# t-test with Non Normal Data

M

#### mi06rasja

Hi

I have a question for you guys regarding paired t-test. I am currently working with measuring vibration on a machine at different rpm. What I do is that I measure the vibration at different rpm and by that I get a curve which tells me how the machine vibrates. I can also see any natural frequency?s with this approach.

However, we have now made some plausible improvement but it?s quite hard to see them using the approach above. So in order to make correct assumption I am trying to make a paired t-test with 95% significance level. But when I am reading about the t-test in my textbook it says that both data need to be normally distributed. If both data are non normal it says that i should use Wilcoxon test instead. The before and after data are however not normally distributed but the differences between them are normally distributed. So my question to you are if I should use a one sample t-test of the differences or if i should use a Wilcoxon test instead?

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
From what you have said so far, I don't think you have a paired t-test. I would be working on more of a scatter plot and regression analysis of vibration versus rpm. I would assume it would be a non-linear regression since you state you have some natural harmonics going on.

Another option is testing at a few critical RPM's and doing ANOVA to see if the various RPM ranges give the same or different amount of vibration.

M

#### mi06rasja

Hi

What can understand from my textbook is that the paired t-test test only checks for differences i.e. before and after. The data that i collect looks like this:

Rpm vibration 1 Vibration 2 diff
100 0,01 0,02 -0,01
200 0,02 0,02 0
300 0,09 0,012 -0,03
.... .... ..... ....

Correct me if i am wrong but even due I have som natural harmonic I only look upon the differences and then it wouldn?t matter if variance1 (in the exemple above) is non normal as long as the diff column is. And then I will be able to make an t-test. Or am I wrong?

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
paired testing required that unit A be tested before and after and unit B be tested before and after, and so on.
then the difference you are testing is differences of the before and after of each unit.

Staff member
Hello there!

What exactly are you trying to accomplish?

Thanks for providing an example of the data. Below:
Rpm vibration 1 Vibration 2 diff
100 0,01 0,02 -0,01
200 0,02 0,02 0
300 0,09 0,012 -0,03

So are you wanting to compare the RPM with the difference of the vibration? So for each RPM, you will calculate the difference between two vibration readings? How many RPM readings will you be taking at each session? Will you be comparing the RPM/ vibration readings for machine 1 to machine 2?

Will you be taking RPM readings each day?

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Hi

Rpm vibration 1 Vibration 2 diff
100 0,01 0,02 -0,01
200 0,02 0,02 0
300 0,09 0,012 -0,03
.... .... ..... ....
Could you please describe what vibration 1 and vibration 2 are? It seems to be you would have a set of vibration readings at 100 RPM, another set at 200 RPM, etc. These would not be differences.

M

#### mi06rasja

Ok I see that I havent been clear in my last statement. What I do is that I only test one specific machine. I start by measuring the amount of vibration at 350rpm then I increase the speed and measure 375, 400, 425, ..., 1200rpm. I then have a total of 34 measurements i.e the subgroup containes 34 samples. The machine is then reinforced in order to vibrate less. I then make the same measurements on the new reinforced machine and calculate the difference.

When analysing the sample data I see that both subgroups when looking at them individually are non normal but their differences are normally distributed. Is it ok to use a one sample t-test on the difference or should I use some other test like for exempel a wilcoxon test as the subgroups are non normal?

Sorry for not beeing clear before, hope the text above explaines my problem better.

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Oh, I see!

Seems like the paired t-test should then work.

However - from an engineering perspective (and also coming from submarine duty where we had to worry a lot about noise) - it seems like a more heavy bracing on the machinery would build up internal stresses and cause failure. I'd be more inclined to search for whatever is unbalanced and try to balance it, rather than trying to force the casing to contain the vibration.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
as Steve pointed out a paired t-test will work. if all 'braced' values are less than the un-braced values at each rpm, there is no doubt* that 'bracing' reduced the vibration for that unit. the paired t test will provide statistical significance if the values for the braced unit aren't all less than the unbraced unit. (this is possible if the bracing works at lower rpms but not at higher rpms or if the vibration variation at each rpm is relatively the same magnitude as the bracing effect.) In any case you should:
- plot your data (you can use a scatter diagram with a 45 degree line or a simple plot with the rpms on the x axis and the before and after values indicated with a different marker)
- test more than one unit to ensure that the bracing is adequate for most units.

*think of flipping a coin that many times and getting heads each time

with the statistical analysis taken care of, I echo Steve's other comment. Vibration is a result off a mehahnical weakness and is an 'energy loss'. bracing a vibrating unit does not stop the extra energy that is being input into the system. it merely redirects it somewhere else in the system. You really should understand the reliability risk of the bracing and get to the causal mechanism of the vibration...

Last edited:
M

#### mi06rasja

Hi

So it is ok to use a t-test aslong as the differences are normal.

Test of Means or Medians for Non Normal Populations? Using Minitab Software 6
Non-Normal Data F test and T test Capability, Accuracy and Stability - Processes, Machines, etc. 19
S Which Normality Test more acceptable to FDA; Also, Non-Normal Threshold? Qualification and Validation (including 21 CFR Part 11) 5
N Analysis of non-normal stratified data for cpk/ppk? Rupture test Capability, Accuracy and Stability - Processes, Machines, etc. 6
J Is a t-test used in non-normal data analysis? Six Sigma 7
Non parametric test for semi-quantitative data. Statistical Analysis Tools, Techniques and SPC 5
Single use non-sterile syringe used in the oral cavity - Laboratory test advice US Food and Drug Administration (FDA) 7
Class 2 medical device - Process Validation - Test sterile or non-sterile units? Qualification and Validation (including 21 CFR Part 11) 4
A "good" non-parametric test summary? Statistical Analysis Tools, Techniques and SPC 0
C Biocompatibility Test for a Non Contact Medical Device US Food and Drug Administration (FDA) 11
S Which non Salmonella organisms show positive in Wellcolex? Test kit ? US Food and Drug Administration (FDA) 1
E How does Non-Linear UUT affect TAR (Test Accuracy Ratio) Calculation? Measurement Uncertainty (MU) 3
N ISO 17025 clause 5.8.3 Records of Non-Conforming Test Items ISO 17025 related Discussions 3
D Calibration & Test Laboratory Non-Conformance Procedure Example wanted General Measurement Device and Calibration Topics 3
S Use of Non-Medically Test Hardware in Medical Environment IEC 60601 - Medical Electrical Equipment Safety Standards Series 15
R 5% to 95% Non-Condensing Humidity Storage Test Conditions and Failure Modes APQP and PPAP 2
J Non-compliance by test house: What to do? Various Other Specifications, Standards, and related Requirements 3
S Looking for A Non-Destructive Crimp Test method to replace Pull Test Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
Part Tolerance and TAR (Test Accuracy Ratio) - Non-Fixed Gaging General Measurement Device and Calibration Topics 2
R MSA gage R&R (GR&R) for Destructive Test (Non-Replicable Data) Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
EN 10247 Laboratory that can perform the non-metallic inclusions test on steel Various Other Specifications, Standards, and related Requirements 2
I Non-sterile device - Rapid Test Kits - ISO 14644 Clean Room required? ISO 13485:2016 - Medical Device Quality Management Systems 12
K Using an "obsolete" test method - TS 16949 Audit Non-Conformance General Measurement Device and Calibration Topics 13
Variations between ASTM A29 Standard for steel bars and Mill test certificates specs Manufacturing and Related Processes 1
Tip test 10° -> 5° IEC 60601 - Medical Electrical Equipment Safety Standards Series 1
Sponsor name presented in the test report EU Medical Device Regulations 4
Packing Validation & Accelerated Aging Test ISO 13485:2016 - Medical Device Quality Management Systems 2
OEM full range calibrations vs Validation special test points Medical Device and FDA Regulations and Standards News 0
IEC 60601 - 8.8.3 Dielectric Strength test. 4kv being applied to the ground conductor?! IEC 60601 - Medical Electrical Equipment Safety Standards Series 2
Shelf Life Test for IFU and Implant Card Other Medical Device Related Standards 1
Mechanical Test Under FDA Freedom of Information Act Medical Device and FDA Regulations and Standards News 5
Critical characteristic on manufacturing operations test procedure Inspection, Prints (Drawings), Testing, Sampling and Related Topics 0
IEC 60601-1 Clause 15.3.2, Push test IEC 60601 - Medical Electrical Equipment Safety Standards Series 0
Knee Implant (Femoral -Cobalt chrome)-Sub chronic toxicity test (ISO 10993-11)choice of root Medical Device and FDA Regulations and Standards News 2
Defining a lower ESD test level in IEC 60601 safety test IEC 60601 - Medical Electrical Equipment Safety Standards Series 5
Is there a need for clinical test of Class IIa products (for MDR)? EU Medical Device Regulations 2
Is calibration of test weight required General Measurement Device and Calibration Topics 4
Disaster Recovery Test IT (Information Technology) Service Management 3
How much does a complete biocompatibility test package cost? Other ISO and International Standards and European Regulations 1
Is it normal / sufficient to have only the IEC 60601-1-2 test report without indicating IEC 60601-1? IEC 60601 - Medical Electrical Equipment Safety Standards Series 2
Is Op Amp Common-Mode Rejection Ratio (CMRR) test applicable to battery operated devices? Other Medical Device Related Standards 0
When to perform accelerated aging studies and transport test(OQ or PQ) Qualification and Validation (including 21 CFR Part 11) 4
Does *anyone* know a lab that will test to EN 455-4 Medical Gloves shelf life determination? EU Medical Device Regulations 1
Test requirements for marketing in US when RATED values are not of US IEC 60601 - Medical Electrical Equipment Safety Standards Series 5
Secondary Circuits, Voltage Test and Clearance/Creepage IEC 60601 - Medical Electrical Equipment Safety Standards Series 0
Fogging test as per DIN 75201(50ug/g ) VDA Standards - Germany's Automotive Standards 3
HV Test of HF Surgical Unit IEC 60601 - Medical Electrical Equipment Safety Standards Series 1
IEC 60601-1 - 11.1.3 e) Test criteria - Temperature Measurements IEC 60601 - Medical Electrical Equipment Safety Standards Series 2
60950-1 resistance to abnormal heat test Various Other Specifications, Standards, and related Requirements 0
User evaluation for self monitoring blood glucose test systems US Food and Drug Administration (FDA) 4