-test3.3、StatBasic

29、 Statistics423.3、StatBasic Statistics1選擇Stat Basic Statistics 2 Proportions.2選擇Summarized data. 3在 First sample的Events里輸入44. 在Trials里輸入50.4在Second sample的Events里輸入42. 在Trials里輸入50. 單擊 OK.StatBasic Statistics p-test433.3、StatBasic StatisticsSession 窗口Test and CI for Two Proportions Sample X N Sample

30、p 1 44 50 0.880000 2 42 50 0.840000Difference = p (1) - p (2)Estimate for difference: 0.0495% CI for difference: (-0.0957903, 0.175790)Test for difference = 0 (vs not = 0): Z = 0.58 P-Value = 0.564Fishers exact test: P-Value = 0.774P1=P2StatBasic Statistics p-test441-Variance2-Variance-test的選擇 1-Var

31、iance 在當(dāng)我們想評價樣本Data的方差和母集團(tuán) (全體集團(tuán))的方差是否相同的時候. 且當(dāng)母集團(tuán)的方差已知的時候適用. 2-Variance 在當(dāng)我們想評價互不相同的集團(tuán)中取出的 樣品的方差是否相同的時候. StatBasic Statistics -test3.3、StatBasic Statistics453.3、StatBasic Statistics1打開 FURNACE.MTW.2選擇Stat Basic Statistics 2 Variances.3選擇Samples in one column.4在Samples, 輸入BTU.In.5在Subscripts, 輸入Damp

32、er. 單擊OK.FURNACE.MTW StatBasic Statistics -test463.3、StatBasic StatisticsSession窗口Test for Equal Variances: BTU.In versus Damper 95% Bonferroni confidence intervals for standard deviationsDamper N Lower StDev Upper 1 40 2.40655 3.01987 4.02726 2 50 2.25447 2.76702 3.56416F-Test (Normal Distribution)

33、Test statistic = 1.19, p-value = 0.558Levenes Test (Any Continuous Distribution)Test statistic = 0.00, p-value = 0.9961=2StatBasic Statistics -test473.4、方差分析（ANOVA)48ANOVA3.4、StatANOVAOne-WayMain Effects PlotGeneral Linear ModelInteraction PlotOne-Way1打開 EXH_AOV.MTW.2選擇Stat ANOVA One-Way.3在 Response

34、, 輸入Durability. 在Factor, 輸入Carpet.4 在各對話框中單擊OK.49One Way ANOVA3.4、StatANOVA503.4、StatANOVASession 窗口One-way ANOVA: Durability versus Carpet Source DF SS MS F PCarpet 3 146.4 48.8 3.58 0.047Error 12 163.5 13.6Total 15 309.9S = 3.691 R-Sq = 47.24% R-Sq(adj) = 34.05%Individual 95% CIs For Mean Based on

35、 Pooled StDevLevel N Mean StDev -+-+-+-+1 4 14.483 3.157 (-*-)2 4 9.735 3.566 (-*-)3 4 12.807 1.506 (-*-)4 4 18.115 5.435 (-*-) -+-+-+-+ 10.0 15.0 20.0 25.0Pooled StDev = 3.691 結(jié)果分析 - 上例中的P-Value=0.047,比0.05小,可說明四種地毯中 至少有一種地毯的耐久性的平均與其它三種不同. P : P-Value P-Value 0.05 的時候 可推斷出各集團(tuán)間Data 平均相同. P-Value 0.0

36、5 的時候 可得知至少有一個集團(tuán)Data 平均與其它不同.上例中的P-Value=0.047,比0.05小, 可說明四種 地毯中至少有一種地毯的耐久性的平均與其它地毯不同. One Way ANOVA51General Linear Model3.4、StatANOVAGLM.MTW 523.4、StatANOVASession 窗口General Linear Model: Burnt French versus Temp, Basket Desig, CycleTime Factor Type Levels ValuesTemp fixed 2 300, 350Basket Design

37、fixed 3 A, B, CCycleTime fixed 3 40, 50, 60Analysis of Variance for Burnt French Fries, using Adjusted SS for TestsSource DF Seq SS Adj SS Adj MS F PTemp 1 136.963 136.963 136.963 48.34 0.000Basket Design 2 6.037 6.037 3.019 1.07 0.355CycleTime 2 743.815 743.815 371.907 131.26 0.000Temp*Basket Desig

38、n 2 17.370 17.370 8.685 3.07 0.059Temp*CycleTime 2 228.926 228.926 114.463 40.40 0.000Basket Design*CycleTime 4 60.519 60.519 15.130 5.34 0.002Temp*Basket Design*CycleTime 4 18.741 18.741 4.685 1.65 0.182Error 36 102.000 102.000 2.833Total 53 1314.370S = 1.68325 R-Sq = 92.24% R-Sq(adj) = 88.58%Gener

39、al Linear ModelGLM.MTW 533.4、StatBasic StatisticsGeneral Linear ModelGLM.MTW 543.4、StatBasic StatisticsGeneral Linear ModelGLM.MTW 553.5、實驗設(shè)計（DOE)56實驗計劃法基礎(chǔ)3.5、StatDOECreate Factorial Design:要因配置法實驗設(shè)計Define Custom Factorial Design:在變更當(dāng)前的 實驗計劃而再指定時使用。Analyze Factorial Design:得出實驗分析結(jié)果Factorial Plot:主效果

40、, 交互效果 plot 作成Contour/Surface(Wireframe)Plots:展現(xiàn)實驗的反應(yīng)表面Overlaid Contour Plot:以視覺性展示多個反應(yīng)變量的妥協(xié)領(lǐng)域Response Optimizer:尋找滿足目標(biāo)值因子的最佳組合以最少的實驗次數(shù)迅速獲得最大的信息量的計劃方法. 把以往的經(jīng)驗或者理論性、 技術(shù)性知識等的原有技術(shù)與依照實驗計劃法的知識結(jié)合起來 Factorial:要因配置實驗RS Design:反應(yīng)表面實驗Mixture Design:混合物實驗Modify Design:對實驗的修正Display Design:實驗計劃后生成的內(nèi)容通過 Workshee

41、t 可見 57DOE 用語因子(Factor)實驗所用的輸入要素(例) 溫度, 濕度,水準(zhǔn)(Level)各實驗因子的設(shè)定值 (例) 溫度 100 200 (-) (+)反應(yīng)值(Response)實驗的數(shù)值性結(jié)果(一般用 Y表示) (例) Y = 267mm主效果(Main Effect)隨一個獨(dú)立因子的水準(zhǔn)變化相應(yīng)的 (例) E1 = 2 反應(yīng)值的影響 E2 = -7交互效果兩個以上的因子結(jié)合后對反應(yīng) (例) E12 = 5 (Interaction Effect)因子產(chǎn)生的影響解析度(Resolution)在部分實施法中表示實驗設(shè)計的攪亂(例) III, IV, V 程度的記號 攪亂(Con

42、founding)以兩個以上因子的效果合并后 (例) 1 + 2 產(chǎn)生的現(xiàn)象難以分離 1+3, 2+23.5、StatDOE582K-Run the Experiment and Collect the DataSet number of factors Keep default setting on 2-level factorial (default)Press the “Designs” button3.5、StatDOE592K-Run the Experiment and Collect the DataEnter the number of replicatesIn this ca

43、se, we will only consider 1 replicate for this experiment; Leave the “Center Points” and “Blocks” fields on their default settingsPress OK and you will return to the previous screenSelect “Full Factorial”3.5、StatDOE60該例有兩個定量性輸入因子 (Temperature and Time) 和一個定性輸入因子 (Chip Mfr.) 產(chǎn)生一個輸出RatingThe factors a

44、nd levels:Temp: 160o C (-1), 180o C (1)Time: (min): 8 (-1), 12 (1)Chip: Brand A (-1), Brand B (1)實驗設(shè)計結(jié)果如下矩陣:用1和 -1 代表因子的水平稱為 Coded Units. 因子的高水平為 1 低水平為 -1. 該例為全因子實驗3.5、StatDOE2K DOE 612K DOE Select “Factors” and enter yourfactor names. We could also list theuncoded levels here, however, ourtask was

45、 to use coded levels.When finished press OK onthis menu and the “CreateFactorial Design” menu The output is in the worksheet3.5、StatDOE622K DOE Ensure you haveselected “RandomizeRuns” and be sure tostore your design in aworksheet3.5、StatDOE632K DOE-Worksheet3.5、StatDOE641. Enter Response2. Identify

46、the Terms to include in the model. Initially include all factors and interactions. 3.5、StatDOE2K DOE-Analyze653. Click on the Graphs button so we can review the Normal probability plot of the Effects4. Identify the Normal and Pareto plots. The default value of Alpha in Minitab 14 is 0.05.3.5、StatDOE

47、2K DOE-Analyze66These are the contrasts you previously calculatedNotice there are no F-values or P-values because there is only one measurement in each cell and the error term can not be calculated.3.5、StatDOE2K DOE-Analyze67We see here that the Effects associated with A(Temp) and the A*C (Temperatu

48、re * Chip) Interaction are important. So we will evaluate the highest order interaction and not worry about the Main Effect.3.5、StatDOE2K DOE-Analyze68This chart paretos the effects and uses a p0.05 as a cutoffYou can see that the A and A*C interactions are identified as good candidatesWe can also r

49、educe the model by removing the ABC interaction and get some analytical basis3.5、StatDOE2K DOE-Analyze69But what is the basis for the red line?The Ho is that there are no significant effects (none of the terms are significant)Therefore, we would expect the Effects to be 0 to support the HoThe red li

50、ne is a confidence limit based on our Alpha level that establishes a basis for saying Anything beyond that limit is different than 0The calculation of the line is based on a few factors:Experimental errora levelTotal number of runs in the experimentDegrees of FreedomAs we reduce the model, the posit

51、ion of the line will also change!3.5、StatDOE2K DOE-Analyze70去掉三因子的交互作用ABC進(jìn)行重復(fù)分析將有足夠的自由度來得到誤差項并給出P值!3.5、StatDOE2K DOEReduced Model71Now we can reduce the model more by removing the interactions that are significantly above our a value of 0.05Remove theseinteractions3.5、StatDOE2K DOEReduced Model723.5、StatDOE2K DOEReduced Model733.5、StatDOE2K DOERed