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t-test with Non Normal Data

M

mi06rasja

#1
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?
 
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Steve Prevette

Deming Disciple
Staff member
Super Moderator
#2
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

#3
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
#4
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.
 

BradM

Staff member
Admin
#5
Hello there! :bigwave:

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
#6
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

#7
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
#8
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
#9
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...
 
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