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I am using the reduced chi-squared statistic to determine the goodness of fit. I run several simulations and determine that a parameter 'p' has a certain range of values that all give values between 0.9-1.1 for the reduced chi-squared. Visually all the fits are deemed acceptable. Is there are a way to estimate the error on the parameter p and is there any literature that deals with the acceptable chi-squared values?

Suggestions along the lines of MCMC are welcomed. Importantly, any frequentist approaches to this problem are also welcomed

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