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Finding Uncertainty in a coefficient with a Chi Squared Test 
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#1
Sep810, 05:41 AM

P: 2

Hello,
I have done a chi squared test on the measurements from a neutron flux experiment to get the best parameters for a function of the form Ysim=Acos(B*X). I used Solver in Excel to find the minimum parameters. The test takes the form chi^2 / dof = SUM(YsimYi)^2/(sigma i)^2 Where Yi are the measured values of the flux at various heights and (sigma i) is the uncertainty in flux i. What I want to do is to find the uncertainty in the parameter B. I have been told that if I shift the parameter B until the minimum value of chi^2 is altered to get chi^2 + 1 then the difference between the original value for B and the new value for B can be used to get the uncertainty in B. Does this make any kind of mathematical sense? I've found hints that this is equivalent to garbageing chi^2 by one standard deviation but I have not found any hard evidence of this. Has anyone seen this method referenced anywhere? 


#2
Sep910, 02:26 AM

P: 2,499

I can't speak to your application but the standard deviation "sd" (as a measure of uncertainty) is calculated from the sampling distribution and employed in the calculation of the chi square statistic: [tex]\chi^{2}= [n1]sd^{2}]/\sigma^{2}[/tex] where [tex]\sigma^{2}[/tex] is the population variance, n is the sample size. Generally the population variance is not known and the estimate from the sampling distribution is used. So this reduces to [tex]\chi^{2}=(OE)^{2}/{E}[/tex] for each degree of freedom with O as the observed value and E as the expected value. 


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