Variance of experimental data, compared to Theory

In summary, the user is looking for a way to compare experimental and theoretical data to determine if it obeys Benford's Law. They are currently using a computer program to calculate the ratio of each reading with the theoretical result and the standard deviation of these ratios. They are also comparing each ratio with the mean to see if it falls within one standard deviation. They are seeking advice on better approaches, particularly with a focus on confirming Benford's Law. A suggestion is made to use a Chi-Square test for goodness of fit, but the user is concerned about discrepancies in the expected and observed frequencies.
  • #1
saad87
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I'm looking for a way to compare experimental and theoretical data and determining if it obeys a certain law.

In particular, I'm writing a computer program that does this and at the moment what I'm doing is, I'm calculating the ratio of each reading with the theoretical result and calculating the standard deviation of the various resultant ratios.

I compare each ratio with the mean to see if its within one standard deviation. Are there any better approached than this? I'm not really a mathematician, and am more of a programmer so any help would be much appreciated.
 
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  • #2
saad87 said:
I'm looking for a way to compare experimental and theoretical data and determining if it obeys a certain law.

Welcome to the world of statistics!

Some more information about the problem is needed. In particular, are you looking to test a formula to see how accurate it is (e.g. whether the errors are "acceptable"), or are you looking to confirm is a sample of random values has a specific distribution?
 
  • #3
bpet said:
Welcome to the world of statistics!

Some more information about the problem is needed. In particular, are you looking to test a formula to see how accurate it is (e.g. whether the errors are "acceptable"), or are you looking to confirm is a sample of random values has a specific distribution?

Basically I'm looking to confirm Benford's law in various files the user wishes to open.
 
  • #4
If you are looking to confirm Benford's Law, then you have the expected distribution of numbers starting with 1,2,3,...,9, and you have the actual distribution given by your data.

I think a Chi-Square test for goodness of fit would be good here.
 
  • #5
I just tried the Chi-square test, but the various online calculators basically tell me the total of my Observed and Expected frequences isn't the same. Is this because this test will fail if the observed freq. are too low than expected?

Thanks for all the help.
 
  • #6
If your total expected does not equal your total observed, you have made some mistake in setting things up.

If you have [tex]N[/tex] (observed) numbers in total and the fraction predicted by Benford's Law to start with i is [tex]f_i[/tex], then the number expected to start with i is [tex]e_i = f_i \cdot N[/tex]. Since the [tex]f_i[/tex]'s sum to 1, the [tex]e_i[/tex]'s sum to [tex]N[/tex].
 

1. What is the definition of variance in relation to experimental data and theory?

Variance is a statistical measure of the spread or variability of a set of data points. In the context of experimental data compared to theory, variance refers to the differences between the actual values obtained from an experiment and the expected values predicted by a theoretical model.

2. Why is it important to compare the variance of experimental data to theory?

Comparing the variance of experimental data to theory allows scientists to assess the accuracy and validity of their theoretical models. If the experimental data and theory have a low variance, it suggests that the theory is a good representation of the real-world phenomenon. On the other hand, a high variance indicates that the theoretical model may need to be refined or revised.

3. How is the variance of experimental data calculated?

The variance of experimental data is calculated by taking the average of the squared differences between each data point and the mean of the data set. This value is then compared to the expected values from the theoretical model to determine the degree of variance.

4. What factors can contribute to a large variance between experimental data and theory?

There can be several factors that contribute to a large variance between experimental data and theory. These can include errors in the experimental setup, limitations of the theoretical model, or unexpected external factors that influence the results. It is important for scientists to carefully analyze and control these factors in order to minimize variance and improve the accuracy of their results.

5. How can scientists use the variance of experimental data to improve their theories?

By comparing the variance of experimental data to theory, scientists can identify areas of their theoretical models that need to be refined or revised. This can lead to a better understanding of the phenomenon being studied and improve the predictive power of the theory. Additionally, scientists can use the variance data to identify trends and patterns that may have been overlooked in the initial development of the theory.

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