ge minitab primer

GE Company ProprietaryVersion 2.0 1

Minitab Primer

Minitab Primer Introduction to StatisticalData Analysis With Minitab


Minitab Primer Introduction

This primer is designed to provide one with the skills necessary to effectively employ Minitab within the Six Sigma framework. 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 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., hypothesis 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 1996


Minitab 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 Two Sample Hypothesis Tests• Perform Simple Linear Regression• Apply Tests and One-Way ANOVA

An Overview of Applied Statistical Techniques Stressing Interpretation of Analytical Results

An Overview of Applied Statistical Techniques Stressing Interpretation of Analytical Results


Minitab Primer File Commands

• New Worksheet

• Open Worksheet

• Merge Worksheet

• Save Worksheet

• Print Window

• Get Worksheet Information

• Display Data

• Restart Minitab

• Exit


Minitab Primer Help and Manip Commands

Help Commands:

• Contents

• Getting Started...

• How Do I...

• Search for Help On...

• Sort

• Stack

• Unstack

Manip Commands:


Minitab Primer Demonstration One

• STAT• Basic Statistics

• Descriptive Statistics• 1-Sample t• 2-Sample t• Correlation

• Tables• Tally• Chisquare Test

• CALC• Probability Distributions

• Normal

• STAT• ANOVA

• ONEWAY

Basic Statistical Analysis

• GRAPH• Plot• Time Series Plot• Histogram• Boxplot• Character Graphs

• Dotplot

• STAT• SPC

• Run Chart

Graphical Analysis

• STAT• Regression

• Regression• Fitted Line Plot

Regression Analysis

Choice of Tool Depends Upon the Requirements of the Analysis



Minitab Primer

Example: Receivables “Days-to-Collection” Data File: days.xlsVariable: Days

Collection terms for receivables is 60 days. 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


Minitab Primer

Receivables Process Characterization Receivables Process Characterization

Descriptive Statistics

Variable 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 68.25

8575655545

20

10

0

Days

Freq

uenc

y

605040302010

90

80

70

60

50

40

Index

Day

s

Histogram... Time Series Plot...

MeasureMeasure - Analyze - Improve - Control


Minitab Primer

Receivables Process - Yield & Sigma ValuesReceivables 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 Outside of Spec

Inverse Cumulative Distribution Function

Normal with mean = 0 and standard deviation = 1.00000

P( X <= x) x ??? ??? ??? z-value (LT)z-value (LT)

Sigma = ???Sigma = ???

Yield = ???



Minitab Primer

Is the Average Days-to-Pay On Target ???Is the Average Days-to-Pay On Target ???

T-Test of the Mean

Test of mu = 50.00 vs mu > 50.00

Variable N Mean StDev SE Mean T P-ValueDays 50 63.80 8.45 1.19 11.55 0.0000

Hypothesis Test of the Mean.....

Business Target: 50 Days = 0.05 Test for Mean > 50 Days Conf. Level = 95.0%

Results.....



Minitab Primer



Demonstration Two





• Normal

• STAT• ANOVA

• ONEWAY



• Dotplot

• STAT• SPC

• Run Chart

Graphical Analysis



Regression Analysis


Minitab Primer

Example: GE Stock DataData File: price.xlsVariable: 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.



Minitab Primer

11510595857565554535

95% Conf idence Int erval f or Mu

656055

95% Conf idence Int erval f or Median

Variable: price

55.000

18.449

61.969

Maximum3rd Quart ileMedian1st Quart ileMinimum

n of dat aKurt osisSkewnessVarianceSt d DevMean

p-value:A-Squared:

57.500

20.866

65.380

109.750 65.812 56.750 49.625 45.500

509.000 0.296 1.338

383.499 19.583 63.674

0.000 51.523

95% Conf idence Int erval f or Median

95% Conf idence Int erval f or Sigma

95% Conf idence Int erval f or Mu

Anderson-Darling Normalit y Test

Descriptive Statistics

500300100

110

100

90

80

70

60

50

Observation

pric

e

1.000 0.000 8.000339.000261.000

1.000 0.000245.000255.475 13.000

Approx p-value f or Oscillat ion:Approx p-value f or Trends:Longest run up or down:Expect ed number of runs:Number of runs up or down:

Approx p-value f or Mixt ures:Approx p-value f or Clust er ing:Longest run about median:Expect ed number of runs:Number of runs about median:

Run Chart for price

Results of GE Stock Price Demonstration Results of GE Stock Price Demonstration



Minitab Primer







• Normal

• STAT• ANOVA

• ONEWAY



• Dotplot

• STAT• SPC

• Run Chart

Graphical Analysis



Regression Analysis

Demonstration Three


Minitab Primer

Example: Comparing Two Different Business Regions

Data 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-efficient) using Reg1$$$ as the response variable and Region1 as the predictor.

Measure - AnalyzeAnalyze - Improve - Control


Minitab Primer

Two Sample T-Test and Confidence Interval

Twosample T for region1 vs region2 N Mean StDev SE Meanregion1 100 46.10 10.1 1.01region2 100 44.48 9.84 0.98

95% C.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= 197

Hypothesis Test Results...

Is There a Difference in the Average Levelof Receivables Ages Between Regions 1 & 2?

Is There a Difference in the Average Levelof Receivables Ages Between Regions 1 & 2?



Minitab Primer

Correlations (Pearson)

Correlation of region1 and reg1$$$ = 0.930

Correlation Coefficient (r)...Scatter Plot...

80706050403020

750

650

550

450

350

250

150

region1

reg1

$$$

Establish a Relationship Between Responseand Predictor Before Building the Model

Establish a Relationship Between Responseand Predictor Before Building the Model



Minitab Primer

80706050403020

850

750

650

550

450

350

250

150

region1

reg1

$$$

R-Squared = 0.865

Y = 29.0826 + 9.65584X

Regression Plot

Fitted Line Plot...



Minitab Primer Regression Analysis

The regression equation isreg1$$$ = 29.1 + 9.66 region1

Predictor Coef Stdev t-ratio pConstant 29.08 18.22 1.60 0.114region1 9.6558 0.3861 25.01 0.000

s = 38.95 R-sq = 86.5% R-sq(adj) = 86.3%

Analysis of Variance

SOURCE DF SS MS F pRegression 1 948965 948965 625.40 0.000Error 98 148702 1517Total 99 1097667

Unusual ObservationsObs. region1 reg1$$$ Fit Stdev.Fit Residual St.Resid 10 45.0 381.00 463.60 3.92 -82.60 -2.13R 31 41.0 525.00 424.97 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 4.18 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...



Minitab Primer



Demonstration Four





• Normal

• STAT• ANOVA

• ONEWAY



• Dotplot

• STAT• SPC

• Run Chart

Graphical Analysis



Regression Analysis


Minitab Primer Demonstration Four

Example: Comparing Many Different Business Regions

Data File: aging.xlsVariables: Country1 - Country5

Evaluate the relative performance of five different business regions using boxplots and dotplots.


Minitab Primer

54321

200

100

0

COUNTRY

AG

ING

Boxplot Results...

Measure - Analyze - ImproveImprove - Control


Minitab Primer

Character Dotplot

. .: :: :: :: :: :: .::: :::: :::: ..:::::. -+---------+---------+---------+---------+---------+-----AGING (1) .: :: :.: . ..:::::: . . . :. ::::::::::.::: -+---------+---------+---------+---------+---------+-----AGING(2) . : : . : : : . . :::.:.:.: : . .:.::::::::: :.:. -+---------+---------+---------+---------+---------+-----AGING (3) .. : . ::: . ..:: . . : .: ... ::::::::::.::....... -+---------+---------+---------+---------+---------+-----AGING(4) . :.: . ::: . : : .: :. :.:::: :..:.::::::.:: . -+---------+---------+---------+---------+---------+-----AGING(5) -40 0 40 80 120 160

Dotplot Results...

One-Way Analysis of Variance

Analysis of Variance on AGING Source DF SS MS F pCOUNTRY 4 424064 106016 246.30 0.000Error 295 126978 430Total 299 551042

Individual 95% 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 70 105

ANOVA Results...



Minitab Primer







• Normal

• STAT• ANOVA

• ONEWAY



• Dotplot

• STAT• Control Charts

• Xbar-S• SPC

• Run Chart

Graphical Analysis



Regression Analysis

Demonstration Five


Minitab Primer

Example: Invoice DisputesData File: chisq.xlsVariables: Process, Invoices, and Disputes

Description: this 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.



Minitab Primer

process invoices disputes1 54 162 47 133 52 154 53 85 49 156 52 2

Results of the Six Trials... Results of the Chi-Square Test...

Hypothesis TestHo: (O-E)2 = 0Ha: (O-E)2 > 0: 0.05: (n-1) = 5

Decision Rule: If p < , Reject Ho

Expected counts are printed below observed counts

invoices disputes Total 1 54 16 70 57.15 12.85

2 47 13 60 48.99 11.01

3 52 15 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 9.91

Total 307 69 376

ChiSq = 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 = 0.035

Is the Result Significant at the 0.05 Alpha Level? Is the Result Significant at the 0.05 Alpha Level?

Measure - Analyze - Improve Improve - Control


Minitab Primer

Example: Receivables Process ControlData File: days.xlsVariables: Days

Description: Collection terms are 60 days. Payments are entered into a data collection system in the same time-order as they are received. Determine whether or not the process isin control and capable of satisfying the terms.

Measure - Analyze - Improve - Control Control


Minitab Primer

Results of Analysis...

Is the Process in Control and Capable? Is the Process in Control and Capable?

Measure - Analyze - Improve - Control Control

109876543210

70

60

50

Subgroup

Mea

ns

20

10

0Std

Dev

iatio

ns

MU=63.80

UCL=75.18

LCL=52.42

S=7.970

UCL=16.65

LCL=0.000

Xbar and S Chart for: Days


Minitab Primer

• State the Goal of Your Work

• Identify the Desired Output

• Collect the “Right” Data…Don’t Use Data “Just Because It’s Available”

• Select the Tool(s) that Will Deliver the Desired Results

Conclusion

Avoid “Over Analysis” ... Identify Your Needs Up-front and Focus on Results

Avoid “Over Analysis” ... Identify Your Needs Up-front and Focus on Results


Minitab Primer Appendices

1) Solutions to Problems Using Excel a) Demonstration Oneb) Demonstration Two

2) Formulae for Calculating Sample Sizea) Attributes Testsb) Variables Tests

3) Minitab Tools and the Breakthrough Strategy


Minitab Primer Appendix 1a - Excel

Results of Receivables Demonstration Using 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

Observations....Descriptive Statistics....

Days

Mean 63.8Standard Error 1.19Median 64Mode 67Standard Deviation 8.4Sample Variance 71.3Kurtosis 0.44Skewness 0.07Range 42Minimum 45Maximum 87Sum 3,190Count 50ConfidLevel(95.000%) 2.34

Data Set....

. .

. .

Payment Days1 552 723 694 665 776 707 798 659 6410 6311 67

Histogram....

Histogram

0

5

10

15

20

25

40 50 60 70 80 90

Days

Frequency

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Run Chart....

Run Chart: Days-to-Collection

40

45

50

55

60

65

70

75

80

85

90

1 3 5 7 9

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

Pay

men

t

Days

avg


Minitab Primer

Graphical Analysis Reveals Unusual EventsGraphical Analysis Reveals Unusual Events

price

0.00

20.00

40.00

60.00

80.00

100.00

120.00

0 100 200 300 400 500 600

price

Run Chart....Data Set....

day price1 104.002 103.633 103.004 103.885 104.386 105.007 105.638 106.009 105.2510 106.8811 107.1312 108.3813 108.7514 108.3815 108.25. .. .. .

Histogram

0

5

10

15

20

25

45.5

0

50.5

6

55.6

2

60.6

8

65.7

4

70.8

0

75.8

5

80.9

1

85.9

7

91.0

3

96.0

9

101.

15

106.

21

Bin

Fre

qu

ency

Frequency

Histogram....

price

Mean 63.67Standard Error 0.87Median 56.75Mode #NUM!Standard Deviation 19.58Sample Variance 383.50Kurtosis 0.32Skewness 1.35Range 64.25Minimum 45.50Maximum 109.75Sum 32410.24Count 509Confidence Level (95.000%) 1.70

Descriptive Statistics....

• Bimodal Data - Two Different Groups• Data Unstable Over Time• Descriptive 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 Split

Observations....

Appendix 1b - Excel


Minitab Primer Appendix 2a - Attributes Sample Size

Estimating Sample Size for Attributes

n =2

)(2

· p · q

Example: 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 size - Z-value for Desired Confidence Level- Desired Precision Widthp - Population Proportion (Use 0.5 if Unknown)q - Complement of p, i.e., (1- p)

n = · )(

2

· 0.5 · 0.5 = 600.25 601


Minitab Primer Appendix 2b - Variables Sample Size

Estimating Sample Size for Variables

n =2 ( )

2

Example: How large a sample size is required to estimate the average value ofunpaid invoices with a standard deviation of $3.50 within a margin of error of +/- $1.00 at a 90% confidence level?

n - sample size - Z-value for Desired Confidence Level- Desired Precision Width - Standard Deviation

n = · · $ $( )

2

= 33.35 34


Minitab Primer

A Sampling of Statistical Tools to Apply With the Breakthrough Strategy...

Measure Analyze Improve Control

• Histograms

• Run Charts

• Descriptive Statistics

• Dotplots

• Boxplots

• Hypothesis Tests

• Boxplots

• Dotplots

• Scatter Plots

• Correlation Analysis

• Regression Analysis

• ANOVA

• Hypothesis Tests • Regression Analysis

• DOE

• Run Charts

• Control Charts

• Confidence Intervals

Appendix 3 - MAIC Tools

Use Tools Creatively....But Avoid “Force Fitting”Use Tools Creatively....But Avoid “Force Fitting”

ge minitab primer

Documents

desired precision width

stat anova oneway

desired confidence level

minitab primerdata set

expect ed number

data collection system

hypothesis testing

data set