Deg. of Freedom Q and Red. Chi^2

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SUMMARY

The discussion centers on determining degrees of freedom (df) for a dataset with 40 observations, divided into 4 sets of 10, each measured at varying temperatures and magnetic fields. The user initially speculates that df = 1 but seeks clarification on this assumption. Additionally, the reduced chi-squared (r-chi^2) value, calculated as chi^2 divided by df, is discussed, with the user inquiring about acceptable r-chi^2 thresholds for comparing experimental data to theoretical models in physics. The conversation emphasizes the importance of correctly defining the null hypothesis, specifically questioning whether sigma(T,B) should be equated to zero.

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FortranMan
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I'm having trouble determining with confidence the deg.s of freedom (df) of a data set I'm dealing with.

I'm dealing with a data set of around 40 observations. 4 sets of 10 observations measure at different temperatures from zero to T (of some interval delta), each set representing a different magnetic field B, giving as an output a value sigma, such that theoretically it should be described by a function sigma(T,B) (the null hypothesis). Since these observations are all distinct, I am guessing the df = 1, right?

Also, I am aware the reduced chi^2 (r-chi^2) value is (chi^2)/df, and that a r-chi^2 value >> 1 or << 1 is bad. What r-chi^2 value is considered a "good" value when comparing experimental data to theoretical models (specifically in phyiscs)? Is there a specific academic source that confirms or supports this value?
 
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I'm having trouble determining with confidence the deg.s of freedom (df) of a data set I'm dealing with.
What is the test you are doing? What are the inputs to the test statistic?

A hypothesis is a mathematical statement, so "sigma(T,B)" cannot be the null hypothesis. Did you mean sigma(T,B) = 0?
 
EnumaElish said:
What is the test you are doing? What are the inputs to the test statistic?

Field variation in superconductors verses temperature and field. I am comparing a graph of that data to a theoretical graph which would hopefully describe the data (satisfying the null hypothesis in that there is no great difference between the data and the model).

A hypothesis is a mathematical statement, so "sigma(T,B)" cannot be the null hypothesis. Did you mean sigma(T,B) = 0?

sigma(T,B) is the function that generates the theoretical graph.
 

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