Data analysis for theoretical vs experimental results

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Discussion Overview

The discussion revolves around methods of data analysis for comparing theoretical results, specifically the function v(x) = cos(x), with experimental data. Participants explore various analytical approaches and presentation techniques for visualizing the relationship between these data sets.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests calculating the average root mean square deviation between the theoretical values and the measured values as a potential analysis method.
  • Another participant emphasizes the importance of visual representation, recommending the use of graphs to display both theoretical and experimental data, ideally with indications of experimental precision.
  • A participant notes that their theoretical and measured data are closely aligned but finds the lab instruction on analysis to be vague.
  • It is proposed that the theoretical data should be represented as a solid line while the experimental data should be plotted as points, with the addition of error bars to illustrate uncertainty in the experimental measurements.
  • One participant mentions that if the theoretical curve intersects the error bars of the experimental data, it indicates an agreement between the two sets of data.

Areas of Agreement / Disagreement

Participants express various methods for data analysis and presentation, but there is no consensus on a singular approach. Multiple viewpoints on how to analyze and represent the data remain present.

Contextual Notes

The discussion highlights the ambiguity in the lab instructions regarding the analysis requirements, which may affect the participants' approaches to the data analysis.

TheBlueDot
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Hello,

My question is what types of data analysis can I perform on a set of theoretical and experimental results? For example, I have v(x) = cos(x) and I plot my observed data to v(x).

Thanks!
 
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It really depends upon what you need to know accurately . Typically one measure would be the average root mean sguare deviation of the predicted values cos(x) from the measured values v(x).
The first best thing to do is look at graph displaying both...preferably displaying expected experimental precision somehow. Then there are many paths to follow but your eyeball is a great tool and this is always my first step.
 
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Thank you for your response. My theoretical and measured data are very close. The lab instruction just asked for analysis which is kinda vague. :D
 
If you have experimental data and the theoretical formula, the best way to present it is draw the theoretical calculated data as a solid line and plot experimental data as points. It is good to include error bars on the experimental data. If the theoretical curve goes through the error bars, then there is an agreement.
 

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