What should I choose as the error on x? (Curve Fitting Matlab)

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SUMMARY

The discussion focuses on determining the appropriate error measurement for angle values derived from X-Ray diffraction data analyzed using MATLAB's curve fitting tool. The user employed Gaussian fitting to identify peak positions but is uncertain whether to use 95% confidence bounds, standard deviation, or full width at half maximum (FWHM) as the error metric. Suggestions include improving data resolution to enhance fit quality, which may alleviate issues with poorly shaped fits. Clear justification for the chosen error measurement is essential for accurate analysis.

PREREQUISITES
  • Understanding of Gaussian curve fitting in MATLAB
  • Familiarity with X-Ray diffraction principles
  • Knowledge of statistical error measurements (confidence bounds, standard deviation, FWHM)
  • Experience with data resolution and its impact on fitting quality
NEXT STEPS
  • Research how to implement Gaussian fitting in MATLAB using the Curve Fitting Toolbox
  • Learn about calculating and interpreting 95% confidence intervals in MATLAB
  • Explore the significance of FWHM in peak analysis and its calculation methods
  • Investigate techniques for improving data resolution in experimental setups
USEFUL FOR

Researchers and students in experimental physics, data analysts working with X-Ray diffraction, and anyone utilizing MATLAB for curve fitting and statistical analysis.

CuppaMuons
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Homework Statement


So I've done an experiment by scanning over a range of angle and measuring the intensity of X-Rays. There are peaks where I have X-Ray diffraction occurring and in order to do analysis I need to identify the values of angle and an error (as in the plus/minus) on this value.

The Attempt at a Solution


The Peaks are very much like a gaussian so I used the curve fitting tool on MATLAB to fit a gaussian to the data and use the value of b (position of the center of the peak) as my value for angle.

An example fit can be seen here: http://imgur.com/0rm2TeB

Now my problem is what to choose for an error?

The fit returns something called 95% confidence bounds so I tried taking the difference between them and the actual value as the error but it seems a little small for some of the fits which are somewhat poorly shaped.

My only other thoughts would be the Standard Deviation or the FWHM but I'm really not sure what I should use, nor how to justify what I choose.
Any Ideas?
 
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just a note... looking at your example, you need more resolution for your data. Would it be possible for you to take your test again?

It might get rid of the some of the "poorly shaped fits." its very possible that the fits are poorly shaped due to the fact that you don't have proper data.
 
I'm also confused about what exactly you are trying to measure, can you clarify?
 

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