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

In summary, the speaker conducted an experiment involving X-Ray diffraction and is now trying to analyze the data by identifying the angle values and an appropriate error. They used a curve fitting tool on MATLAB and are considering using the 95% confidence bounds, standard deviation, or full width at half maximum (FWHM) as the error value. However, they are unsure of which to choose and how to justify their choice. Another person suggests taking the test again to improve the data resolution. The speaker is also asked to clarify what they are trying to measure.
  • #1
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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  • #2
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.
 
  • #3
I'm also confused about what exactly you are trying to measure, can you clarify?
 

1. What is the purpose of choosing an error on x in curve fitting?

Choosing an error on x helps to quantify the uncertainty in the independent variable. This allows for a more accurate representation of the data and improves the reliability of the curve fitting results.

2. How do I determine the error on x for my data?

The error on x can be determined through a variety of methods, such as using experimental measurements or statistical analysis. It is important to consider the nature of your data and the specific needs of your study when choosing a method for determining the error on x.

3. Is there a specific formula for calculating the error on x?

There is no one-size-fits-all formula for calculating the error on x in curve fitting. The method for determining this error may vary depending on the type of data and the desired level of precision. It is important to consult with a statistician or refer to reliable sources for guidance on selecting an appropriate method for your specific data set.

4. Can I use the same error on x for all data points?

It is not recommended to use the same error on x for all data points. This is because the uncertainty in the independent variable may vary across the range of your data. It is best to consider the individual characteristics of each data point and determine the appropriate error on x for each one.

5. How does the error on x affect the curve fitting results?

The error on x can significantly impact the curve fitting results. Using an incorrect or insufficient error on x can lead to inaccurate and unreliable curve fitting outcomes. It is important to carefully consider and accurately determine the error on x in order to obtain meaningful and valid results.

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