1、GE Company ProprietaryVersion 2.01Minitab Primer Minitab Primer Introduction to StatisticalData Analysis With Minitab GE Company ProprietaryVersion 2.02Minitab Primer IntroductionThis primer is designed to provide one with the skills necessary to effectively employ Minitab within the Six Sigma frame
2、work.It begins with an introduction to selected file,data manipulation,and help functions,followed by a series of demonstrations related to transaction and service quality.The student is encouraged to work through each demonstration,following the lead of the instructor.Each demonstration begins with
3、 a page highlighting the Minitab functions applied in working-through the examples.These pages reflect the commands that the user would see on the screen while using Minitab(the heirarchical structure of Minitab is preserved).It is assumed that the user is familiar with basic statistics,e.g.,hypothe
4、sis testing and regression analysis.A companion primer,entitled Statistics Primer-Introduction to Statistics Through Graphical Analysis is available on the World-Wide-Web(GE Corporate)for those requiring a review of fundamental statistics.Augie Stagliano Pittsfield,MAOctober 1996GE Company Proprieta
5、ryVersion 2.03Minitab Primer Takeaways After Completing This Training,You Will Be Able To.Import Data Files Perform Basic Data Manipulation Techniques Use Functions to Perform Calculations Construct and Interpret Various Graph Types Generate and Interpret Basic Statistical Information Apply One and
6、Two Sample Hypothesis Tests Perform Simple Linear Regression Apply c2 Tests and One-Way ANOVA An Overview of Applied Statistical Techniques Stressing Interpretation of Analytical ResultsGE Company ProprietaryVersion 2.04Minitab Primer File Commands New Worksheet Open Worksheet Merge Worksheet Save W
7、orksheet Print Window Get Worksheet Information Display Data Restart Minitab ExitGE Company ProprietaryVersion 2.05Minitab Primer Help and Manip Commands Help Commands:Contents Getting Started.How Do I.Search for Help On.Sort Stack UnstackManip Commands:GE Company ProprietaryVersion 2.06Minitab Prim
8、er Demonstration One STAT Basic Statistics Descriptive Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare Test CALC Probability Distributions Normal STAT ANOVA ONEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Graphs Dotplot STAT SPC Run ChartG
9、raphical Analysis STAT Regression Regression Fitted Line PlotRegression AnalysisChoice of Tool Depends Upon the Requirements of the AnalysisGE Company ProprietaryVersion 2.07Minitab Primer Example:Receivables“Days-to-Collection”Data File:days.xlsVariable:DaysCollection terms for receivables is 60 da
10、ys.Payments are entered into a data collection system in the same time-order as they are received.Characterize this process and determine its long term z-value and sigma.Also,test that the average days-to-collection is equal to 50 days(Business Target).Demonstration One GE Company ProprietaryVersion
11、 2.08Minitab Primer Receivables Process Characterization Descriptive StatisticsVariable N N*Mean Median TrMean StDev SEMeanDays 50 0 63.80 64.00 63.75 8.45 1.19 Variable Min Max Q1 Q3Days 45.00 87.00 58.75 68.25857565554520100DaysFrequency605040302010908070605040I ndexDaysHistogram.Time Series Plot.
12、-Analyze-Improve-Control GE Company ProprietaryVersion 2.09Minitab Primer Receivables Process-Yield&Sigma Values Days Count 45 1 48 2 49 1 53 1 54 3 55 1 58 3 59 3 60 1 61 2 62 1 63 4 64 4 65 1 66 2 67 6 68 2 69 1 70 2 71 2 72 1 74 2 77 1 78 1 79 1 87 1 N=50 16 Items Within Spec(60 days)34 Items Out
13、side of Spec Inverse Cumulative Distribution Function Normal with mean=0 and standard deviation=1.00000 P(X 50.00Variable N Mean StDev SE Mean T P-ValueDays 50 63.80 8.45 1.19 11.55 0.0000Hypothesis Test of the Mean.Business Target:50 Days a a=0.05 Test for Mean 50 DaysConf.Level=95.0%Results.-Analy
14、ze-Improve-Control GE Company ProprietaryVersion 2.011Minitab Primer Choice of Tool Depends Upon the Requirements of the AnalysisDemonstration Two STAT Basic Statistics Descriptive Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare Test CALC Probability Distributions Normal STAT ANO
15、VA ONEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Graphs Dotplot STAT SPC Run ChartGraphical Analysis STAT Regression Regression Fitted Line PlotRegression AnalysisGE Company ProprietaryVersion 2.012Minitab Primer Example:GE Stock DataData File:price.xlsVari
16、able:Price Description:this data set contains actual daily price data for atime period of approximately two years.The data is ordered in its original time sequence.Characterize the data and checkfor stability over time.-Analyze-Improve-Control GE Company ProprietaryVersion 2.013Minitab Primer 115105
17、9585756555453595%Confidence Interval for Mu65605595%Confidence Interval for MedianVariable:price 55.000 18.449 61.969Maximum3rd QuartileMedian1st QuartileMinimumn of dataKurtosisSkewnessVarianceStd DevMeanp-value:A-Squared:57.500 20.866 65.380109.750 65.812 56.750 49.625 45.500509.000 0.296 1.338383
18、.499 19.583 63.674 0.000 51.52395%Confidence Interval for Median95%Confidence Interval for Sigma95%Confidence Interval for MuAnderson-Darling Normality TestDescriptive Statistics5003001001101009080706050Observationprice 1.000 0.000 8.000339.000261.000 1.000 0.000245.000255.475 13.000Approx p-value f
19、or Oscillation:Approx p-value for Trends:Longest run up or down:Expected number of runs:Number of runs up or down:Approx p-value for Mixtures:Approx p-value for Clustering:Longest run about median:Expected number of runs:Number of runs about median:Run Chart for priceResults of GE Stock Price Demons
20、tration-Analyze-Improve-Control GE Company ProprietaryVersion 2.014Minitab Primer Choice of Tool Depends Upon the Requirements of the Analysis STAT Basic Statistics Descriptive Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare Test CALC Probability Distributions Normal STAT ANOVA O
21、NEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Graphs Dotplot STAT SPC Run ChartGraphical Analysis STAT Regression Regression Fitted Line PlotRegression AnalysisDemonstration ThreeGE Company ProprietaryVersion 2.015Minitab Primer Example:Comparing Two Differe
22、nt Business RegionsData File:receive.xlsVariables:region1,region2(t-test)region1,reg1$(scatter diagram,correlation,and regression)Evaluate the relative performance of these two business regions using hypothesis testing.Also,prepare a scatter diagram and regression model(calculate correlation co-effi
23、cient)using Reg1$as the response variable and Region1 as the predictor.Measure-Improve-Control GE Company ProprietaryVersion 2.016Minitab Primer Two Sample T-Test and Confidence IntervalTwosample T for region1 vs region2 N Mean StDev SE Meanregion1 100 46.10 10.1 1.01region2 100 44.48 9.84 0.9895%C.
24、I.for mu region1-mu region2:(-1.2,4.40)T-Test mu region1=mu region2(vs not=):T=1.14 P=0.26 DF=197Hypothesis Test Results.Is There a Difference in the Average Levelof Receivables Ages Between Regions 1&2?Measure-Improve-Control GE Company ProprietaryVersion 2.017Minitab Primer Correlations(Pearson)Co
25、rrelation of region1 and reg1$=0.930Correlation Coefficient(r).Scatter Plot.80706050403020750650550450350250150region1reg1$Establish a Relationship Between Responseand Predictor Before Building the ModelMeasure-Improve-Control GE Company ProprietaryVersion 2.018Minitab Primer 80706050403020850750650
26、550450350250150region1reg1$R-Squared=0.865Y=29.0826+9.65584XRegression PlotFitted Line Plot.Measure-Improve-Control GE Company ProprietaryVersion 2.019Minitab Primer Regression AnalysisThe regression equation isreg1$=29.1+9.66 region1Predictor Coef Stdev t-ratio pConstant 29.08 18.22 1.60 0.114regio
27、n1 9.6558 0.3861 25.01 0.000s=38.95 R-sq=86.5%R-sq(adj)=86.3%Analysis of VarianceSOURCE DF SS MS F pRegression 1 948965 948965 625.40 0.000Error 98 148702 1517Total 99 1097667Unusual ObservationsObs.region1 reg1$Fit Stdev.Fit Residual St.Resid 10 45.0 381.00 463.60 3.92 -82.60 -2.13R 31 41.0 525.00
28、424.97 4.36 100.03 2.58R 53 75.0 739.00 753.27 11.82 -14.27 -0.38 X 64 59.0 513.00 598.78 6.33 -85.78 -2.23R 70 47.0 404.00 482.91 3.91 -78.91 -2.04R 76 23.0 251.00 251.17 9.73 -0.17 -0.00 X 78 69.0 648.00 695.34 9.67 -47.34 -1.25 X 92 20.0 176.00 222.20 10.80 -46.20 -1.23 X 95 50.0 598.00 511.87 4.
29、18 86.13 2.22R 98 45.0 558.00 463.60 3.92 94.40 2.44R R denotes an obs.with a large st.resid.X denotes an obs.whose X value gives it large influence.Regression Results.Measure-Improve-Control GE Company ProprietaryVersion 2.020Minitab Primer Choice of Tool Depends Upon the Requirements of the Analys
30、isDemonstration Four STAT Basic Statistics Descriptive Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare Test CALC Probability Distributions Normal STAT ANOVA ONEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Graphs Dotplot STAT SPC Run ChartG
31、raphical Analysis STAT Regression Regression Fitted Line PlotRegression AnalysisGE Company ProprietaryVersion 2.021Minitab Primer Demonstration Four Example:Comparing Many Different Business RegionsData File:aging.xlsVariables:Country1-Country5Evaluate the relative performance of five different busi
32、ness regions using boxplots and dotplots.GE Company ProprietaryVersion 2.022Minitab Primer 543212001000COUNTRYAGINGBoxplot Results.Measure-Analyze-Control GE Company ProprietaryVersion 2.023Minitab Primer Character Dotplot .:.:.:.-+-+-+-+-+-+-AGING(1).:.:.:.:.:.:-+-+-+-+-+-+-AGING(2).:.:.:.:.:.:.:.:
33、.:.-+-+-+-+-+-+-AGING(3).:.:.:.:.:.:.:.-+-+-+-+-+-+-AGING(4).:.:.:.:.:.:.:.:.:.:.-+-+-+-+-+-+-AGING(5)-40 0 40 80 120 160Dotplot Results.One-Way Analysis of VarianceAnalysis of Variance on AGING Source DF SS MS F pCOUNTRY 4 424064 106016 246.30 0.000Error 295 126978 430Total 299 551042 Individual 95
34、%CIs For Mean Based on Pooled StDev Level N Mean StDev -+-+-+-1 60 25.93 4.87 (*-)2 60 13.97 16.54 (-*)3 60 46.00 16.20 (*-)4 60 118.25 27.76 (-*)5 60 25.53 28.66 (*-)-+-+-+-Pooled StDev=20.75 35 70 105ANOVA Results.Measure-Analyze-Control GE Company ProprietaryVersion 2.024Minitab Primer Choice of
35、Tool Depends Upon the Requirements of the Analysis STAT Basic Statistics Descriptive Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare Test CALC Probability Distributions Normal STAT ANOVA ONEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Grap
36、hs Dotplot STAT Control Charts Xbar-S SPC Run ChartGraphical Analysis STAT Regression Regression Fitted Line PlotRegression AnalysisDemonstration Five GE Company ProprietaryVersion 2.025Minitab Primer Example:Invoice DisputesData File:chisq.xlsVariables:Process,Invoices,and DisputesDescription:this
37、data set contains the number of invoices issued to customers using six different processes.Invoices is thenumber issued and Disputes is the number of customer issuespending problem resolution.Determine whether the results of this test indicate a difference in the six processes.Measure-Analyze-Contro
38、l GE Company ProprietaryVersion 2.026Minitab Primer processinvoicesdisputes1541624713352154538549156522Results of the Six Trials.Results of the Chi-Square Test.Hypothesis TestHo:(O-E)2=0Ha:(O-E)2 0a:0.05n:(n-1)=5Decision Rule:If p a,Reject HoExpected counts are printed below observed counts invoices
39、 disputesTotal 1 54 1670 57.15 12.85 2 47 13 60 48.99 11.01 3 5215 67 54.70 12.30 4 53 8 61 49.81 11.19 5 49 15 64 52.26 11.74 6 52 2 54 44.09 9.91Total 307 69 376ChiSq=0.174+0.775+0.081+0.359+0.134+0.595+0.205+0.911+0.203+0.902+1.419+6.313=12.071df=5,p=0.035Is the Result Significant at the 0.05 Alp
40、ha Level?Measure-Analyze-Control GE Company ProprietaryVersion 2.027Minitab Primer Example:Receivables Process ControlData File:days.xlsVariables:DaysDescription:Collection terms are 60 days.Payments are entered into a data collection system in the same time-order as they are received.Determine whet
41、her or not the process isin control and capable of satisfying the terms.Measure-Analyze-Improve-GE Company ProprietaryVersion 2.028Minitab Primer Results of Analysis.Is the Process in Control and Capable?Measure-Analyze-Improve-109876543210706050SubgroupMeans20100Std DeviationsMU=63.80UCL=75.18LCL=5
42、2.42S=7.970UCL=16.65LCL=0.000Xbar and S Chart for:DaysGE Company ProprietaryVersion 2.029Minitab Primer State the Goal of Your Work Identify the Desired Output Collect the“Right”DataDont Use Data“Just Because Its Available”Select the Tool(s)that Will Deliver the Desired Results Conclusion Avoid“Over
43、 Analysis”.Identify Your Needs Up-front and Focus on ResultsGE Company ProprietaryVersion 2.030Minitab Primer Appendices1)Solutions to Problems Using Excel a)Demonstration Oneb)Demonstration Two2)Formulae for Calculating Sample Sizea)Attributes Testsb)Variables Tests 3)Minitab Tools and the Breakthr
44、ough StrategyGE Company ProprietaryVersion 2.031Minitab Primer Appendix 1a-ExcelResults of Receivables Demonstration Using Excel Normally Distributed Data Data Stable Over Time Average 64 Days-to-Collection About 68%of the Payments Occur Between 56 and 72 Days About 50%of the Payments Exceed 64 Days
45、 Observations.Descriptive Statistics.DaysMean63.8Standard Error1.19Median64Mode67Standard Deviation8.4Sample Variance71.3Kurtosis0.44Skewness0.07Range42Minimum45Maximum87Sum3,190Count50ConfidLevel(95.000%)2.34Data Set.Payment Days15527236946657767077986596410631167Histogram.His tog r am051 01 52 02
46、54 05 06 07 08 09 0D a y sFrequency0%1 0%2 0%3 0%4 0%5 0%6 0%7 0%8 0%9 0%1 0 0%Run Chart.Run Chart:Days-to-Collection4045505560657075808590135791113151719212325272931333537394143454749PaymentDaysavgGE Company ProprietaryVersion 2.032Minitab Primer Graphical Analysis Reveals Unusual Eventsprice0.0020
47、.0040.0060.0080.00100.00120.000100200300400500600priceRun Chart.Data Set.dayprice1104.002103.633103.004103.885104.386105.007105.638106.009105.2510106.8811107.1312108.3813108.7514108.3815108.25.Histogram051015202545.5050.5655.6260.6865.7470.8075.8580.9185.9791.0396.09101.15106.21BinFrequencyFrequency
48、Histogram.priceMean63.67Standard Error0.87Median56.75Mode#NUM!Standard Deviation19.58Sample Variance383.50Kurtosis0.32Skewness1.35Range64.25Minimum45.50Maximum109.75Sum32410.24Count509Confidence Level(95.000%)1.70Descriptive Statistics.Bimodal Data-Two Different Groups Data Unstable Over Time Descri
49、ptive Statistics Unreliable Due to Data Distribution&Instability Significant Event Occurred at Time“100”Data is Upward Trending After Time“100”The Data Set is GE Stock Price and the Significant Event is a Stock SplitObservations.Appendix 1b-ExcelGE Company ProprietaryVersion 2.033Minitab Primer Appe
50、ndix 2a-Attributes Sample SizeEstimating Sample Size for Attributesn=2 Za/2 w)(2 p qExample:How large a sample size is required to estimate the proportion ofunpaid invoices with a margin of error of+/-4%at a 95%confidence level?n -sample sizeZa/2 -Z-value for Desired Confidence Levelw -Desired Preci
