GEMS Minitab Handbook 13

11 Rev 1

The materials in this handbook were developed by Master Black Belts at General Electric Medical Systems to assist Black Belts and Green Belts in completing Minitab Analyses. It is assumed that the user has a basic understanding of statistical tools.

Please feel free to contact us if you would like additional copies of this or other Six Sigma material, or have any questions, comments, or suggestions.

Stephanie Spencer414.548.46738* 320.4673

GEMS-Am Six Sigma Office414.548.51118* 320.5111

For Additional Information . . .For Additional Information . . .

22 Rev 1

Overview of Key Changes from Minitab Version 10Overview of Key Changes from Minitab Version 10

Added Six Sigma 밚 1?Analysis

Six Sigma 밚 1?& 밚 2?as Drop Down Menu Items

Gage R&R Studies as Drop Down Menu Items

New DoE Interface

Improved Mathematical Manipulations with 밅 alculator

Graphing Options Added to Many Analysis Dialog Boxes

New Probability Plot for Lognormal, Weibull and Exponential Distributions

Fitted Line Plots Include Options for Quadratic and Cubic as well as Linear

Box-Cox Transformations

Toolbars (Windows 95 only)

Insert and Delete Columns

Launch Minitab and Open Files from File Manager or Explorer

Session Window Does Not Display Command Language Unless Selected

Longer File Names (Windows 95 only)

Added Features:Added Features: More More Info?Info?

18

18,22

28

76

10 x

62 x

58 x

90 x

24

7

Minitab Help

33 Rev 1

Table of ContentsTable of Contents

The Basics -- PAGE• Minitab Windows 6• Toolbars 7• Performing Calculations 10

Working with Data --• Changing Data Type 14• Stacking Data / Data Blocks 16• Creating Patterned Data 20• Re-coding Data 22• Transforming Data 24

Gather Tools --• Gage R&R 28• The 밚 1?-- Product Report 32• The 밚 2?-- Process Report 34

Graphing --• Statistical Problem Description 40• Basic Plot 46• Graph Brushing & Editing 48• Copying to Other Applications 51• Grouping Variables 52• Multi-vari Plots 54• Box Plots 56• Normal Probability Plots 58

Statistical Tests --• One Sample t-tests 62• Two Sample t-tests 64• Homogeneity of Variance 66• Analysis of Variance 68• Chi Squared

70DoE --• Create Factorial DoE Design 76• Analyze Factorial DoE Design 78• Analyze Custom Factorial DoE Design 80• Main Effects Plot 82• Interaction Plots 84

Regression --• Regression 88• Fitted Line Plots 90• Residuals Analysis 92

55 Rev 1

66The Basics --

• Minitab Windows• Toolbars• Performing Calculations

66 Rev 1

Minitab BasicsMinitab Basics

Data Window:• A Worksheet, not a Spreadsheet• Column names are above first row• Everything in a column is considered

to be the same variable

Menu Bar

Session Window:• Analytical Output

Info Window:• Synopsis of worksheet

History Window:• Stores Commands

Minitab WindowsMinitab Windows

Four Interactive Windows. Only One Open at a Time. Windows Saved Separately.

77 Rev 1

Toolbars -- Windows 95Toolbars -- Windows 95

The Data Window ToolbarThe Data Window Toolbar

These commands can also be found in drop down menus, or accessed with shortcut keys.

Open File

Save File

Print Window

Cut

Copy

Paste

Undo

Insert Cells

Insert RowsInsert Columns

Move ColumnsClear Cells

Last Dialog Box

Session Window

Previous Brushed Row

Next Brushed Row

Data Window

Manage Graphs

Cancel

Help

Close Graphs

88 Rev 1

The Session Window ToolbarThe Session Window Toolbar

Open File

Save File

Print Window

Cut

Copy

Paste

Undo

Previous Command

Next CommandFind

Find Next

Last Dialog Box

Session Window

Data Window

Manage Graphs

Close Graphs

Cancel

Help



99 Rev 1

The Graph Window ToolbarThe Graph Window Toolbar


Open File

Save File

Print Window

Cut

Copy

Paste

Undo

View Mode

Edit Mode

Brush Mode

Last Dialog Box

Session Window

Data Window

Manage Graphs

Close Graphs

Cancel

Help


1010 Rev 1

Mathematical CalculationsMathematical Calculations

Setting it up --Setting it up --Select: Calc > Calculator Enter column

where results of calculation will be

stored.

Click OK to get results.

Enter formula. Can

click on functions from list

and/or keys.

1111 Rev 1

The Worksheet Output --The Worksheet Output --

Original data Log (c1)

Note: The output column DOES NOT update if a value in a input column is changed. The column will only update if commands are executed again.

Mathematical CalculationsMathematical Calculations

1313 Rev 1

66• Changing Data Type• Stacking Data / Data Blocks• Creating Patterned Data• Re-coding Data• Transforming Data

Working with Data --

1414 Rev 1

If a column is coded as text and needs to be recoded as numeric --

Select: Manip > Change Data Type > Text to Numeric

The Initial Column. Note text is left justified.

Changing Data TypeChanging Data Type

Setting it up --Setting it up --

Other recoding options

Column to be changed.

Column for converted data. May be same column as original, if desired.


1515 Rev 1

Column type is now numeric. Note that numeric columns are right justified.

Non numeric values are replaced with asterisk.


Changing Data TypeChanging Data Type

1616 Rev 1

Stack DataStack Data

Setting it up --Setting it up --Select: Manip > Stack/Unstack > Stack The Initial

Worksheet.

Enter columns to stack. First column entered will be at top of the stacked column followed by second column, etc.

Enter column for the stacked output.

Subscripts can be used to identify the separate input columns.


1717 Rev 1

Stack DataStack Data


Data from the three original columns is now stacked into one column.

Subscripts can be used to identify original column/group.

}}}

1818 Rev 1

Stack Data BlocksStack Data Blocks

Setting it up --Setting it up --Select: Manip > Stack/Unstack > Stack Blocks

Columns contained in first data block. These will be across columns at top of stacked block.

Columns contained in second data block. Up to five blocks can be stacked with this dialog box.

Columns to store new stacked blocks. Optional subscript

columns for tracking block origin.Click OK to get results.

1919 Rev 1

Stack Data BlocksStack Data Blocks


First data block

Second data block

Original data

Optional subscript column. Can use to track blocks. In this example, the first block contained data for standard equipment, the second contained data for new equipment.

2020 Rev 1

Create Patterned DataCreate Patterned Data

Setting it up --Setting it up --Select: Calc > Make Patterned Data > Simple Set of Numbers

Select column that will contain the patterned data.

First number in pattern.

Last number in pattern.

Increment number by ?

Use to repeat numbers, i.e. 1,1,2,2...

Use to repeat entire list, i.e. 1,2,3,1,2,3...


Note: Date/Time sequence data can be generated with Calc > Make Patterned Data > Date/Time Values

2121 Rev 1

Create Patterned DataCreate Patterned Data


Example shown in dialog box.

Any patterned sequence can be generated.

An example for repeated values.

An example for a date sequence.

2222 Rev 1

Re-coding DataRe-coding Data

Setting it up --Setting it up --To improve 뱔 ser friendliness?of graphs by using text labels --

Select: Manip > Code > Numeric to Text

Other recoding options

The Initial Column.

ShiftSelect initial column with numeric data.

Select column for text data.

Enter numeric data value.

Enter text data corresponding to numeric data.


2323 Rev 1


Recoding DataRecoding Data

Column type is now text.

1 뭩 in original column were replaced with First Shift, 2 뭩 with Second Shift, 3 뭩 with Third Shift.

A sample application is graphs generated with X variables as text. Text to numeric coding may be needed for statistical analyses.

2424 Rev 1

Transforming DataTransforming Data

Setting it up --Setting it up --Select: Stat > Control Charts > Box-Cox Transformation(Note: This transformation is for positive data only!)

Column for Transformed Data.

Enter subgroup size if applicable. If not, use 1.

Data to be Transformed.


2525 Rev 1

Transforming DataTransforming Data


Original Data. Transformed Data.

The Graphical Output --The Graphical Output --

3.02.52.01.51.00.50.0-0.5-1.0

2.5

1.5

0.5

95% Confidence Interval

StD

ev

Lambda

Last Iteration Info

0.593

0.593

0.593

0.056

0.000

-0.056

StDevLambda

Up

Est

Low

Box-Cox Plot for time

Transform power used to generate C2.

Transformation Power(p)

Cube 3

Square 2

No Change 1

Square Root 0.5

Logarithm 0

Reciprocal Root -0.5

Reciprocal -1Objective is to minimize standard deviation. 95 % confidence interval for lambda (power).

2727 Rev 1

66• Gage R&R• The 밚 1?-- Product Report• The 밚 2?-- Process Report

Gather Tools --

2828 Rev 1

Gage R&RGage R&R

Select: Stat > Quality Tools > Gage R & R Studies

Click OK (twice) to get results.

Enter tolerance range.

Enter columns containing data for :


2929 Rev 1

Misc:Tolerance:Reported by:Date of study:Gage name:

0

1.11.00.90.80.70.60.50.40.3

321Xbar Chart by Operator

Sam

ple

Mea

n

X=0.80753.0SL=0.8796-3.0SL=0.7354

0

0.15

0.10

0.05

0.00

321R Chart by Operator

Sam

ple

Ran

ge

R=0.03833

3.0SL=0.1252

-3.0SL=0.000

10 9 8 7 6 5 4 3 2 1

1.11.00.90.80.70.60.50.4

Part ID

OperatorOperator*Part Interaction

Aver

age

123

321

1.11.00.90.80.70.60.50.4

Oper ID

By Operator

10 9 8 7 6 5 4 3 2 1

1.11.00.90.80.70.60.50.4

Part ID

By Part%Total Var%Study Var%Toler

Part-to-PartReprodRepeatGage R&R

1009080706050403020100

Components of Variation

Perc

ent

Gage R&R (ANOVA) for Measure


What percentage of the total variation is

coming from the gage?

Is repeatability or reproducibility the

issue?

How much difference does each operator see between 1st and 2nd readings?

How much variation is

coming from the parts?

How do the average readings for each operator

compare?

How much variation do we

see in readings for the same part?

How do the distribution of readings for

each operator compare?

Gage R&RGage R&R

3030 Rev 1

What Contained in the Session What Contained in the Session Window Output?Window Output?

First Table» ANOVA table

• Shows whether part, operator or part*operator interaction are major contributors to variations in the data. Look for p-values < .05.

Second Table» Variance components » Standard deviations» A constant multiple of the standard deviations,

usually 5.15*sigma• 99% of the area under a curve is within an interval 5.15 standard

deviations wide.• This number is also called the study variation and used to estimate

how wide an interval one would need to capture 99% of the measurements from a process.

Third Table» % Contribution to total variation made by each varian

ce component• Each component is divided by the total variation then multiplied by 10

0.

» % Study variation• Standard Deviation of each component is divided by the total Standar

d Deviation. Total WILL NOT sum to 100.

» % Tolerance• Enter tolerance range (Upper limit - Lower limit) under options, if desir

ed.

Gage R&RGage R&R

3131 Rev 1

Gage R&RGage R&R

The Session Window Output --The Session Window Output --Gage R&R Study - ANOVA MethodANOVA Table With Operator*Part InteractionSource DF SS MS F P Parts 9 2.05871 0.228745 39.7178 0.00000Operators 2 0.04800 0.024000 4.1672 0.03256Oper*Part 18 0.10367 0.005759 4.4588 0.00016Repeatability 30 0.03875 0.001292 Total 59 2.24912

Gage R&RSource VarComp StdDev 5.15*Sigma Total Gage R&R 0.004437 0.066615 0.34306 Repeatability 0.001292 0.035940 0.18509 Reproducibility 0.003146 0.056088 0.28885 Operator 0.000912 0.030200 0.15553 Oper*Part 0.002234 0.047263 0.24340 Part-To-Part 0.037164 0.192781 0.99282 Total Variation 0.041602 0.203965 1.05042

Source %Contribution %Study Var %Tolerance Total Gage R&R 10.67 32.66 34.31 Repeatability 3.10 17.62 18.51 Reproducibility 7.56 27.50 28.89 Operator 2.19 14.81 15.55 Oper*Part 5.37 23.17 24.34 Part-To-Part 89.33 94.52 99.28 Total Variation 100.00 100.00 105.04

Number of Distinct Categories = 4

% Gage R&R.Ideal is < 10 % of tolerance.

What are major contributors? Look for p-values <.05.

Estimate of interval needed to capture 99% of measurements.

Distinct Categories the measuring system can distinguish. If less than 2, measurement system can 뭪 distinguish. Two is go / no go. Need 4 for good system.

3232 Rev 1

Product Report --Product Report -- 밚밚 1 Spreadsheet1 Spreadsheet

Select: Stat > Quality Tools > Six Sigma Product Reportor, if loaded special Six Sigma Disk:Six Sigma > Six Sigma Product Report

Enter Defect Type, Defects, Units, Opportunities in Data Window --

Enter columns containing data for :

Click OK.


Enter columns containing

defect type if desired:

Enter shift, if known,

otherwise default of 1.5 will be used.

3333 Rev 1

Total

Others

Chips

Solder

Welds

Dimensions

Spots

Characteristic

3.915

3.554

3.312

5.040

2.580

3.055

2.580

ZBench

1.500

1.500

1.500

1.500

1.500

1.500

1.500

ZShift

7857

20000

35000

200

140000

60000

140000

PPM

0.007857

0.020000

0.035000

0.000200

0.140000

0.060000

0.140000

DPO

0.020

0.070

0.010

0.140

0.060

0.140

DPU

5600

100

200

5000

100

100

100

TotOpps

1

2

50

1

1

1

Opps

100

100

100

100

100

100

Units

44

2

7

1

14

6

14

Defs

Report 7: Product Performance

ZSTThe Session Window Output --The Session Window Output --


1000000

100000

10000

1000

100

10

1

6543210

Z.Bench (Short-Term)

PPM

Report 8A: Product Benchmarks

Zone of AverageTechnology

Zone ofTypicalControl

3.0

2.5

2.0

1.5

1.0

0.5

0.0

6543210

Z.Shift

Z.Bench (Short-Term)

World-ClassPerformance

Report 8B: Product Benchmarks

The spreadsheet view -- L1 Look-alike.

Where the Z values fall.

Four block of Z values (assumes 1.5 shift unless a known shift was entered).

How to do . . . How to do . . . Product Report --Product Report -- 밚밚 1 Spreadsheet1 Spreadsheet

Rollup Statistics

Charact Defs Units Opps TotOpps DPU DPO PPM ZShift ZBenchSpots 14 100 1 100 0.140 0.140000 140000 1.500 2.580 Dimensio 6 100 1 100 0.060 0.060000 60000 1.500 3.055 Welds 14 100 1 100 0.140 0.140000 140000 1.500 2.580 Solder 1 100 50 5000 0.010 0.000200 200 1.500 5.040 Chips 7 100 2 200 0.070 0.035000 35000 1.500 3.312 Others 2 100 1 100 0.020 0.020000 20000 1.500 3.554 Total 44 5600 0.007857 7857 1.500 3.915

3434 Rev 1

Process Report --Process Report -- 밚밚 2 Spreadsheet2 Spreadsheet

Click here to select optional reports 3-6. Reports 1 and 2 are default reports.

Select: Stat > Quality Tools > Six Sigma Process Reportor, if loaded special Six Sigma Disk:Six Sigma > Six Sigma Process ReportNote: MUST have subgroups to run!

Enter columns containing subgroups:

Enter Specification Limits. Target value

is optional.

Click OK.


3535 Rev 1

The Graphical Output -- The Graphical Output -- Report 1Report 1


Actual (LT) Potential (ST)

44.543.542.541.540.539.538.537.536.535.5

Process Performance

USLLSL

Actual (LT) Potential (ST)

1,000,000

100,000

10,000

1000

100

10

1

50403020100

Potential (ST)Actual (LT)

Sigma

PPM

(Z.Bench)

Process Benchmarks

36935.4

1.34

90489.3

1.79

Process Demographics

40

3842

Hardness

Casting

Brake DiShoe cas

Terry L.09/14/95

Opportunity:

Nominal:

Lower Spec:Upper Spec:

Units:Characteristic:

Process:

Department:Project:

Reported by:Date:

Report 1: Executive Summary

Depiction of Process.

PPM:Number of defects per

million parts.

Demographics -- Must enter data in Worksheet. Click on Help in Dialog Box for format.

Process Entitlement

Best the process can be, if centered.

Long Term Process Performance

Shift = Short Term - Long Term

3636 Rev 1

2

1

0

S=0.9022

3.0SL=1.885

-3.0SL=0.000

50403020100

42

41

40

39

38

Xbar and S Chart

Subgroup

X=40.00

3.0SL=41.29

-3.0SL=38.71

4238

42.879337.1207

Potential (ST) CapabilityProcess Tolerance

Specifications

III

III4238

43.549536.4537

Actual (LT) CapabilityProcess Tolerance

Specifications

III

III

Mean

StDev

Z.USL

Z.LSL

Z.Bench

Z.Shift

P.USL

P.LSL

P.Total

Yield

PPM

Cp

Cpk

Pp

Ppk

LTST

Capability Indices

Data Source:T ime Span:Data Trace:

0.56

0.56

90489.3

90.9511

0.090489

0.045116

0.045373

0.4497

1.3377

1.6942

1.6915

1.1815

40.0016

0.69

0.69

36935.4

96.3065

0.036935

0.018468

0.018468

0.4497

1.7874

2.0865

2.0865

0.9586

40.0000

Report 2: Process Capability for C1

The Graphical Output -- The Graphical Output -- Report 2Report 2


Plot of subgroup averages. How much variation is seen from subgroup to subgroup?

Plot of subgroup standard deviations. How much variation is seen within subgroups?

Process Statistics. Find Z.B.LT, Z.B.ST and ZSHIFT.

Compare short term and long term process performance against specification.

3737 Rev 1

The Graphical Output -- The Graphical Output --


Report 3:Report 3:Contains statistical parameters such as mean, standard deviation, kurtosis, skewness, confidence intervals, etc.

Report 4:Report 4:Displays graphs of standard deviation, sum of squares and mean by subgroup.

Report 5:Report 5:Displays graphs of ZLT, ZST, and ZShift , by subgroup.

Report 6:Report 6:Displays normal plot, histograms for data and for subgroup means, and scatter plots to test for correlations of means and standard deviations.

3939 Rev 1

66• Statistical Problem Description• Basic Plot• Graph Brushing & Editing• Copying to Other Applications• Grouping Variables• Multi-vari Plots• Box Plots• Normal Probability Plots

Graphing --

4040 Rev 1

Statistical Problem DescriptionStatistical Problem Description

Setting it up --Setting it up --Select: Stat > Quality Tools > Capability Analysis

Enter Specification Limits. At least one required. Check 밐 ard Limit?if applicable, i.e., cycle time can 뭪

go below zero.

Enter column containing data. Enter

subgroup size.


(Option 1)

For subgroup size of 1, select overall

standard deviation. For subgroups >1,

select pooled standard deviation.

4141 Rev 1

585654525048464442

Upper SpecLower Spec

sMean-3sMean+3sMean

nkLSLUSLTarg

CpmPpkPPLPPUPp

Long-Term Capability

0520 0

192

0.000.050.000.02

ObsPPM<LSL Exp

ObsPPM>USL Exp

Obs %<LSL Exp

Obs %>USL Exp

2.342542.654856.709649.6822

30.0000 0.039742.000058.0000

*

*1.091.091.181.14

Process Capability Analysis for C1

The Output -- The Output --

Note that 3(Ppk) = ZLT ,if overall standard deviation was selected.

Process mean and standard deviation.

Minitab will always draw normal curve line, even if the data isn 뭪 normal! Can select under edit mode and delete. See Graph Editing.


(Option 1)

Histogram of data.

4242 Rev 1


(Option 2)Setting it up --Setting it up --

Enter Specification Limits. At least one required. Check 밐 ard Limit?if applicable, e.g., cycle time can 뭪

go below zero.

Enter column containing data. Enter 1 for subgroup size.


Select: Stat > Quality Tools > Capability Sixpack

(Subgroup size =1)

For subgroup size of 1, select overall

standard deviation.

4343 Rev 1

100500

55

50

45

40

Indiv idual and MR Chart

Obser.

Indi

vidua

l Val

ue

X=50.08

3.0SL=57.87

-3.0SL=42.29

12

8

4

0

Mov

.Ran

ge

1

R=2.930

3.0SL=9.574

-3.0SL=0.000

1009080

Last 25 Observations

52.5

50.0

47.5

45.0

Observation Number

Valu

es

5842

57.713842.4444

Pp: 1.05 PPU: 1.04 PPL: 1.06 Ppk: 1.04

Capability PlotProcess Tolerance

SpecificationsStDev: 2.54490

III

III

555045

Normal Prob Plot

555045

Capability Histogram

Process Capability Sixpack for C1

The Output -- The Output --

Run chart of all data values. Moving range chart. Use these charts to look for trends.

Run chart of last 25 data values.

(Subgroup size =1)

Histogram of data. Minitab will always draw normal curve line, even if the data isn 뭪 normal! Can go into edit mode, select normal curve and delete.

Top line is +/- 3 process range. Compare this against process specifications shown in bottom line. Do you need to shift the mean, shrink the variance or both?

Is the data normally distributed?


(Option 2)

4444 Rev 1

(Option 2)Setting it up --Setting it up --

Enter column containing data. Enter subgroup size.

Select: Stat > Quality Tools > Capability Sixpack


(Subgroup size > 1)

For subgroups >1, select pooled

standard deviation.

Enter Specification Limits. At least one required. Check 밐 ard Limit?if applicable, e.g., cycle time can 뭪

go below zero.


4545 Rev 1

20100

53.5

51.0

48.5

46.0

Xbar and R Chart

Subgr

Mea

ns

X=50.08

3.0SL=53.62

-3.0SL=46.54

15

10

5

0

Ran

ges

R=6.131

3.0SL=12.96

-3.0SL=0.000

20100

Last 20 Subgroups57

53

49

45

Subgroup Number

Valu

es

5842

57.987142.1711

Cp: 1.01 CPU: 1.00 CPL: 1.02 Cpk: 1.00

Capability PlotProcess Tolerance

SpecificationsStDev: 2.63601

III

III

555045

Normal Prob Plot

555045

Capability Histogram

Process Capability Sixpack for C1

(Subgroup size >1)The Output -- The Output --

Histogram of data. Minitab will always draw normal curve line, even if the data isn 뭪 normal! Can select under edit mode and delete. See Graph Editing.

Top line is +/- 3 process range. Compare this against process specifications shown in bottom line. Do you need to shift the mean, shrink the variance or both?

Is the data normally distributed?

Top chart shows subgroup averages. Use this chart to see subgroup to subgroup variation. Middle chart shows range of values within a subgroup.

Plot of up to 25 subgroups of datapoints. Use this chart to see variation within a subgroup.


(Option 2)

4646 Rev 1

Select: Graph > Plot

Basic PlotBasic Plot

Setting it up --Setting it up --Enter Y and X

variables.

Use to change graph set up default. Scale can be changed with Min and Max.

Add jitter to X or Y variables so that multiple points are plotted with offset, rather than on top of each other.

Select to adjust position of figure, data or legend

Select to edit display features.


4747 Rev 1

Basic PlotBasic Plot


750700650

600

500

400

300

Hardness

Abra

sion

Note: A new graph will be generated each time the dialog box is used. For example, going back to the dialog box to change the symbol type or scale will produce another graph instead of updating the existing one. Any editing done with the edit toolbars on an existing graph will not appear on the new one. It is best to get the graph fundamentals in place before editing!

4848 Rev 1

With Graph Window Active --Select: Editor > Brush(Activates Brush Mode)

Editor > Set ID Variables

Graph BrushingGraph Brushing


Click OK to brush graph.

Enter columns to be displayed.

4949 Rev 1

Graph BrushingGraph Brushing

Brushing --Brushing --

Select point to brush by clicking with mouse (mouse arrow has changed to a hand) or select several points by drawing a box around them.

Values from selected columns will be displayed. A dot will also appear beside row numbers in worksheet.

5050 Rev 1

Graph EditingGraph Editing

Setting it up --Setting it up --To Edit, Select: Editor > Edit (Graph window must be active)or double click on the graph.These toolbars will appear:

Add Text

Draw Circle

Draw SymbolFreeform (not closed) Freeform

Draw Box

Return to Cursor

Change FontChange Color

Draw Line

Text EditingChange Size

Change Line TypeChange Line ColorChange Line Thickness

Line Editing

Fill

Symbol Editing

Add Arrowheads

Change / Add FillFill Color

Change Symbol TypeChange Symbol ColorChange Symbol Size

Selecting a graph feature to edit will activate the applicable feature tools.

5151 Rev 1

Copying to Other ApplicationsCopying to Other Applications

From Session Window --From Session Window --• Highlight Text to Copy• Select Edit > Copy (or Cntl-c)• Open Application copying into• Select Edit > Paste (or Cntl-v)• Use New Courier font to preserv

e column spacing

From Graph Window --From Graph Window --• Must be in View Mode • Select Editor > View• Select Edit > Copy Graph• Open Application copying into• Select Edit > Paste (or Cntl-v)• If using Powerpoint, select Draw > S

cale to size graph as desired

5252 Rev 1




Using Grouping VariablesUsing Grouping Variables

Enter Y and X variables.

Click on 밊 or Each?down arrow and sele

ct Group.

Select a 밽 rouping variable? For this example, one symbol will be used for the group of data points from equip #1 and a different symbol will be used for data points from equipment #2. Each X value of time contains a 밽 roup?of points from different pieces of

equipment.

5353 Rev 1

The Output --The Output --

Using Grouping VariablesUsing Grouping Variables

1 2

54321

9.6

9.1

8.6

times

resp

onse

Key for equipment types (grouping variable).

5454 Rev 1



A Multivari Plot ExampleA Multivari Plot Example

To connect the points for each X (part) with a solid line --

Click on Line Type to highlight entire column. Select Solid to change all line types to solid.

Enter Y and X variables.

Change to Group to get symbols for each groove type. Change symbol type, if desired, with Edit Attributes.

Select Legend under Regions and deselect 밪 how Legend?A groove dimension was

measured for each of 4 grooves on several parts.

How much variation is seen from part to part? Within a

part?

Click OK for each box to get results.

5555 Rev 1

1 2 3 4

15

20100

10

0

-10

part

act-s

pec


A Multivari Plot ExampleA Multivari Plot Example

How does part to part variation compare to within part variation?

With different symbols, can see that groove #1 has a higher value than others.

5656 Rev 1

Select: Graph > Boxplot

Box PlotsBox Plots

Setting it up --Setting it up --Enter Y variable. If have Y

responses for more than one X value, enter X

variable column.


Use to change graph set up default. Scale can be changed with Min and Max.

Select to adjust position of figure, data or legend.

Select to edit display features. Will typically use defaults for boxplots.

Can transpose X and Y as Option.

5757 Rev 1

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9.6

9.1

8.6

equip-no

resp

onse


Box PlotsBox Plots

50th Percentile (Median)

25th Percentile

75th Percentile

min of (1.5 x Interquartile Range or minimum value)Outliers

Outliers

Middle50% of

Data

Box Plot Interpretation

max of (1.5 x Interquartile Range or maximum value)

*

***

5858 Rev 1

Normal Probability PlotsNormal Probability Plots

Select: Stat > Basic Statistics > Normality Test



Enter column.

Various statistical normality tests.

Anderson-Darling is typically fine as

default.

Alternate Option: Stat > Basic Statistics > Normality Test

Enter column.

Select Distribution Type.

5959 Rev 1

100 90 80 70 60 50 40 30

99

95

90

80

7060504030

20

10

5

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Data

Perc

ent

StDev:Mean:

10.000070.0000

Normal Probability Plot for C1


Normal Probability PlotsNormal Probability Plots

P-Value: 0.328A-Squared: 0.418

Anderson-Darling Normality Test

N: 500StDev: 10.0000Average: 70.0000

1069686766656463626

.999

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.95

.80

.50

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.05

.01

.001

Pro

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C1

Normal Probability Plot

The higher the p-value, the more likely the data is normally distributed.

Alternate Option:

This option shows 95% confidence intervals.

6161 Rev 1

66• One Sample t-tests• Two Sample t-tests• Homogeneity of Variance• Analysis of Variance• Chi Squared

Statistical Tests --

6262 Rev 1

One sample t-testsOne sample t-tests

Setting it up --Setting it up --Select: Stat > Basic Statistics > 1 - sample t

Enter column containing data.

Enter test mean.

Select Ha from drop down box.

Select a graph option, if desired --


6363 Rev 1

1101051009590858075

8

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C1

Freq

uenc

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Histogram of C1(with Ho and 95% t-conf idence interval for the mean)

[ ]X_

Ho

One sample t-testsOne sample t-tests

The Session Window Output --The Session Window Output --

If p < .05, reject Ho.


t-calc

Test mean is outside the 95% confidence interval, reject Ho.

T-Test of the Mean

Test of mu = 100.00 vs mu not = 100.00

Variable N Mean StDev SE Mean T PC1 30 92.55 9.16 1.67 -4.45 0.0001

6464 Rev 1

Two sample t-testsTwo sample t-tests

Setting it up --Setting it up --Select: Stat > Basic Statistics > 2 - sample t

Enter columns containing data.

Select Ha from drop down box.

Select a graph option, if desired --


6565 Rev 1

Two Sample T-Test and Confidence Interval

Two sample T for C1 vs C2 N Mean StDev SE MeanC1 30 92.55 9.16 1.7C2 50 95.1 10.2 1.4

95% CI for mu C1 - mu C2: ( -6.9, 1.9)

T-Test mu C1 = mu C2 (vs not =): T= -1.14 P=0.26 DF= 66

C2C1

120

110

100

90

80

70

Boxplots of C1 and C2(means are indicated by solid circles)

Two sample t-testsTwo sample t-tests


If p > .05, accept Ho.


Distributions overlap -- Accept Ho.

If the 95 % confidence interval for difference between sample averages crosses zero, then accept Ho.

6666 Rev 1

Homogeneity of VarianceHomogeneity of Variance

Setting it up --Setting it up --Select: Stat > ANOVA > Homogeneity of VarianceNote: Data must be stacked for this analysis. Use a subscript column to identify groups.

Enter column containing

stacked data.

Enter column containing subscripts

that identify from which group data came.


6767 Rev 1

3.53.02.52.0

95% Confidence Intervals for Sigmas

P-Value : 0.082

Test Statistic: 3.092

Levene's Test

P-Value : 0.142

Test Statistic: 2.158

Bartlett's Test

Factor Levels

2

1

Homogeneity of Variance Test for C1


Use Bartlett 뭩 Test when the data comes from a normal distribution. Use Levene 뭩 Test when the data comes from a continuous but not necessarily normal distribution. P-values < .05 indicate the groups have different variances.

The 95% Confidence Intervals. The middle dot is the standard deviation of that group.

Homogeneity of VarianceHomogeneity of Variance

6868 Rev 1

Analysis of VarianceAnalysis of Variance

Setting it up --Setting it up --Select: Stat > ANOVA > Oneway

Note: If data is not stacked, Select: Stat > ANOVA > Oneway (unstacked)

Enter column with stacked data.

Enter column with stacked data.


Can generate boxplot or dotplot of data as an option.

6969 Rev 1

321

20

15

10

Factor

resp

Boxplots of resp by Factor(means are indicated by solid circles)

One-Way Analysis of VarianceAnalysis of Variance for resp Source DF SS MS F PFactor 2 117.73 58.87 8.66 0.005Error 12 81.60 6.80Total 14 199.33 Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ----------+---------+---------+------1 5 13.200 3.271 (-------*------) 2 5 15.800 1.643 (------*------) 3 5 20.000 2.646 (------*------) ----------+---------+---------+------Pooled StDev = 2.608 14.0 17.5 21.0



If p < .05, there is a statistical difference between factor levels.

Determine % contribution to variance by dividing SSfactor by SStotal. Likewise, determine % error (unaccounted-for variation) by SSerror / SStotal.

How much overlap do you see in the confidence intervals? The more overlap, the less likely that there is a statistical difference.

Analysis of VarianceAnalysis of Variance

• Do distributions overlap? • Are variances similar?

ANOVA requires variances to be approximately the same. Test with Homogeneity of Variance.

7070 Rev 1

Setting it up --Setting it up --Select: Stat > Tables > Chisquare Test

Enter columns

with table.


Chi Chi 22

Use this option when data is a table containing total counts.

The Worksheet Setup.

7171 Rev 1

Chi-Square Test

Expected counts are printed below observed counts

Pass Fail Total 1 77 35 112 84.47 27.53

2 63 22 85 64.10 20.90

3 87 17 104 78.43 25.57

Total 227 74 301

Chi-Sq = 0.660 + 2.024 + 0.019 + 0.058 + 0.936 + 2.871 = 6.568DF = 2, P-Value = 0.037

Chi-calc

If p-value < .05, there is a difference.


Chi Chi 22

7272 Rev 1

Chi Chi 22 -- Cross Tabulation -- Cross Tabulation

Setting it up --Setting it up --Select: Stat > Tables > Cross Tabulation

The Worksheet Setup.

Enter columns with data.


Use this option when raw data is arranged in columns.

PassFail

7373 Rev 1


Chi Chi 22 -- Cross Tabulation -- Cross Tabulation

Tabulated Statistics Rows: Shift Columns: PassFail 1 2 All 1 77 35 112 84.47 27.53 112.00 2 63 22 85 64.10 20.90 85.00 3 87 17 104 78.43 25.57 104.00 All 227 74 301 227.00 74.00 301.00 Chi-Square = 6.568, DF = 2, P-Value = 0.037

Cell Contents -- Count Exp Freq

If p-value < .05, there is a difference.

Chi-calc

Expected counts are shown below observed counts.

7575 Rev 1

66• Create Factorial DoE Design• Analyze Factorial DoE Design• Analyze Custom Factorial DoE D

esign• Main Effects Plot• Interaction Plots

DoE --

7676 Rev 1

Create Factorial DoE DesignCreate Factorial DoE Design

Setting it up --Setting it up --Select: Stat > DOE > Create Factorial Design Select number of factors. The default

generators normally sufficient.Select

design from options listed.

Can enter factor names and levels, if desired.

Select applicable options. Randomize is default.

Click OK for each box.

7777 Rev 1

The Session Window Output --The Session Window Output --Create Factorial DoE DesignCreate Factorial DoE Design

Factorial Design

Full Factorial Design

Factors: 3 Base Design: 3, 8 Runs: 8 Replicates: 1 Blocks: none Center pts (total): 0

All terms are free from aliasing

If had selected a fractional design, the confounding pattern would be listed here.


Actual factor names and values appear on datasheet, if entered as option. If not, matrix will contain -1, and +1.

Run Order would be the same as Standard Order, if the randomize option wasn 뭪 selected.

Note: Each design is entered on a new worksheet.

7878 Rev 1

Analyze Factorial DoE DesignAnalyze Factorial DoE Design

Setting it up --Setting it up --Select: Stat > DOE > Analyze Factorial Design

Click OK for each box.

Enter Response Column. Select for

covariates.

Select Terms to be included in model. Can select up to desired order through drop down box or individually with > or < buttons. The >> or << buttons move all terms.

Select to store fits, residuals, etc.

Select to display means for each factor level.

Select to get effects and/or residual plots.

Note: For designs created in Minitab 10.X, see Analyze Custom Design.

7979 Rev 1

Analyze Factorial DoE DesignAnalyze Factorial DoE Design


Fractional Factorial Fit

Estimated Effects and Coefficients for Distance

Term Effect Coef StDev Coef T PConstant 3.519 0.03125 112.60 0.006Pin -2.362 -1.181 0.03125 -37.80 0.017No. 1.763 0.881 0.03125 28.20 0.023Start 3.112 1.556 0.03125 49.80 0.013Pin*No. -0.387 -0.194 0.03125 -6.20 0.102Pin*Start -0.837 -0.419 0.03125 -13.40 0.047No.*Start 0.837 0.419 0.03125 13.40 0.047

Analysis of Variance for Distance

Source DF Seq SS Adj SS Adj MS F PMain Effects 3 36.7509 36.7509 12.2503 2E+03 0.0192-Way Interactions 3 3.1059 3.1059 1.0353 132.52 0.064Residual Error 1 0.0078 0.0078 0.0078Total 7 39.8647

The average effect of moving the factor from the low to high setting.

The coefficient for regression equation. Equal to effect/2.

t-calc for coefficient. Is it = 0?

If p< .05, this is a statistically significant factor.

Determine % contribution to variance by dividing SSsource by SStota

l. Likewise, determine % error (unaccounted-for variation) by SSerror / SStotal.

Adj SS/DF

Adj MSsource

Adj MSerror

8080 Rev 1

Analyze Custom Factorial DoE DesignAnalyze Custom Factorial DoE Design

Setting it up --Setting it up --Select: Stat > DOE > Analyze Custom Design

Select Design Type.

Enter Response Column. Enter

Factors (no pipes).

Select Terms to be included in model. Can select up to desired order through drop down box. Individual terms can be taken out by highlighting and using Remove button. Click OK for each box.

8181 Rev 1

The Output --The Output --Analyze Custom Factorial DoE DesignAnalyze Custom Factorial DoE Design

Fractional Factorial Fit

Estimated Effects and Coefficients for Distance

Term Effect Coef StDev Coef T PConstant 3.519 0.03125 112.60 0.006Pin -2.362 -1.181 0.03125 -37.80 0.017No. 1.763 0.881 0.03125 28.20 0.023Start 3.112 1.556 0.03125 49.80 0.013Pin*No. -0.387 -0.194 0.03125 -6.20 0.102Pin*Start -0.837 -0.419 0.03125 -13.40 0.047No.*Start 0.837 0.419 0.03125 13.40 0.047

Analysis of Variance for Distance

Source DF Seq SS Adj SS Adj MS F PMain Effects 3 36.7509 36.7509 12.2503 2E+03 0.0192-Way Interactions 3 3.1059 3.1059 1.0353 132.52 0.064Residual Error 1 0.0078 0.0078 0.0078Total 7 39.8647

The average effect of moving the factor from the low to high setting.

The coefficient for regression equation. Equal to effect/2.

t-calc for coefficient. Is it = 0?

If p< .05, this is a statistically significant factor.

Determine % contribution to variance by dividing SSsource by SStota

l. Likewise, determine % error (unaccounted-for variation) by SSerror / SStotal.

Adj SS/DF

Adj MSsource

Adj MSerror

Note: Identical to Analyze Factorial Design

8282 Rev 1

Main Effect PlotsMain Effect Plots

Setting it up --Setting it up --Select: Stat > ANOVA > Main Effects Plots

Enter Response Column.

Enter Factors.


8383 Rev 1

Main Effect PlotsMain Effect Plots


Strt AngN_RubBndPin Pos

5.2

4.4

3.6

2.8

2.0

Dist

Main Effects Plot - Means for Dist

Check range of experimental results. Was it large enough to be of practical significance?

The steeper the slope, the larger the effect.

-1 setting

+1 setting

8484 Rev 1

Interaction PlotsInteraction Plots

Setting it up --Setting it up --Select: Stat > ANOVA > Interaction Plots

Enter Response Column.

Enter Factors.


8585 Rev 1

Interaction PlotsInteraction Plots


1

1

-1

-1

1

1

-1

-1 1

1

-1

-1Pin Pos

N_RubBnd

Strt Ang

Interaction Plot - Means for Dist

Read across to identify Y axes.

Read down to identify X axes.

The stronger the interaction, the more non-parallel the lines.

Low level for X axis factor.

High level for X axis factor.

Solid line is low level for Y axis factor.

Dashed line is high level for Y axis factor.

8787 Rev 1

66• Regression• Fitted Line Plots• Residuals Analysis

Regression --

8888 Rev 1

Select: Stat > Regression > Regression

RegressionRegression


Y variable in equation. Possible X 뭩

.

Store fits, residuals, coefficients, etc.Graph options

for residuals.


8989 Rev 1

Regression Analysis

The regression equation isAbrasion = 2693 - 3.16 Hardness

Predictor Coef StDev T PConstant 2692.8 242.9 11.09 0.000Hardness -3.1607 0.3462 -9.13 0.000

S = 41.94 R-Sq = 78.4% R-Sq(adj) = 77.4%

Analysis of Variance

Source DF SS MS F PRegression 1 146569 146569 83.34 0.000Error 23 40451 1759Total 24 187020

Unusual ObservationsObs Hardness Abrasion Fit StDev Fit Residual St Resid 4 756 297.00 303.34 20.78 -6.34 -0.17 X 9 718 340.00 423.44 10.23 -83.44 -2.05R

R denotes an observation with a large standardized residualX denotes an observation whose X value gives it large influence.


RegressionRegression

t-test for constant coefficient (Y-intercept) versus constant of zero. If p is > .05, constant could be zero.

t-test for factor coefficient versus zero. If p is < .05, coefficient is significant.

R-sq is % of variation in Y that is explained by equation. If several X 뭩 in equation, use R-sq adj, as it adjust for degrees of freedom.

How good is the regression model?

Unusual residual observations. Can use graphs to evaluate.

9090 Rev 1

Select: Stat > Regression > Fitted Line Plot

Fitted Line PlotsFitted Line Plots



Identify Y and X columns.

Choose type of regression to fit.

Optional display of confidence bands and prediction bands.

Can transform data here, if needed.

9191 Rev 1

Fitted Line PlotsFitted Line Plots


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700

600

500

400

300

200

Hardness

Abra

sion

R-Sq = 0.784Y = 2692.80 - 3.16067X

95% PI

95% CI

Regression

Regression Plot

Regression

The regression equation isy = 2693 - 3.16 x

Predictor Coef StDev T PConstant 2692.8 242.9 11.09 0.000x -3.1607 0.3462 -9.13 0.000

S = 41.94 R-Sq = 78.4% R-Sq(adj) = 77.4%

Analysis of Variance

Source DF SS MS F PRegression 1 146569 146569 83.34 0.000Error 23 40451 1759Total 24 187020

t-test for constant coefficient (Y-intercept) versus constant of zero. If p is > .05, constant could be zero.

t-test for factor coefficient versus zero. If p is < .05, coefficient is significant.

R-sq is % of variation in Y that is explained by equation. If several X뭩 in equation, use R-sq adj, as it adjust for degrees of freedom.

How good is the regression model?

•Black line is line of best fit.•Dotted line (red) is 95% confidence interval for line.•Dashed line (blue) is prediction interval for any point.


9292 Rev 1

Select: Stat > Regression > Regression

Residuals AnalysisResiduals Analysis


Select graph options for residuals plots.


Selecting standardized will convert residuals to z-like value.

Select desired plots.

Note: Can also generate with Stat > Regression > Residuals Plots, but must have stored fits and resid 뭩 and can 뭪 select standardized option.

9393 Rev 1

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Observation Order

Stan

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Res

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Residuals Versus the Order of the Data(response is Abrasion)

2.01.51.00.50.0-0.5-1.0-1.5-2.0

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Standardized Residual

Freq

uenc

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Histogram of the Residuals(response is Abrasion)

252015105

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-2

Observation Order

Stan

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Residuals Versus the Order of the Data(response is Abrasion)

210-1-2

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-1

-2

Normal Score

Stan

dard

ized

Res

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Normal Probability Plot of the Residuals(response is Abrasion)

Residuals AnalysisResiduals Analysis


How normal are the residuals?

Individual residuals -- trends? outliers? 95% should be within +/- 2 standardized residuals.

Histogram -- bell curve?(Ignore for data sets < 30)

Random about zero without trends?

Point noted with unusual residual in session window output.

Documents

GEMS Minitab Handbook 13