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There is a flaw in Step 2. The formula should read, $$(\frac{\Delta C}{C}) = (\frac{\Delta m}{m}) + 2(\frac{\Delta d}{d}) + (\frac{\Delta h}{h}) $$ I still don't see how you arrived at your formula. It is completely wrong. Though it looks close to the formula for variance. Maybe that's where you got it confused. Conceptually, for $f(x,y,z,...)$ ...


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The $\chi^2$ statistic is independent of the number of degrees of freedom. But converting that statistic to some type of $p$-value does depend on the degrees of freedom. That is, you calculate $\chi^2$, then with that number and the degrees of freedom you look it up the $p$-value in a $\chi^2$ table. As for the "corrected" version of this test, you may find ...


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As far as I can see this is just going to be the uncertainty of the mean of your dataset. To determine this you must know the uncertainty in the individual data points. For the simple case where you can consider the uncertainty in the data to be constant for all points then the the uncertainty of the mean is $$ u_c=\frac{u}{\sqrt n}$$ for the case where ...



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