# P-value is 0.05 - Normal or non-normal data?

R

#### RMedrano

Someone brought a capability study to me this morning, after running it through minitab...the distribution looked slightly bimodal.. I ran a normality test on the data and it kicked out a p-value of 0.050 i was always told tha a p > 0.05 was normal

does that mean 0.05 is non-normal?

Elsmar Forum Sponsor

#### Miner

##### Forum Moderator
Staff member
Admin
RMedrano said:
Someone brought a capability study to me this morning, after running it through minitab...the distribution looked slightly bimodal.. I ran a normality test on the data and it kicked out a p-value of 0.050 i was always told tha a p > 0.05 was normal

does that mean 0.05 is non-normal?
You are correct. A p-value > 0.05 means the null hypothesis (that the distribution is normal) is accepted. A p-value < 0.05 means that the null hypothesis is rejected and the distribution is not normal.

From your question, do you have a p-value of exactly 0.05?

At this point, it is time to be practical. Trust your eyes. If the distribution looks bimodal, look for possible reasons why it could be bimodal. Do the products come from more than one process stream? Plot the data on a run chart in time sequence. Is there a process shift? Does your gage have inadequate resolution? Did more than one person take the measurements? Were the measurements taken on different gages, or at different times?

If the answers to all of these questions are no, try repeating the study using a larger sample size. This should force the p-value higher or lower than 0.05 and make the histogram more obvious.

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Which test of normality did you run? I prefer the Wilks-Shapiro method for larger sample sizes (greater than 50), and the Kolmogorov-Smirnoff Test for smaller sample sizes.

R

#### RMedrano

this was coming from the minitab graphical summary function which uses the anderson darling method i believe.

I concluded after close examination of the data that it appeared to be bimodal.

after speaking with the technician who gathered the data, found that he took a total of 30 parts, but took one part off of each fixture of the machine in question. In that process we track each fixture with a seperate spc chart, because each can be adjusted seperatly... with 14 fixtures it was much more than bimodal is there a word for having 14 different modes? LOL

thanks for the help guys. Im just starting to learn this stuff, you have been a great help.

#### Tim Folkerts

Super Moderator
And a distribution that only sort of has a hump in the middle is named after a person who sort of had a hump...

The Quasimodal distribution

Sorry! I just couldn't help myself ....

E

#### Ehsan Heidari

You are correct. A p-value > 0.05 means the null hypothesis (that the distribution is normal) is accepted. A p-value < 0.05 means that the null hypothesis is rejected and the distribution is not normal.

From your question, do you have a p-value of exactly 0.05?

At this point, it is time to be practical. Trust your eyes. If the distribution looks bimodal, look for possible reasons why it could be bimodal. Do the products come from more than one process stream? Plot the data on a run chart in time sequence. Is there a process shift? Does your gage have inadequate resolution? Did more than one person take the measurements? Were the measurements taken on different gages, or at different times?

If the answers to all of these questions are no, try repeating the study using a larger sample size. This should force the p-value higher or lower than 0.05 and make the histogram more obvious.
I have been confused!!
I have 125 datas in 25 groups (subgroup size=5), so i did normality test in minitab but I recived so diffrent answer for same data:
with Anderson-Darling :
AD=30.47
P-value<0.005 so it`s nonnormal

with Ryan-Joiner :
RJ=1
P-value>0.1 so it`s normal

with Koimogorv-Smirnov:
KS=0.084
P-value=0.037 so it`s nonnormal

so, which models I should use?

Last edited by a moderator:

#### bobdoering

##### Stop X-bar/R Madness!!
Trusted Information Resource
I really don't like doing the analysis in this manner. My preference is to run curve fitting and check to see which curve fits best. If it is the normal curve, then fine.

But, here is the thing: Minitab is a tool to aid understanding, not to provide understanding. What is the process, and what would one expect the distribution to be? Often the time-ordered run chart has as much to say about the distribution than just jumping to normality checking. Also, can you prepare the total variance equation? (click link to see example) What are the expected distributions of each of the contributors of variation? Assuming a process has one net variation is simultaneously assuming that all of the variation in the total variation equation are insignificant except one big factor. Sometimes that is true - sometimes the biggest factor is measurement error, which tends to be normal, and does a great job of masking the true process variation distribution.

So, the first question is: why do you need to know if the distribution is normal? Is it to determine capability? Then you probably jumped ahead a few steps.
-First step is figure out your total variance equation.
-Then, ensure all of the factors that should be held statistically insignificant are - measurement error, gage error, material variation, etc. - so that the resulting variation is the one you are trying to study. If there are more than one factor that are significant, you can get more than one "modes". Is that "not capable" or "not in control"? Of course not - but simpler statistical thinkers may have you thinking that is the case. Fact is, what are the odds that you will only have one significant factor looking at the total variance equation? Pretty slim.
-The next step is to prepare a run chart to see if there was any significant trends, or if the data was truly random and discrete (what you want for a normal distribution).
-Finally, run the data through a distribution fit analysis, and find the best fit. If, as an example, the best fit is p=.6 and the normal curve fit p=.4, you can likely use the normal statistics as an estimate of the curve behavior. But, the best fit is p=.6 and the normal curve fit p=.05, then you need to look at the correct distribution's statistics or...as a last choice, perform transformation.

Last edited:

#### Miner

##### Forum Moderator
Staff member
Admin
I have been confused!!
I have 125 datas in 25 groups (subgroup size=5), so i did normality test in minitab but I recived so diffrent answer for same data:
with Anderson-Darling :
AD=30.47
P-value<0.005 so it`s nonnormal

with Ryan-Joiner :
RJ=1
P-value>0.1 so it`s normal

with Koimogorv-Smirnov:
KS=0.084
P-value=0.037 so it`s nonnormal

so, which models I should use?
Could you attach your data?

Anderson-Darling is a modification of the Komolgorov-Smirnov test that makes it more sensitive to deviations in the tails of the distribution.

I have not used the Ryan-Joiner test, but know that it is correlation-based and is supposed to be of similar sensitivity as the A-D test.

I would have to see the data to be certain, but it would have to be something in the tail of the distribution that does not strongly impact correlation.

E

#### Ehsan Heidari

Normality Test with Minitab

Hello Minner

I attached my data.
If you have any experience about Runs Test(in mintab) please help me because of I did RUNS TEST in the same data and the P-value=0.97.

#### Attachments

• 118 KB Views: 350
Last edited by a moderator:
Thread starter Similar threads Forum Replies Date
KAPPA index Reference Value for Visual inspection IATF 16949 - Automotive Quality Systems Standard 1
Value of an "inspected by" sticker on finished products Manufacturing and Related Processes 10
Can someone help me explain P-Value with a simple word please? Capability, Accuracy and Stability - Processes, Machines, etc. 11
Determining a tolerance value for Measuring devices in-house inspection General Measurement Device and Calibration Topics 12
Improving low p-value Statistical Analysis Tools, Techniques and SPC 13
Registrars with VAR (Value Added Reseller) experience Registrars and Notified Bodies 8
Best approach to get a real value as average? Statistical Analysis Tools, Techniques and SPC 6
Missing value of Uncertainty B Measurement Uncertainty (MU) 10
Calibration certificate content - Average Value and True Value ISO 17025 related Discussions 6
In BAC5300 we have machining mismatch allowed is 3tau, what is the value of tau? Document Control Systems, Procedures, Forms and Templates 1
Change value of target during a batch Capability, Accuracy and Stability - Processes, Machines, etc. 0
Acceptance p-value for linearity and bias analysis in minitab results Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 0
Torque Value for Different types of Fasteners (Socket Head, Button Head, CSK) Manufacturing and Related Processes 2
IATF 16949 - 8.5.6.1.1 Providing a list of process controls: Does this requirement add value to QMS? IATF 16949 - Automotive Quality Systems Standard 4
Cycle times, value stream mapping, inventory, average values? Lean in Manufacturing and Service Industries 1
What are the criteria for setting a target KPI value against a quality objective? Benchmarking 7
S Adding Value prior to signing EASA Form 1 EASA and JAA Aviation Standards and Requirements 5
M Creating a Plant Level Value Stream Map Process Maps, Process Mapping and Turtle Diagrams 1
A IMDS - Changing the Locked Weight Value RoHS, REACH, ELV, IMDS and Restricted Substances 1
T Value Chain Map for Food Services Industry Service Industry Specific Topics 1
O P-Value less than 0.05. but everything else in control Statistical Analysis Tools, Techniques and SPC 19
P x I = Value interpretation for residual risk? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 1
O CPK with a P value less than 0.005 Manufacturing and Related Processes 8
What degrees of freedom means in uncertainty budget and how do I set the value Measurement Uncertainty (MU) 2
Q Really do they add value (Vision, Mission, Values)? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 1
What is the exact Temperature Coefficient Value to be set on a Conductivity Meter? General Measurement Device and Calibration Topics 2
M Value Stream Mapping Calculations Process Maps, Process Mapping and Turtle Diagrams 5
L How to interpret the average R bar Value shown in the R Chart Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
Non Value Added Corrective Actions IATF 16949 - Automotive Quality Systems Standard 15
R How To Calculate & Print CDF and Lower Bound CDF value for some t(time) with Minitab? Using Minitab Software 1
P Purpose of calculating Uncertainty value in calibration study Measurement Uncertainty (MU) 5
J Agenda of Value Stream Mapping workshop required Quality Tools, Improvement and Analysis 1
What is the value of documenting in-process rework for easily-detectable issues? Quality Manager and Management Related Issues 4
VSM - Value Stream Mapping (catheter manufacturing unit) Customer Complaints 10
W Quality for value adding or certification? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 23
T Cpk for 0 as Ideal Value Statistical Analysis Tools, Techniques and SPC 1
Internal Audit Value - What is the point of conducting internal audits to a checklist Internal Auditing 40
L 5 minutes only for this Survey on the Value of PDCA and Your EMS Miscellaneous Environmental Standards and EMS Related Discussions 1
M How calculate P value for Linearity and Bias using Excel Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
J F and P-value in L9 Taguchi Design Using Minitab Software 22
S Value of Ppk or Cpk when targeting thinner material Statistical Analysis Tools, Techniques and SPC 4
B How to validate Microsoft Excel Spreadsheet Calculations for the Cpk value Capability, Accuracy and Stability - Processes, Machines, etc. 9
Analysis of 'Value Added' System & Process Steps - Inspection Pharmaceuticals (21 CFR Part 210, 21 CFR Part 211 and related Regulations) 2
P Which ISO 13485 clause(es) are applicable for Value Proposition Creation ISO 13485:2016 - Medical Device Quality Management Systems 1
R The Value and Effectiveness of In Process Inspection Quality Manager and Management Related Issues 17
D Value-Added Analysis - Staff (Employee) Satisfaction Quality Tools, Improvement and Analysis 11
T ISO Auditor Training - What online training is actually value added? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 13
M Specific Capability case - Target Value is same as the Lower Limit Capability, Accuracy and Stability - Processes, Machines, etc. 9
S GR&R for an "R" value instrument installed on my 10K Horizontal Tester Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 5
S Value Stream Mapping for a Product Family Lean in Manufacturing and Service Industries 5