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Deg. of Freedom Q and Red. Chi^2

  1. Feb 3, 2008 #1
    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?
  2. jcsd
  3. Feb 3, 2008 #2


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    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?
  4. Feb 3, 2008 #3
    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).

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