Experimental Data - Error in slope

Click For Summary

Discussion Overview

The discussion revolves around the methodology for calculating the average modulus of elasticity from multiple tensile test specimens, specifically focusing on how to combine the errors associated with each slope derived from linear regression analyses of the data. The scope includes experimental data analysis and statistical methods for error propagation.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant describes conducting tensile tests on five specimens and seeks guidance on averaging the errors associated with the slopes obtained from linear regression.
  • Another participant suggests using a weighted average for combining the errors.
  • A different participant questions whether this method of combining uncertainties is commonly accepted in scientific experiments.
  • One reply proposes that while a weighted average could be used, a multilevel model might be more appropriate if the slopes are interrelated.
  • Another participant agrees that combining uncertainties is typical but cautions that if the specimens are comparable, the errors should not differ significantly, implying that judgment may be necessary in the averaging process.
  • Concerns are raised about potential outliers due to defects or variations in specimen composition, suggesting that some data might need to be disregarded in the averaging process.

Areas of Agreement / Disagreement

Participants express differing views on the best method for averaging errors, with some advocating for weighted averages and others suggesting a more nuanced approach that considers the relationship between the specimens. The discussion remains unresolved regarding the optimal method for combining errors.

Contextual Notes

Participants note potential limitations in the assumptions about the specimens' comparability and the influence of outliers on the error calculations, indicating that these factors could affect the validity of the averaging method chosen.

raniero
Messages
39
Reaction score
0
I have conducted a tensile test on five specimens. I intend to do a linear regression for every set of data and get a value for the slope (modulus of elasticity) and its error by finding the standard deviation (using LINEST function on excel) of the slope.

I will now end up with 5 slope values and 5 errors. I will then find the average of 5 slopes, but, how can I find the 'average' of the 5 errors to finally obtain one value for the modulus of elasticity and one error?

Thanks in advance
 
Physics news on Phys.org
BvU said:
Google weighted average. For the error you have this

Thanks for your reply. Is this method to combine uncertainties typically used in science experiments ?
 
You could do some kind of weighted average, but if you think the slopes are related in such a way that the ""average slope" makes sense, then this really calls for some kind of multilevel model. I recommend looking up (or finding someone in your department familiar with) mixed-effect model.
 
raniero said:
Thanks for your reply. Is this method to combine uncertainties typically used in science experiments ?
Yes. But Number9 has a good point. If your experiments are comparable and your specimens are unsuspect (*), there is no good reason to assume the errors should come out significantly different. Some judgement comes in. Mechanically following the algorithms may not be the best way to go (*) suppose one test strip has a mechanical defect or a slightly different composition -- that would produce an outlier and you simple want to ignore that and average the others - maybe even without weighting.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
6K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 11 ·
Replies
11
Views
5K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 30 ·
2
Replies
30
Views
5K