# Quantitative way to compare theoretical values to experimental values

• Whiteblooded
In summary, the conversation discusses the process of comparing different theoretical models for the cross-sectional shape of a sagging membrane. The main challenge is determining a reliable method for measuring the "goodness" of a model fit. Suggestions for this include using a chi-squared test and scaling the sum of squared deviations by the maximum sag or area averaged sag. The conversation also raises questions about the discrepancies between theoretical predictions and observations, as well as the existence of different models for the same problem.
Whiteblooded
I am looking at the cross-sectional shape of a sagging membrane. I have several theoretical models, neither of which fit perfectly. So rather than comparing values, I'm comparing shapes. One model fits fairly well, however I'm unsure of which quantity is correct to specify a 'goodness' of a model.

I'm thinking of some sort of sum of squared deviations (the quantity which least-squared fits minimises). The main problem with this is that the sum of squared deviations on its own will not really tell us about how good the fit is - I think I'll need to divide it by something else?..

You can scale either by the maximum sag, or by the area averaged sag. This will give you a much better shot at comparing the shapes. I would also recommend an area weighted square deviation, divided by the area (in case you are not using equal areas for the elements of surface). The big question is "why don't the predictions and observations match quantitatively." Another question would be "why would there be different theoretical model predictions to the same problem?"

## What is a quantitative way to compare theoretical values to experimental values?

A common method for comparing theoretical and experimental values is through statistical analysis, such as calculating the mean, standard deviation, and confidence intervals for each set of data.

## Why is it important to compare theoretical and experimental values?

Comparing theoretical and experimental values allows for the evaluation of a hypothesis or model's accuracy and validity. It can also help identify any discrepancies or errors in the experimental procedure.

## What does it mean if the theoretical and experimental values are similar?

If the theoretical and experimental values are similar, it suggests that the hypothesis or model used to calculate the theoretical values is accurate and applicable to the experimental data.

## What factors can affect the comparison of theoretical and experimental values?

The accuracy and precision of the experimental measurements, the assumptions made in the theoretical calculations, and any sources of error in the experimental procedure can all impact the comparison of theoretical and experimental values.

## How can the results of a comparison between theoretical and experimental values be used?

The results of this comparison can be used to support or reject a hypothesis, improve the accuracy of a model, or guide future research and experimentation in the field.

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