Deg. of Freedom Q and Red. Chi^2

[FortranMan]

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?

 

[EnumaElish]

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?

 

[FortranMan]

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.