1 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 Spencer 414.548.4673 8* 320.4673 GEMS-Am Six Sigma Office 414.548.5111 8* 320.5111 For Additional Information . . . For Additional Information . . .
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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
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.
Click OK to get results.
1515 Rev 1
Column type is now numeric. Note that numeric columns are right justified.
Non numeric values are replaced with asterisk.
The Worksheet Output --The Worksheet Output --
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.
Click OK to get results.
1717 Rev 1
Stack DataStack Data
The Worksheet Output --The Worksheet Output --
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
The Worksheet Output --The Worksheet Output --
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...
Click OK to get results.
Note: Date/Time sequence data can be generated with Calc > Make Patterned Data > Date/Time Values
2121 Rev 1
Create Patterned DataCreate Patterned Data
The Worksheet Output --The Worksheet Output --
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.
Click OK to get results.
2323 Rev 1
The Worksheet Output --The Worksheet Output --
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.
Click OK to get results.
2525 Rev 1
Transforming DataTransforming Data
The Worksheet Output --The Worksheet Output --
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 :
Setting it up --Setting it up --
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
The Graphical Output --The Graphical Output --
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
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.
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.
Setting it up --Setting it up --
3535 Rev 1
The Graphical Output -- The Graphical Output -- Report 1Report 1
Process Report --Process Report -- 밚밚 2 Spreadsheet2 Spreadsheet
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
Process Report --Process Report -- 밚밚 2 Spreadsheet2 Spreadsheet
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 --
Process Report --Process Report -- 밚밚 2 Spreadsheet2 Spreadsheet
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.
Click OK (twice) to get results.
(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.
Statistical Problem DescriptionStatistical Problem Description
(Option 1)
Histogram of data.
4242 Rev 1
Statistical Problem DescriptionStatistical Problem Description
(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.
Click OK (twice) to get results.
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?
Statistical Problem DescriptionStatistical Problem Description
(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
Statistical Problem DescriptionStatistical Problem Description
(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.
Click OK (twice) to get results.
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.
Statistical Problem DescriptionStatistical Problem Description
(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.
Click OK to get results.
4747 Rev 1
Basic PlotBasic Plot
The Graphical Output --The Graphical Output --
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
Setting it up --Setting it up --
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
Select: Graph > Plot
Setting it up --Setting it up --
Click OK to get results.
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
Select: Graph > Plot
Setting it up --Setting it up --
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
The Output --The Output --
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.
Click OK to get results.
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
21
9.6
9.1
8.6
equip-no
resp
onse
The Graphical Output --The Graphical Output --
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
Setting it up --Setting it up --
Click OK to get results.
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
1
Data
Perc
ent
StDev:Mean:
10.000070.0000
Normal Probability Plot for C1
The Graphical Output --The Graphical Output --
Normal Probability PlotsNormal Probability Plots
P-Value: 0.328A-Squared: 0.418
Anderson-Darling Normality Test
N: 500StDev: 10.0000Average: 70.0000
1069686766656463626
.999
.99
.95
.80
.50
.20
.05
.01
.001
Pro
babi
lity
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 --
Click OK (twice) to get results.
6363 Rev 1
1101051009590858075
8
4
0
C1
Freq
uenc
y
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.
The Graphical Output --The Graphical Output --
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 --
Click OK (twice) to get results.
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
The Session Window Output --The Session Window Output --
If p > .05, accept Ho.
The Graphical Output --The Graphical Output --
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.
Click OK to get results.
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
The Output --The Output --
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.
Click OK to get results.
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
The Session Window Output --The Session Window Output --
The Graphical Output --The Graphical Output --
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.
Click OK to get results.
Chi Chi 22
Use this option when data is a table containing total counts.
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.
The Worksheet Output --The Worksheet Output --
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
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