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TE Taylor Enterprises, Inc. www.variation.com

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Validation Report for Excel Spreadsheet:

STAT-18 - Skewness Kurtosis Normality Tests

Report Number: TE-17-1

Approvals:

___________________________________ September 1, 20177

Dr. Wayne A. Taylor Date Study Director

___________________________________ September 1, 2017

Ann B. Taylor Date President


2

Validation Protocol for Excel Spreadsheet: STAT-18 - Skewness Kurtosis Normality Tests

Report Number: TE-17-1

1.0 Introduction The book Statistical Procedures for the Medical Device Industry by Dr. Wayne Taylor (2017) includes several Excel Spreadsheets that can be downloaded from www.variation.com/procedures. One of these spreadsheets is STAT-18 – Skewness Kurtosis Normality Tests – Protected.xls. This spreadsheet is password protected to prevent changes. The first tab displays the information below. The version being validated is Revision 1 with a date of 8/30/2017.

For those purchasing the book Statistical Procedures for the Medical Device Industry, this file contains a spreadsheet for performing the Skewness Kurtosis All and Specific normality tests. Further information about the use of this spreadsheet is provided in the book.

STATISTICAL PROCEDURES FOR THE MEDICAL DEVICE INDUSTRY

STAT-18: Normality Testing and Transformations

Dr. Wayne A. Taylor

www.variation.com/proceduresBook Link:

Revision 1: 8/30/2017

Copyright © 2017 Taylor Enterprises, Inc.All rights reserved.

[email protected]

This spreadsheet performs two normality tests. The first test is the skewness-kurtosis all general normality test. It is designed to detect all types of departures from normality. This normality test is described in STAT-18, Appendix A of the book. This test is included in the R software package under the name D’Agostino Chi2 Omnibus test.

The second test is the skewness-kurtosis specific normality test. It is designed to detect specific departures from normality that can cause false acceptances of a variable sampling plan. This normality test is described in STAT-18, Appendix C of the book. It is a combination of the D’Agostino Z3 Skewness and D’Agostino Z4 Kurtosis tests. It is designed to reject for tails longer than the normal distribution as evidenced by skewness towards a specification limit or high kurtosis. Formulas and references for both tests are provided in STAT-18, Appendix C of the book.

A key property of the spreadsheet is that tabs are independent of each other so tabs can be copied and the copied tab performs correctly and tabs can be deleted without affecting other tabs.

http://www.variation.com/procedures


3

2.0 Protocol Protocol Number: TE-17-1, Validation Protocol for Excel Spreadsheet: STAT-18 - Skewness Kurtosis Normality Tests was written to validate this spreadsheet. It can be found in Appendix A. It lists the requirements, test cases and a matrix linking the tests to the requirements demonstrating complete coverage of the requirements.

3.0 Testing The test script was executed on two machines. The first one had Windows 10 and Excel 2016 installed. The results were saved in the file STAT-18 -Windows 10. It is included as Appendix B.

The second machine had Windows 7 and Excel 2007 installed. The results were saved in the file STAT-18 -Windows 7. It is included as Appendix C.

4.0 Test Results All tests passed on both machines as shown in Appendices B and C. The validation has been successively completed.


Appendix A

Validation Protocol for Excel Spreadsheet:


Protocol Number: TE-17-1


1

Validation Protocol for Excel Spreadsheet:



Approvals:

___________________________________ August 30, 2017

Dr. Wayne A. Taylor Date Study Director

___________________________________ August 30, 2017

Ann B. Taylor Date President


2

Validation Protocol for Excel Spreadsheet: STAT-18 - Skewness Kurtosis Normality Tests


1.0 Introduction The book Statistical Procedures for the Medical Device Industry by Dr. Wayne Taylor (2017) includes several Excel Spreadsheets that can be downloaded from www.variation.com/procedures. One of these spreadsheets is STAT-18 – Skewness Kurtosis Normality Tests – Protected.xls. This spreadsheet is password protected to prevent changes. The first tab displays the information below. The version being validated is Revision 1 with a date of 8/30/2017.

For those purchasing the book Statistical Procedures for the Medical Device Industry, this file contains a spreadsheet for performing the Skewness Kurtosis All and Specific normality tests. Further information about the use of this spreadsheet is provided in the book.

STATISTICAL PROCEDURES FOR THE MEDICAL DEVICE INDUSTRY

STAT-18: Normality Testing and Transformations

Dr. Wayne A. Taylor

www.variation.com/proceduresBook Link:

Revision 1: 8/30/2017

Copyright © 2017 Taylor Enterprises, Inc.All rights reserved.

[email protected]

This spreadsheet performs two normality tests. The first test is the skewness-kurtosis all general normality test. It is designed to detect all types of departures from normality. This normality test is described in STAT-18, Appendix A of the book. This test is included in the R software package under the name D’Agostino Chi2 Omnibus test.

The second test is the skewness-kurtosis specific normality test. It is designed to detect specific departures from normality that can cause false acceptances of a variable sampling plan. This normality test is described in STAT-18, Appendix C of the book. It is a combination of the D’Agostino Z3 Skewness and D’Agostino Z4 Kurtosis tests. It is designed to reject for tails longer than the normal distribution as evidenced by skewness towards a specification limit or high kurtosis. Formulas and references for both tests are provided in STAT-18, Appendix C of the book.

A key property of the spreadsheet is that tabs are independent of each other so tabs can be copied and the copied tab performs correctly and tabs can be deleted without affecting other tabs.

http://www.variation.com/procedures


3

2.0 Requirements Table 1 lists the user requirements to be validated.

Table 1: User Requirements for STAT-18 - Skewness Kurtosis Normality Tests

ID Description

1

Input of Data:

a. Data can be typed or pasted into the data column of the spreadsheet

b. A header or name for the data can be typed into the top cell of the data column, which is displayed at the top of the summary data section

c. The type of specification limit can be typed into the specification cell of the spreadsheet

d. Only the data column, including header, and the type of specification cell can be changed

2

Data Checking:

a. Sample size is zero when there are no valid values. Otherwise it is the number of valid values

b. Average is blank when there are no valid values. Otherwise it is the average of the valid values.

c. Standard deviation is blank when there are 1 or fewer valid values. Otherwise it is the standard deviation of the valid values.

d. Skewness is blank when there are 2 or fewer valid values or the standard deviation is 0. Otherwise it is skewness of the valid values.

e. Kurtosis is blank when there are 3 or fewer valid values or the standard deviation is 0. Otherwise it is the kurtosis of the valid values.

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Skewness Kurtosis All test:

a. If there are less than 15 valid values or the standard deviation is 0, no p-value is displayed and an error message is displayed

b. Otherwise, the p-value is displayed

c. If the p-value is displayed and is > 0.05, a message that the data passes SK All normality test is displayed

d. If the p-value is displayed and is ≤ 0.05, a message that the data fails SK All normality test" is displayed

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Skewness Kurtosis Specific test:

a. If there are less than 15 valid values, the standard deviation is 0 or the type of specification limit is not a “T”, “U” or “L”, an error message is displayed

b. Otherwise, the pass/fail conclusion is displayed along with the type of specification limit.

5 Tabs:

a. Tabs are independent of each other so tab can be copied and all other tab deleted with tab results remaining the same.


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3.0 Test Environment All testing will be performed at the facilities of Taylor Enterprises, Inc. (TEI), Libertyville, IL USA

All individuals performing the testing described below shall have a thorough knowledge of STAT-018 and associated spreadsheet and be proficient in its use.

The spreadsheet does not include any macros. All functionality is through equations including the standard functions included with Excel that have remained unchanged since early versions of Excel. The purpose of this document is to describe the validation of this spreadsheet across a range of systems. The validation tests described in the following sections shall performed on a newer system with Windows 10 / Excel 2016 and an older system with Windows 7 / Excel 2007.

4.0 Test Script For each system run the test script in Appendix A. The test script includes instructions for documenting the system used, the downloading of the spreadsheet and test cases to run.

Make a copy of Appendix A in a separate Word document for each system. Copy the evidence of each test case into this word file. All test cases should be run by the same person on a single day. When done save the file, print it, and then sign and date the printed copy.

The first two items in the test script provide evident the system, software and spreadsheet use. They are not linked to the requirements. The remaining test cases are designed to cover all the requirements. A matrix showing the linkage is provided in Appendix B.

Appendix C provides evidence of the correct results for the test cases. Averages, standard deviations, skewness and kurtosis tests are calculated using Minitab, version 18 (www.minitab.com). The p-value for SK All (called omnibus), ZS, two-sided p-value for skewness and ZK are calculated using the R software package, version 3.2.4 (cran.r-project.org). The other p-values are calculated using the following equations in Excel:

Skewness upper one-sided p-value =NORMDIST(-ZS,0,1,TRUE)

Skewness lower one-sided p-value =NORMDIST(ZS,0,1,TRUE)

Kurtosis upper one-sided p-value =NORMDIST(-ZK,0,1,TRUE)


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Appendix A: Test Script

1. Document System Used

1.1. Capture a screen shot showing the computer make and model

<Insert screen shot here>

1.2. Capture a screen shot showing the operating system including version number


1.3. Capture a screen shot showing the version of Excel used


2. Download Spreadsheet and Open

2.1. Download the spreadsheet from http://www.variation.com/procedures/SK_normality_tests.html. Download the protected version. Save it to the hard drive. Capture a screen shot showing the file downloaded.


2.2. Double click the spreadsheet to open it. Capture a screen shot of the section of the first tab showing the version and date.


Acceptance Criteria: The following is displayed “Revision 1: 8/30/2017”

Pass or Fail: XXXX Initials: XXX Date: XXX

3. Input of Data When Normality Test Cannot Be Performed

3.1. Double click on at least 10 non-yellow cells on each of the three sheets (Req. 1d).


Acceptance Criteria: Each time a message should be displayed that the cell is protected.


3.2. Go to the Skewness Kurtosis Norm Tab. Change cell D7 to “1” (Req. 1c).


Acceptance Criteria: The cell should change to “1”.


http://www.variation.com/procedures/SK_normality_tests.html


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3.3. Change cell B11 to “Diameter” (Req. 1b).


Acceptance Criteria: Both B11 and D11 should change to “Diameter”. The sample size should be 0. The average, SD, skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.


3.4. Change cell B12 to “A” (2-4 for invalid values. n=0)


Acceptance Criteria: The sample size should be 0. The average, SD, skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.


3.5. Change cell B14 to “1” (Req. 2-4 for n=1)


Acceptance Criteria: The sample size and average should be 1. The standard deviation, skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.




Acceptance Criteria: The sample size should be 2. The average should be 1. The standard deviation should be 0. The skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.


3.7. Change cell B17 to “1” (Req. 2-4 for n=3 and SD=0)









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3.9. Copy cell B18 to clipboard. Select cells B12 to B211 and then select paste “1” (Req. 1a, 2-4 for n=200 and SD=0)


Acceptance Criteria: The data column should be filled with “1”. The sample size should be 200. The average should be 1. The standard deviation should be 0. The skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.


4. Input of Data When Normality Test Can Be Performed

4.1. Clear Cells B12:B211. Then paste the following into cells B12:B15. (Req. 2-4 for n=4 and SD>0).

0.1257 0.1249 0.1257 0.125


Acceptance Criteria: The sample size should be 4. The average should round to 0.12532. The standard deviation should round to 0.00043. The skewness should round to -0.04558. The kurtosis should round to -5.73743. The p-value should be blank. The conclusions should indicate there is insufficient data.


4.2. Paste the following into cells B16:B25 (Req. 2-4 for n=14 and SD>0).

0.1264

0.1238

0.1254

0.1248

0.1253

0.1234

0.1262

0.1262

0.1269

0.1245


Acceptance Criteria: The sample size should be 14. The average should round to 0.12530. The standard deviation should round to 0.00099. The skewness should round to -0.366071.


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The kurtosis should round to -0.264172. The p-value should be blank. The conclusions should indicate there is insufficient data.


4.3. Type 0.1252 into cell B26 (Req. 3-4 for n>=15, Normal data, Invalid type of specification).


Acceptance Criteria: The sample size should be 15. A p-value should be given. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be incorrect type of specification.


4.4. Change cell D7 to “T” and paste cells D10:29 of Example Data Sets tab into cells B12:31 (Req. 3-4 for n>=15, normal data, two-sided specification)


Acceptance Criteria: The sample size should be 20. The p-value should round to 0.8047. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for a two-sided specification. Cell J17 should round to -0.659 (ZS). Cell J18 should round to 0.5099 (p-value 2-sided skewness). Cell J29 should round to -0.0156 (ZK). Cell J31 should round to 0.5062 (p-value positive kurtosis). Note that these cells are not visible unless selected.


4.5. Change cell D7 to “U” (Req. 3-4 for n>=15, normal data, upper specification)


Acceptance Criteria: The sample size should be 20. The p-value should round to 0.8047. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for an upper specification. Cell J17 should round to -0.659 (ZS). Cell J19 should round to 0.7450 (p-value positive skewness). Cell J29 should round to -0.0156 (ZK) Cell J31 should round to 0.5062 (p-value positive kurtosis). Note that these cells are not visible unless selected.


4.6. Change cell D7 to “L” (Req. 3-4 for n>=15, normal data, lower specification)


Acceptance Criteria: The sample size should be 20. The p-value should round to 0.8047. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to -0.659 (ZS). Cell J20 should round to 0.2550 (p-value negative skewness). Cell J29 should round to -0.0156 (ZK).


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Cell J31 should round to 0.5062 (p-value positive kurtosis). Note that these cells are not visible unless selected.


4.7. Change cell D7 to “T” and cell B12:B31 to the values below (Req. 3-4 for n>=15, positive kurtosis data, two-sided specification)

0.1 -1 0.2 0.2 -2.9 2.6 0.1 1.1 -0.9 -0.2 -0.6 -0.3 1.3 0.4 0

-0.3 -0.1 -0.2 0.1 -1.4


Acceptance Criteria: The sample size should be 20. The p-value should round to 0.1057. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it fails for a two-sided specification. Cell J17 should round to -0.1734 (ZS). Cell J18 should round to 0.8624 (p-value 2-sided skewness). Cell J29 should round to 2.1131 (ZK). Cell J31 should round to 0.0173 (p-value positive kurtosis). Note that these cells are not visible unless selected.




Acceptance Criteria: The sample size should be 20. The p-value should round to 0.1057. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it fails for an upper specification. Cell J17 should round to -0.1734 (ZS).


10

Cell J19 should round to 0.5688 (p-value positive skewness). Cell J29 should round to 2.1131 (ZK). Cell J31 should round to 0.0173 (p-value positive kurtosis). Note that these cells are not visible unless selected.




Acceptance Criteria: The sample size should be 20. The p-value should round to 0.1057. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it fails for a lower specification. Cell J17 should round to -0.1734 (ZS). Cell J20 should round to 0.4312 (p-value negative skewness). Cell J29 should round to 2.1131 (ZK). Cell J31 should round to 0.0173 (p-value positive kurtosis). Note that these cells are not visible unless selected.


4.10. Change cell D7 to “T” and cell B12:B31 to the values below (Req. 3-4 for n>=15, negative kurtosis data, two-sided specification)

-1.1 -0.5 -0.4 1.1 -1 1.2 -0.8 1.2 -1.2 -1 0.6 -1.1 1.2 -1.2

1 -0.8 -1.1

1 1.2 1.2


Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0000 The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for a two-sided


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specification. Cell J17 should round to 0.3238 (ZS). Cell J18 should round to 0.7461 (p-value 2-sided skewness). Cell J29 should round to -5.0793 (ZK) Cell J31 should round to 1.0000 (p-value positive kurtosis). Note that these cells are not visible unless selected.




Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0000. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for an upper specification. Cell J17 should round to 0.3238 (ZS). Cell J19 should round to 0.3730 (p-value positive skewness). Cell J29 should round to -5.0793 (ZK). Cell J31 should round to 1.0000 (p-value positive kurtosis). Note that these cells are not visible unless selected.




Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0000. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to 0.3238 (ZS). Cell J20 should round to 0.6270 (p-value negative skewness). Cell J29 should round to -5.0793 (ZK). Cell J31 should round to 1.0000 (p-value positive kurtosis). Note that these cells are not visible unless selected.


4.13. Change cell D7 to “T” and cell B12:B31 to the values below (Req. 3-4 for n>=15, positive skewness data, two-sided specification)

-0.7 -0.4 -0.4 -0.6 1.8 -0.4 -0.4 1.1 1.5 -0.4 0.3


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-0.7 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.3 0.7


Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it fails for a two-sided specification. Cell J17 should round to 2.6691 (ZS). Cell J18 should round to 0.0076 (p-value 2-sided skewness). Cell J29 should round to 1.1275 (ZK). Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.




Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it fails for an upper specification. Cell J17 should round to 2.6691 (ZS). Cell J19 should round to 0.0038 (p-value positive skewness). Cell J29 should round to 1.1275 (ZK). Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.




Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to 2.6691 (ZS). Cell J20 should round to 0.9962 (p-value negative skewness). Cell J29 should round to 1.1275 (ZK). Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.



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4.16. Change cell D7 to “T” and cell B12:B31 to the values below (Req. 3-4 for n>=15, negative skewness data, two-sided specification)

0.7 0.4 0.4 0.6 -1.8 0.4 0.4 -1.1 -1.5 0.4 -0.3 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.3 -0.7


Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it fails for a two-sided specification. Cell J17 should round to -2.6691 (ZS). Cell J18 should round to 0.0076 (p-value 2-sided skewness). Cell J29 should round to 1.1275 (ZK). Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.




Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for an upper specification. Cell J17 should round to -2.6691 (ZS). Cell J19 should round to 0.9962 (p-value positive skewness). Cell J29 should round to 1.1275 (ZK).


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Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.




Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it fails for a lower specification. Cell J17 should round to -2.6691 (ZS). Cell J20 should round to 0.0038 (p-value negative skewness). Cell J29 should round to 1.1275 (ZK). Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.


4.19. Change cell D7 to “T” and cell B12:B211 to the values below (Req. 3-4 for n=200, normal data, two-sided specification)

2.1 0.1 -0.5 0.1 -0.6

1 -0.4 0.1 -2.4 -1

0.6 0.1 -0.3 2.3 -1

0.3 -0.3

2 -0.9 0.1 0.8 -1.5

1 2.1 0.7 -0.1 -0.4


15

0.6 -1

-0.5 0.4 0.2 -0.1 -0.3 -2.5 -0.2 0.3 -0.8 -0.2 -3

1.9 0.7 -0.2 0.4 -3.4 0.9 -1.8 0.8 0

-0.2 0

-0.1 0.8 -1.1 1.4 2.5 0.5 -0.1 -1.8 0.9 0.1 0.2 1.3 0.1 -0.1 0.7 -0.9 0.3 -0.2 -0.1 1.3


16

2.3 0.5 0.6 1.1 1

-2.2 2.5 1.6 1.2 1.7 -0.9 2.1 0.6 0.6 0.3 1.1 0.5 -0.9 0.7 -0.4 -0.7 0.9 0.1 0.5 -0.2 -1.3 -1

-2.3 1.3 -0.5 -0.3 1.9 1

-0.2 -0.1 1.2 -0.7 2.1 1.1 1.4 -0.5

2 -0.3 0.3


17

-0.2 1.3 1.1 -1.3 -0.6 -0.8 -0.2 1.2 -0.7 -2.7 0.1 -1.1 -0.8 -0.8 -0.3 1.1 0

-0.5 1.6 0.5 0.5 -1.6 2.4 -0.3 0.6 -0.5

0 0.8 1.9 -0.4 0.3 -0.2 1.6 -0.5 -0.8 -1.2 -1.6 0.4 1.3 0.4 -1.4 -0.6 -0.5 -0.4


18

0.2 1.4 -1.5 1.3 -0.2 -0.1 -0.8 0.7 -0.3 -1.2 0.5 -0.7 -0.7 0.7 -0.3 -1

0.5 0.6 1.6 1 1

0.7 -0.1 -0.9 -0.1

1 0.7 0.1 0.6 0.2 1.6 -0.5 -0.7 -1.1 0.4 -0.6 1.9 -0.7 -0.2 -0.5 -0.7



19

Acceptance Criteria: The sample size should be 200. The average should round to 0.11150. The standard deviation should round to 1.07923. The skewness should round to -0.196780. The kurtosis should round to 0.386000. The p-value should round to 0.2651. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for a two-sided specification. Cell J17 should round to -1.1567 (ZS). Cell J18 should round to 0.2474 (p-value 2-sided skewness). Cell J29 should round to 1.1478 (ZK). Cell J31 should round to 0.1255 (p-value positive kurtosis). Note that these cells are not visible unless selected.


4.20. Change cell D7 to “U” (Req. 3-4 for n=200, normal data, upper specification)


Acceptance Criteria: The sample size should be 200. The p-value should round to 0.2651. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for an upper specification. Cell J17 should round to -1.1567 (ZS). Cell J19 should round to 0.8763 (p-value positive skewness). Cell J29 should round to 1.1478 (ZK). Cell J31 should round to 0.1255 (p-value positive kurtosis). Note that these cells are not visible unless selected.


4.21. Change cell D7 to “L” (Req. 3-4 for n=200, normal data, lower specification)


Acceptance Criteria: The sample size should be 200. The p-value should round to 0.2651. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to -1.1567 (ZS). Cell J20 should round to 0.1237 (p-value negative skewness). Cell J29 should round to 1.1478 (ZK). Cell J31 should round to 0.1255 (p-value positive kurtosis). Note that these cells are not visible unless selected.


5. Independence of tab

5.1. Copy the Skewness Kurtosis Tests tab. Delete all tab but the copy.


Acceptance Criteria: The sample size should be 200. The average should round to 0.11150. The standard deviation should round to 1.07923.


20

The skewness should round to -0.196780. The kurtosis should round to 0.386000. The p-value should round to 0.2651. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to -1.1567 (ZS). Cell J20 should round to 0.1237 (p-value negative skewness). Cell J29 should round to 1.1478 (ZK). Cell J31 should round to 0.1255 (p-value positive kurtosis). Note that these cells are not visible unless selected.


6. Saving and Signing File

6.1. Determine if all tests passed

All Test Cases for Computer Pass? yes no

6.2. Save File and show name and date.

Name of File:

Data of File:

Signature: ________________________________ Date: XXX


21

Appendix B: Test Matrix Table 2 shows for each requirement the tests that demonstrate the requirement is meet with justification the test cases cover the requirement.

Table 2: Test Cases Matching User Requirements ID Description

1

Input of Data:

a. Data can be typed or pasted into the data column of the spreadsheet

3.9

b. A header or name for the data can be typed into the top cell of the data column, which is displayed at the top of the summary data section

3.3

c. The type of specification limit can be typed into the specification cell of the spreadsheet

3.2

d. Only the data column, including header, and the type of specification cell can be changed

3.1

2

Data Checking:

a. Sample size is zero when there are no valid values. Otherwise it is the number of valid values

No valid values – 3.3, 3.4 covers no values and invalid value

Otherwise – 3.5 to 3.9 cover full range of n=1 to 200

b. Average is blank when there are no valid values. Otherwise it is the average of the valid values.

No valid values – 3.3, 3.4 covers no values and invalid value

Otherwise – 3.5 to 3.9, 4.1, 4.2, 4.19 cover full range of n=1 to 200

c. Standard deviation is blank when there are 1 or fewer valid values. Otherwise it is the standard deviation of the valid values.

1 or fewer valid values – 3.3 to 3.5 covers no values, invalid value, n=1

Otherwise – 3.6 to 3.9, 4.1, 4.2, 4.19 cover full range of n=2 to 200

d. Skewness is blank when there are 2 or fewer valid values or the standard deviation is 0. Otherwise it is skewness of the valid values.

2 or fewer valid values– 3.3 to 3.6 covers no values, invalid value, n=1, n=2

Standard deviation is 0 – 3.7 to 3.9 cover full range of n=3 to 200

Otherwise –4.1, 4.2, 4.19 cover range of n=4 to 200

e. Kurtosis is blank when there are 3 or fewer valid values or the standard deviation is 0. Otherwise it is the kurtosis of the valid values.

3 or fewer valid values– 3.3 to 3.7 covers no values, invalid value, n=1, n=2, n=3

Standard deviation is 0 – 3.3 to 3.9 cover full range of n=4 to 200.

Otherwise –4.1, 4.2, 4.19 cover full range of n=4 to 200


22

3

Skewness Kurtosis All test:

a. If there are less than 15 valid values or the standard deviation is 0, no p-value is displayed and an error message is displayed

3.3 to 3.9, 4.1, 4.2 for n=0 to 14

b. Otherwise, the p-value is displayed

4.3 to 4.21 for n=15 to n=200

c. If the p-value is displayed and is > 0.05, a message that the data passes SK All normality test is displayed

4.3 to 4.9, 4.19 to 4.21

d. If the p-value is displayed and is ≤ 0.05, a message that the data fails SK All normality test" is displayed

4.10 to 4.18,

4

Skewness Kurtosis Specific test:

a. If there are less than 15 valid values, the standard deviation is 0 or the type of specification limit is not a “T”, “U” or “L”, an error message is displayed

3.3 to 3.9, 4.1, 4.2. 4.3

b. Otherwise, the pass/fail conclusion is displayed along with the type of specification limit.

4.4 to 4.21 – 18 test cases cover 3 type of specification limits for six cases n=20, normal, n=200 normal, positive skewness, negative skewness, positive kurtosis and negative kurtosis.

5

Tabs:

a. Tabs are independent of each other so tab can be copied and all other tab deleted with tab results remaining the same.

5.1


23

Appendix C: Verification of Results 4.1 From Minitab version 18.0.

1st Quartile 0.12492Median 0.125353rd Quartile 0.12570Maximum 0.12570

0.12463 0.12602

0.12490 0.12570

0.00025 0.00162

A-Squared 0.49P-Value 0.093

Mean 0.12532StDev 0.00043Variance 0.00000Skewness -0.04558Kurtosis -5.73743N 4

Minimum 0.12490

Anderson-Darling Normality Test

95% Confidence Interval for Mean

95% Confidence Interval for Median

95% Confidence Interval for StDev

0.12560.12540.12520.1250

Median

Mean

0.126000.125750.125500.125250.125000.124750.12450

95% Confidence Intervals

Summary Report for Diameter n=4

4.2 From Minitab version 18.0


0.12473 0.12587

0.12478 0.12620

0.00072 0.00159



Minimum 0.12340





0.1270.1260.1250.124

Median

Mean

0.12640.12600.12560.12520.1248


Summary Report for Diameter n= 14


24

4.3 From Minitab version 18.0


0.12477 0.12582

0.12484 0.12601

0.00070 0.00150



Minimum 0.12340





0.1270.1260.1250.124

Median

Mean

0.12600.12580.12560.12540.12520.12500.1248


Summary Report for Diameter n=15

4.4-6 From R version 3.2.4 - Normal

> install.packages("fBasics") > library("fBasics") > Diameter <-scan("D:\\Diameter.txt") Read 20 items > dagoTest(Diameter) Title: D'Agostino Normality Test Test Results: STATISTIC: Chi2 | Omnibus: 0.4345 Z3 | Skewness: -0.659 Z4 | Kurtosis: -0.0156 P VALUE: Omnibus Test: 0.8047 Skewness Test: 0.5099 Kurtosis Test: 0.9875

Skewness: p-value of 0.5099 is for two-sided case. For the other cases:

Upper spec limit =NORMDIST(--0.65897,0,1,TRUE) 0.745042483 Lower spec limit =NORMDIST(-0.65897,0,1,TRUE) 0.254957517

Kurtosis: The upper limit has p-value: Positive kurtosis =NORMDIST(--0.01564,0,1,TRUE) 0.506239203


25

4.7-9 From R version 3.2.4 – Positive Kurtosis

> install.packages("fBasics") > library("fBasics") >PositiveKurtosis <-scan("D:\\Positive Kurtosis.txt") Read 20 items >dagoTest(PositiveKurtosis)

Title: D'Agostino Normality Test Test Results: STATISTIC: Chi2 | Omnibus: 4.4951 Z3 | Skewness: -0.1734 Z4 | Kurtosis: 2.1131 P VALUE: Omnibus Test: 0.1057 Skewness Test: 0.8624 Kurtosis Test: 0.0346

Skewness: p-value of -2.0806 is for two-sided case. For the other cases:


Kurtosis: The upper limit has p-value: Positive kurtosis =NORMDIST(-2.1131,0,1,TRUE) 0.017296105 4.10-12 From R version 3.2.4 – Negative Kurtosis

> install.packages("fBasics") > library("fBasics") >NegativeKurtosis <-scan("D:\\Negative Kurtosis.txt") Read 20 items >dagoTest(NegativeKurtosis)

Title: D'Agostino Normality Test Test Results: STATISTIC: Chi2 | Omnibus: 25.9043 Z3 | Skewness: 0.3238 Z4 | Kurtosis: -5.0793 P VALUE: Omnibus Test: 2.371e-06 Skewness Test: 0.7461 Kurtosis Test: 3.788e-07


Upper spec limit =NORMDIST(-0.3238,0,1,TRUE) 0.373044728 Lower spec limit =NORMDIST(0.3238,0,1,TRUE) 0.626955272


26

Kurtosis: The upper limit has p-value:

Positive kurtosis =NORMDIST(--5.079,0,1,TRUE) 0.99999981 4.13-15 From R version 3.2.4 – Positive Skewness

> install.packages("fBasics") > library("fBasics") >PositiveSkewness <-scan("D:\\Positive Skewness.txt") Read 20 items >dagoTest(PositiveSkewness)

Title: D'Agostino Normality Test Test Results: STATISTIC: Chi2 | Omnibus: 8.3954 Z3 | Skewness: 2.6691 Z4 | Kurtosis: 1.1275 P VALUE: Omnibus Test: 0.01503 Skewness Test: 0.007605 Kurtosis Test: 0.2595


Upper spec limit =NORMDIST(-2.6691,0,1,TRUE) 0.00380274 Lower spec limit =NORMDIST(2.6691,0,1,TRUE) 0.99619726

Kurtosis: The upper limit has p-value: Positive kurtosis =NORMDIST(-1.1275,0,1,TRUE) 0.12976557 4.16-18 From R version 3.2.4 – Negative Skewness

> install.packages("fBasics") > library("fBasics") > NegativeSkewness <-scan("D:\\Negative Skewness.txt") Read 20 items >dagoTest(NegativeSkewness)



27



Kurtosis: The upper limit has p-value: Positive kurtosis =NORMDIST(-1.1275,0,1,TRUE) 0.12976557 4.19-21 From R version 3.2.4 – n=200, normal

> install.packages("fBasics") > library("fBasics") > Normal200 <-scan("D:\\Normal n=200.txt") Read 20 items >dagoTest(Normal200)




Kurtosis: The upper limit has p-value: Positive kurtosis =NORMDIST(-1.1478,0,1,TRUE) 0.125525569


28

4.19-21 From Minitab version 18 – n=200, normal

1st Quartile -0.50000Median 0.100003rd Quartile 0.80000Maximum 2.50000

-0.03899 0.26199

-0.10000 0.30000

0.98282 1.19679


Mean 0.11150StDev 1.07923Variance 1.16474Skewness -0.196780Kurtosis 0.386000N 200

Minimum -3.40000





210-1-2-3

Median

Mean

0.30.20.10.0-0.1


Summary Report for n=200


Appendix B

File: STAT-18 -Windows 10


1




>



2




2.2. Double click the spreadsheet to open it. Capture a screen shot of the section of the first tab showing the

version and date.



3


Pass or Fail: Pass Initials: WT Date: 8/31/17









Acceptance Criteria: Both B11 and D11 should change to “Diameter”.

The sample size should be 0. The average, SD, skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.




4

Acceptance Criteria: The sample size should be 0.

The average, SD, skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.



Acceptance Criteria: The sample size and average should be 1.

The standard deviation, skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.




5


The average should be 1. The standard deviation should be 0. The skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.








6






7


8

Acceptance Criteria: The data column should be filled with “1”. The sample size should be 200. The average should be 1. The standard deviation should be 0. The skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.




0.1257 0.1249 0.1257 0.125


The average should round to 0.12532. The standard deviation should round to 0.00043. The skewness should round to -0.04558. The kurtosis should round to -5.73743. The p-value should be blank. The conclusions should indicate there is insufficient data.



0.1264

0.1238

0.1254


9

0.1248

0.1253

0.1234

0.1262

0.1262

0.1269

0.1245






10


A p-value should be given. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be incorrect type of specification.




11

Skewness = -0.29569 Y = -0.62532 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -0.65897 p-value <> = 0.509914 p-value > = 0.745043 p-value < = 0.254957 Kurtosis = 2.549802 Eb2 = 2.714286 VarB2 = 0.579237 x = -0.21612 3StdMom = 1.737522 A = 18.32027 0.969103 Z= -0.01564 p-value <> = 0.987519 p-value > = 0.50624 p-value < = 0.49376 K^2 0.434488 p-value 0.804734





12

Skewness = -0.29569 Y = -0.62532 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -0.65897 p-value <> = 0.509914 p-value > = 0.745043 p-value < = 0.254957 Kurtosis = 2.549802 Eb2 = 2.714286 VarB2 = 0.579237 x = -0.21612 3StdMom = 1.737522 A = 18.32027 0.969103 Z= -0.01564 p-value <> = 0.987519 p-value > = 0.50624 p-value < = 0.49376 K^2 0.434488 p-value 0.804734


13

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.8047. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for an upper specification. Cell J17 should round to -0.659 (ZS). Cell J19 should round to 0.7450 (p-value positive skewness). Cell J29 should round to -0.0156 (ZK) Cell J31 should round to 0.5062 (p-value positive kurtosis). Note that these cells are not visible unless selected.



Skewness = -0.29569 Y = -0.62532 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -0.65897 p-value <> = 0.509914 p-value > = 0.745043 p-value < = 0.254957 Kurtosis = 2.549802 Eb2 = 2.714286 VarB2 = 0.579237


14

x = -0.21612 3StdMom = 1.737522 A = 18.32027 0.969103 Z= -0.01564 p-value <> = 0.987519 p-value > = 0.50624 p-value < = 0.49376 K^2 0.434488 p-value 0.804734

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.8047. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to -0.659 (ZS). Cell J20 should round to 0.2550 (p-value negative skewness). Cell J29 should round to -0.0156 (ZK). Cell J31 should round to 0.5062 (p-value positive kurtosis). Note that these cells are not visible unless selected.



0.1 -1 0.2 0.2 -2.9 2.6 0.1 1.1 -0.9 -0.2 -0.6 -0.3 1.3 0.4 0

-0.3 -0.1 -0.2 0.1 -1.4


15

Skewness = -0.07718 Y = -0.16321 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -0.17338 p-value <> = 0.862353 p-value > = 0.568824 p-value < = 0.431176 Kurtosis = 4.890742 Eb2 = 2.714286 VarB2 = 0.579237 x = 2.859708 3StdMom = 1.737522 A = 18.32027 0.430621 Z= 2.113056 p-value <> = 0.034596 p-value > = 0.017298 p-value < = 0.982702 K^2 4.495066 p-value 0.10566


16






17

x = 2.859708 3StdMom = 1.737522 A = 18.32027 0.430621 Z= 2.113056 p-value <> = 0.034596 p-value > = 0.017298 p-value < = 0.982702 K^2 4.495066 p-value 0.10566

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.1057. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it fails for an upper specification. Cell J17 should round to -0.1734 (ZS). Cell J19 should round to 0.5688 (p-value positive skewness). Cell J29 should round to 2.1131 (ZK). Cell J31 should round to 0.0173 (p-value positive kurtosis). Note that these cells are not visible unless selected.



Skewness = -0.07718 Y = -0.16321 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899


18

Alpha = 2.718712 Z = -0.17338 p-value <> = 0.862353 p-value > = 0.568824 p-value < = 0.431176 Kurtosis = 4.890742 Eb2 = 2.714286 VarB2 = 0.579237 x = 2.859708 3StdMom = 1.737522 A = 18.32027 0.430621 Z= 2.113056 p-value <> = 0.034596 p-value > = 0.017298 p-value < = 0.982702 K^2 4.495066 p-value 0.10566




-1.1 -0.5 -0.4 1.1 -1 1.2 -0.8 1.2 -1.2 -1 0.6 -1.1 1.2


19

-1.2 1

-0.8 -1.1

1 1.2 1.2

Skewness = 0.144366

Y = 0.3053 B2 = 3.577778 W2 = 1.270585

Delta = 2.8899 Alpha = 2.718712

Z = 0.323845 p-value <> = 0.746055 p-value > = 0.373028 p-value < = 0.626972

Kurtosis = 1.167515 Eb2 = 2.714286

VarB2 = 0.579237 x = -2.03235

3StdMom = 1.737522 A = 18.32027


20

3.704331

Z= -5.07932 p-value <> = 3.79E-07 p-value > = 1 p-value < = 1.89E-07

K^2 25.90433 p-value 2.37E-06

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0000 The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for a two-sided specification. Cell J17 should round to 0.3238 (ZS). Cell J18 should round to 0.7461 (p-value 2-sided skewness). Cell J29 should round to -5.0793 (ZK) Cell J31 should round to 1.0000 (p-value positive kurtosis). Note that these cells are not visible unless selected.



Skewness = 0.144366 Y = 0.3053 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899


21

Alpha = 2.718712 Z = 0.323845 p-value <> = 0.746055 p-value > = 0.373028 p-value < = 0.626972 Kurtosis = 1.167515 Eb2 = 2.714286 VarB2 = 0.579237 x = -2.03235 3StdMom = 1.737522 A = 18.32027 3.704331 Z= -5.07932 p-value <> = 3.79E-07 p-value > = 1 p-value < = 1.89E-07 K^2 25.90433 p-value 2.37E-06





22

Skewness = 0.144366 Y = 0.3053 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = 0.323845 p-value <> = 0.746055 p-value > = 0.373028 p-value < = 0.626972 Kurtosis = 1.167515 Eb2 = 2.714286 VarB2 = 0.579237 x = -2.03235 3StdMom = 1.737522 A = 18.32027 3.704331 Z= -5.07932 p-value <> = 3.79E-07 p-value > = 1 p-value < = 1.89E-07 K^2 25.90433 p-value 2.37E-06


23

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0000. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to 0.3238 (ZS). Cell J20 should round to 0.6270 (p-value negative skewness). Cell J29 should round to -5.0793 (ZK). Cell J31 should round to 1.0000 (p-value positive kurtosis). Note that these cells are not visible unless selected.



-0.7 -0.4 -0.4 -0.6 1.8 -0.4 -0.4 1.1 1.5 -0.4 0.3 -0.7 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.3 0.7


24

Skewness = 1.363523 Y = 2.883529 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = 2.669104 p-value <> = 0.007605 p-value > = 0.003803 p-value < = 0.996197 Kurtosis = 3.493619 Eb2 = 2.714286 VarB2 = 0.579237 x = 1.023988 3StdMom = 1.737522 A = 18.32027 0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150.


25

The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it fails for a two-sided specification. Cell J17 should round to 2.6691 (ZS). Cell J18 should round to 0.0076 (p-value 2-sided skewness). Cell J29 should round to 1.1275 (ZK). Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.



Skewness = 1.363523 Y = 2.883529 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = 2.669104 p-value <> = 0.007605 p-value > = 0.003803 p-value < = 0.996197 Kurtosis = 3.493619 Eb2 = 2.714286 VarB2 = 0.579237 x = 1.023988 3StdMom = 1.737522 A = 18.32027


26

0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503






27

Alpha = 2.718712 Z = 2.669104 p-value <> = 0.007605 p-value > = 0.003803 p-value < = 0.996197 Kurtosis = 3.493619 Eb2 = 2.714286 VarB2 = 0.579237 x = 1.023988 3StdMom = 1.737522 A = 18.32027 0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503




0.7 0.4 0.4 0.6 -1.8 0.4 0.4 -1.1 -1.5 0.4 -0.3


28

0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.3 -0.7

Skewness = -1.36352 Y = -2.88353 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -2.6691 p-value <> = 0.007605 p-value > = 0.996197 p-value < = 0.003803 Kurtosis = 3.493619 Eb2 = 2.714286


29

VarB2 = 0.579237 x = 1.023988 3StdMom = 1.737522 A = 18.32027 0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503




Skewness = -1.36352


30

Y = -2.88353 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -2.6691 p-value <> = 0.007605 p-value > = 0.996197 p-value < = 0.003803 Kurtosis = 3.493619 Eb2 = 2.714286 VarB2 = 0.579237 x = 1.023988 3StdMom = 1.737522 A = 18.32027 0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for an upper specification. Cell J17 should round to -2.6691 (ZS). Cell J19 should round to 0.9962 (p-value positive skewness). Cell J29 should round to 1.1275 (ZK). Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.




31



32




2.1 0.1 -0.5 0.1 -0.6

1 -0.4 0.1 -2.4 -1

0.6 0.1 -0.3 2.3 -1

0.3 -0.3

2 -0.9 0.1 0.8 -1.5

1 2.1 0.7 -0.1 -0.4 0.6 -1

-0.5 0.4 0.2 -0.1


33

-0.3 -2.5 -0.2 0.3 -0.8 -0.2 -3

1.9 0.7 -0.2 0.4 -3.4 0.9 -1.8 0.8 0

-0.2 0

-0.1 0.8 -1.1 1.4 2.5 0.5 -0.1 -1.8 0.9 0.1 0.2 1.3 0.1 -0.1 0.7 -0.9 0.3 -0.2 -0.1 1.3 2.3 0.5 0.6 1.1 1

-2.2


34

2.5 1.6 1.2 1.7 -0.9 2.1 0.6 0.6 0.3 1.1 0.5 -0.9 0.7 -0.4 -0.7 0.9 0.1 0.5 -0.2 -1.3 -1

-2.3 1.3 -0.5 -0.3 1.9 1

-0.2 -0.1 1.2 -0.7 2.1 1.1 1.4 -0.5

2 -0.3 0.3 -0.2 1.3 1.1 -1.3 -0.6 -0.8


35

-0.2 1.2 -0.7 -2.7 0.1 -1.1 -0.8 -0.8 -0.3 1.1 0

-0.5 1.6 0.5 0.5 -1.6 2.4 -0.3 0.6 -0.5

0 0.8 1.9 -0.4 0.3 -0.2 1.6 -0.5 -0.8 -1.2 -1.6 0.4 1.3 0.4 -1.4 -0.6 -0.5 -0.4 0.2 1.4 -1.5 1.3 -0.2 -0.1


36

-0.8 0.7 -0.3 -1.2 0.5 -0.7 -0.7 0.7 -0.3 -1

0.5 0.6 1.6 1 1

0.7 -0.1 -0.9 -0.1

1 0.7 0.1 0.6 0.2 1.6 -0.5 -0.7 -1.1 0.4 -0.6 1.9 -0.7 -0.2 -0.5 -0.7


37


38






39


Acceptance Criteria: The sample size should be 200. The p-value should round to 0.2651. The conclusions for the SK All test should be it passes.


40

The conclusion for the SK Spec test should be it passes for an upper specification. Cell J17 should round to -1.1567 (ZS). Cell J19 should round to 0.8763 (p-value positive skewness). Cell J29 should round to 1.1478 (ZK). Cell J31 should round to 0.1255 (p-value positive kurtosis). Note that these cells are not visible unless selected.



Skewness = -0.1953 Y = -1.14457 B2 = 3.159828 W2 = 1.078378 Delta = 5.14828 Alpha = 5.051471 Z = -1.15675 p-value <> = 0.247376 p-value > = 0.876312 p-value < = 0.123688 Kurtosis = 3.346567 Eb2 = 2.970149 VarB2 = 0.11136 x = 1.127987 3StdMom = 0.967701 A = 42.06667 0.756788


41

Z= 1.147805 p-value <> = 0.251049 p-value > = 0.125525 p-value < = 0.874475 K^2 2.655517 p-value 0.265071






42

Skewness = -0.1953 Y = -1.14457 B2 = 3.159828 W2 = 1.078378 Delta = 5.14828 Alpha = 5.051471 Z = -1.15675 p-value <> = 0.247376 p-value > = 0.876312 p-value < = 0.123688 Kurtosis = 3.346567 Eb2 = 2.970149 VarB2 = 0.11136 x = 1.127987 3StdMom = 0.967701 A = 42.06667 0.756788 Z= 1.147805


43

p-value <> = 0.251049 p-value > = 0.125525 p-value < = 0.874475 K^2 2.655517 p-value 0.265071

Acceptance Criteria: The sample size should be 200. The average should round to 0.11150. The standard deviation should round to 1.07923. The skewness should round to -0.196780. The kurtosis should round to 0.386000. The p-value should round to 0.2651. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to -1.1567 (ZS). Cell J20 should round to 0.1237 (p-value negative skewness). Cell J29 should round to 1.1478 (ZK). Cell J31 should round to 0.1255 (p-value positive kurtosis). Note that these cells are not visible unless selected.




All Test Cases for Computer Pass? X yes no


Name of File: STAT-18 – Windows 10

Data of File: August 31, 2017

Signature: ________________________________ Date: August 31, 2017


Appendix C

File: STAT-18 -Windows 7


1






2




2.2. Double click the spreadsheet to open it. Capture a screen shot of the section of the first tab showing the

version and date.



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4




Acceptance Criteria: Both B11 and D11 should change to “Diameter”.

The sample size should be 0. The average, SD, skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.


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The average, SD, skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.




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Acceptance Criteria: The sample size and average should be 1. The standard deviation, skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.








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The average should be 1. The standard deviation should be 0.


8

The skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.



Acceptance Criteria: The data column should be filled with “1”.

The sample size should be 200. The average should be 1.


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The standard deviation should be 0. The skewness, kurtosis and p-value should be blank. The conclusions should indicate there is insufficient data.




0.1257 0.1249 0.1257 0.125





0.1264

0.1238

0.1254

0.1248

0.1253

0.1234


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0.1262

0.1262

0.1269

0.1245






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A p-value should be given. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be incorrect type of specification.




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Skewness = -0.29569 Y = -0.62532 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -0.65897 p-value <> = 0.509914 p-value > = 0.745043 p-value < = 0.254957 Kurtosis = 2.549802 Eb2 = 2.714286 VarB2 = 0.579237 x = -0.21612 3StdMom = 1.737522 A = 18.32027 0.969103 Z= -0.01564 p-value <> = 0.987519 p-value > = 0.50624 p-value < = 0.49376





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Skewness = -0.29569 Y = -0.62532 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -0.65897 p-value <> = 0.509914 p-value > = 0.745043 p-value < = 0.254957 Kurtosis = 2.549802 Eb2 = 2.714286 VarB2 = 0.579237 x = -0.21612 3StdMom = 1.737522 A = 18.32027 0.969103 Z= -0.01564 p-value <> = 0.987519 p-value > = 0.50624 p-value < = 0.49376

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.8047. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for an upper


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specification. Cell J17 should round to -0.659 (ZS). Cell J19 should round to 0.7450 (p-value positive skewness). Cell J29 should round to -0.0156 (ZK) Cell J31 should round to 0.5062 (p-value positive kurtosis). Note that these cells are not visible unless selected.



Skewness = -0.29569 Y = -0.62532 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -0.65897 p-value <> = 0.509914 p-value > = 0.745043 p-value < = 0.254957 Kurtosis = 2.549802 Eb2 = 2.714286 VarB2 = 0.579237 x = -0.21612 3StdMom = 1.737522 A = 18.32027 0.969103 Z= -0.01564


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p-value <> = 0.987519 p-value > = 0.50624 p-value < = 0.49376 K^2 0.434488 p-value 0.804734

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.8047. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to -0.659 (ZS). Cell J20 should round to 0.2550 (p-value negative skewness). Cell J29 should round to -0.0156 (ZK). Cell J31 should round to 0.5062 (p-value positive kurtosis). Note that these cells are not visible unless selected.



0.1 -1 0.2 0.2 -2.9 2.6 0.1 1.1 -0.9 -0.2 -0.6 -0.3 1.3 0.4 0

-0.3 -0.1 -0.2 0.1 -1.4


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Skewness = -0.07718 Y = -0.16321 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -0.17338 p-value <> = 0.862353 p-value > = 0.568824 p-value < = 0.431176 Kurtosis = 4.890742 Eb2 = 2.714286 VarB2 = 0.579237 x = 2.859708 3StdMom = 1.737522 A = 18.32027 0.430621 Z= 2.113056 p-value <> = 0.034596 p-value > = 0.017298 p-value < = 0.982702 K^2 4.495066


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p-value 0.10566






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x = 2.859708 3StdMom = 1.737522 A = 18.32027 0.430621 Z= 2.113056 p-value <> = 0.034596 p-value > = 0.017298 p-value < = 0.982702 K^2 4.495066 p-value 0.10566

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.1057. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it fails for an upper specification. Cell J17 should round to -0.1734 (ZS). Cell J19 should round to 0.5688 (p-value positive skewness). Cell J29 should round to 2.1131 (ZK). Cell J31 should round to 0.0173 (p-value positive kurtosis). Note that these cells are not visible unless selected.



Skewness = -0.07718 Y = -0.16321 B2 = 3.577778 W2 = 1.270585


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Delta = 2.8899 Alpha = 2.718712 Z = -0.17338 p-value <> = 0.862353 p-value > = 0.568824 p-value < = 0.431176 Kurtosis = 4.890742 Eb2 = 2.714286 VarB2 = 0.579237 x = 2.859708 3StdMom = 1.737522 A = 18.32027 0.430621 Z= 2.113056 p-value <> = 0.034596 p-value > = 0.017298 p-value < = 0.982702 K^2 4.495066 p-value 0.10566




-1.1 -0.5 -0.4 1.1 -1 1.2 -0.8 1.2 -1.2 -1 0.6


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-1.1 1.2 -1.2

1 -0.8 -1.1

1 1.2 1.2

Skewness = 0.144366 Y = 0.3053 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = 0.323845 p-value <> = 0.746055 p-value > = 0.373028 p-value < = 0.626972 Kurtosis = 1.167515 Eb2 = 2.714286 VarB2 = 0.579237


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x = -2.03235 3StdMom = 1.737522 A = 18.32027 3.704331 Z= -5.07932 p-value <> = 3.79E-07 p-value > = 1 p-value < = 1.89E-07 K^2 25.90433 p-value 2.37E-06

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0000 The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for a two-sided specification. Cell J17 should round to 0.3238 (ZS). Cell J18 should round to 0.7461 (p-value 2-sided skewness). Cell J29 should round to -5.0793 (ZK) Cell J31 should round to 1.0000 (p-value positive kurtosis). Note that these cells are not visible unless selected.

Pass or Fail: Passes Initials: WT Date: 9/1/17


Skewness = 0.144366 Y = 0.3053 B2 = 3.577778 W2 = 1.270585


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Delta = 2.8899 Alpha = 2.718712 Z = 0.323845 p-value <> = 0.746055 p-value > = 0.373028 p-value < = 0.626972 Kurtosis = 1.167515 Eb2 = 2.714286 VarB2 = 0.579237 x = -2.03235 3StdMom = 1.737522 A = 18.32027 3.704331 Z= -5.07932 p-value <> = 3.79E-07 p-value > = 1 p-value < = 1.89E-07 K^2 25.90433 p-value 2.37E-06





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Skewness = 0.144366 Y = 0.3053 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = 0.323845 p-value <> = 0.746055 p-value > = 0.373028 p-value < = 0.626972 Kurtosis = 1.167515 Eb2 = 2.714286 VarB2 = 0.579237 x = -2.03235 3StdMom = 1.737522 A = 18.32027 3.704331 Z= -5.07932 p-value <> = 3.79E-07 p-value > = 1 p-value < = 1.89E-07 K^2 25.90433 p-value 2.37E-06

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0000.


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The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to 0.3238 (ZS). Cell J20 should round to 0.6270 (p-value negative skewness). Cell J29 should round to -5.0793 (ZK). Cell J31 should round to 1.0000 (p-value positive kurtosis). Note that these cells are not visible unless selected.



-0.7 -0.4 -0.4 -0.6 1.8 -0.4 -0.4 1.1 1.5 -0.4 0.3 -0.7 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.3 0.7


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Skewness = 1.363523 Y = 2.883529 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = 2.669104 p-value <> = 0.007605 p-value > = 0.003803 p-value < = 0.996197 Kurtosis = 3.493619 Eb2 = 2.714286 VarB2 = 0.579237 x = 1.023988 3StdMom = 1.737522 A = 18.32027 0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503


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Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it fails for a two-sided specification. Cell J17 should round to 2.6691 (ZS). Cell J18 should round to 0.0076 (p-value 2-sided skewness). Cell J29 should round to 1.1275 (ZK). Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.



Skewness = 1.363523 Y = 2.883529 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = 2.669104 p-value <> = 0.007605 p-value > = 0.003803 p-value < = 0.996197 Kurtosis = 3.493619 Eb2 = 2.714286 VarB2 = 0.579237 x = 1.023988


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3StdMom = 1.737522 A = 18.32027 0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503






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Alpha = 2.718712 Z = 2.669104 p-value <> = 0.007605 p-value > = 0.003803 p-value < = 0.996197 Kurtosis = 3.493619 Eb2 = 2.714286 VarB2 = 0.579237 x = 1.023988 3StdMom = 1.737522 A = 18.32027 0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503




0.7 0.4 0.4 0.6 -1.8 0.4 0.4 -1.1 -1.5 0.4 -0.3 0.7


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0.8 0.8 0.8 0.8 0.8 0.8 0.3 -0.7

Skewness = -1.36352 Y = -2.88353 B2 = 3.577778 W2 = 1.270585 Delta = 2.8899 Alpha = 2.718712 Z = -2.6691 p-value <> = 0.007605 p-value > = 0.996197 p-value < = 0.003803 Kurtosis = 3.493619 Eb2 = 2.714286 VarB2 = 0.579237 x = 1.023988 3StdMom = 1.737522


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A = 18.32027 0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503




Skewness = -1.36352 Y = -2.88353 B2 = 3.577778 W2 = 1.270585


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Delta = 2.8899 Alpha = 2.718712 Z = -2.6691 p-value <> = 0.007605 p-value > = 0.996197 p-value < = 0.003803 Kurtosis = 3.493619 Eb2 = 2.714286 VarB2 = 0.579237 x = 1.023988 3StdMom = 1.737522 A = 18.32027 0.644279 Z= 1.127517 p-value <> = 0.259524 p-value > = 0.129762 p-value < = 0.870238 K^2 8.395412 p-value 0.01503

Acceptance Criteria: The sample size should be 20. The p-value should round to 0.0150. The conclusions for the SK All test should be it fails. The conclusion for the SK Spec test should be it passes for an upper specification. Cell J17 should round to -2.6691 (ZS). Cell J19 should round to 0.9962 (p-value positive skewness). Cell J29 should round to 1.1275 (ZK). Cell J31 should round to 0.1298 (p-value positive kurtosis). Note that these cells are not visible unless selected.




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2.1 0.1 -0.5 0.1 -0.6

1 -0.4 0.1 -2.4 -1

0.6 0.1 -0.3 2.3 -1

0.3 -0.3

2 -0.9 0.1 0.8 -1.5

1 2.1 0.7 -0.1 -0.4 0.6 -1

-0.5 0.4 0.2 -0.1


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-0.3 -2.5 -0.2 0.3 -0.8 -0.2 -3

1.9 0.7 -0.2 0.4 -3.4 0.9 -1.8 0.8 0

-0.2 0

-0.1 0.8 -1.1 1.4 2.5 0.5 -0.1 -1.8 0.9 0.1 0.2 1.3 0.1 -0.1 0.7 -0.9 0.3 -0.2 -0.1 1.3 2.3 0.5 0.6 1.1 1

-2.2


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2.5 1.6 1.2 1.7 -0.9 2.1 0.6 0.6 0.3 1.1 0.5 -0.9 0.7 -0.4 -0.7 0.9 0.1 0.5 -0.2 -1.3 -1

-2.3 1.3 -0.5 -0.3 1.9 1

-0.2 -0.1 1.2 -0.7 2.1 1.1 1.4 -0.5

2 -0.3 0.3 -0.2 1.3 1.1 -1.3 -0.6 -0.8


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-0.2 1.2 -0.7 -2.7 0.1 -1.1 -0.8 -0.8 -0.3 1.1 0

-0.5 1.6 0.5 0.5 -1.6 2.4 -0.3 0.6 -0.5

0 0.8 1.9 -0.4 0.3 -0.2 1.6 -0.5 -0.8 -1.2 -1.6 0.4 1.3 0.4 -1.4 -0.6 -0.5 -0.4 0.2 1.4 -1.5 1.3 -0.2 -0.1


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-0.8 0.7 -0.3 -1.2 0.5 -0.7 -0.7 0.7 -0.3 -1

0.5 0.6 1.6 1 1

0.7 -0.1 -0.9 -0.1

1 0.7 0.1 0.6 0.2 1.6 -0.5 -0.7 -1.1 0.4 -0.6 1.9 -0.7 -0.2 -0.5 -0.7


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Skewness = -0.1953 Y = -1.14457 B2 = 3.159828


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W2 = 1.078378 Delta = 5.14828 Alpha = 5.051471 Z = -1.15675 p-value <> = 0.247376 p-value > = 0.876312 p-value < = 0.123688

Kurtosis = 3.346567 Eb2 = 2.970149 VarB2 = 0.11136 x = 1.127987 3StdMom = 0.967701 A = 42.06667

0.756788

Z= 1.147805 p-value <> = 0.251049 p-value > = 0.125525 p-value < = 0.874475

K^2 2.655517 p-value 0.265071





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Acceptance Criteria: The sample size should be 200. The p-value should round to 0.2651. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for an upper specification. Cell J17 should round to -1.1567 (ZS). Cell J19 should round to 0.8763 (p-value positive skewness). Cell J29 should round to 1.1478 (ZK). Cell J31 should round to 0.1255 (p-value positive kurtosis). Note that these cells are not visible unless selected.



Skewness = -0.1953 Y = -1.14457 B2 = 3.159828 W2 = 1.078378 Delta = 5.14828 Alpha = 5.051471 Z = -1.15675 p-value <> = 0.247376 p-value > = 0.876312 p-value < = 0.123688 Kurtosis = 3.346567 Eb2 = 2.970149 VarB2 = 0.11136 x = 1.127987


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3StdMom = 0.967701 A = 42.06667 0.756788 Z= 1.147805 p-value <> = 0.251049 p-value > = 0.125525 p-value < = 0.874475 K^2 2.655517 p-value 0.265071






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Skewness = -0.1953 Y = -1.14457 B2 = 3.159828 W2 = 1.078378 Delta = 5.14828 Alpha = 5.051471 Z = -1.15675 p-value <> = 0.247376 p-value > = 0.876312 p-value < = 0.123688 Kurtosis = 3.346567 Eb2 = 2.970149 VarB2 = 0.11136 x = 1.127987 3StdMom = 0.967701 A = 42.06667 0.756788 Z= 1.147805 p-value <> = 0.251049 p-value > = 0.125525 p-value < = 0.874475


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K^2 2.655517 p-value 0.265071

Acceptance Criteria: The sample size should be 200. The average should round to 0.11150. The standard deviation should round to 1.07923. The skewness should round to -0.196780. The kurtosis should round to 0.386000. The p-value should round to 0.2651. The conclusions for the SK All test should be it passes. The conclusion for the SK Spec test should be it passes for a lower specification. Cell J17 should round to -1.1567 (ZS). Cell J20 should round to 0.1237 (p-value negative skewness). Cell J29 should round to 1.1478 (ZK). Cell J31 should round to 0.1255 (p-value positive kurtosis). Note that these cells are not visible unless selected.




All Test Cases for Computer Pass? X yes no


Name of File: STAT-18 – Window 7

Data of File: 9/1/17

Signature: ________________________________ Date: September 1, 2017

validation report for excel spreadsheet: stat-18 ... - skewness kurtosis normalit… · te taylor...

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