# Finding Uncertainty in a coefficient with a Chi Squared Test

by neutrino45
Tags: coefficient, squared, test, uncertainty
The $$\chi^{2}$$ distribution has only one parameter: k, which is the number of degrees of freedom. The mean is simply k, the variance is 2k. The shifting of the parameter by one would correspond to adding or subtracting one degree of freedom.
$$\chi^{2}= [n-1]sd^{2}]/\sigma^{2}$$ where $$\sigma^{2}$$ 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 $$\chi^{2}=(O-E)^{2}/{E}$$ for each degree of freedom with O as the observed value and E as the expected value.