Standard Deviation

(ii) Now is not quite correct because if we determine the theoretical parameters to minimize then implicitly are also random variables that are functions of .

• It is not too hard to show that in this case, one should just replace N by N-n (number of degrees of freedom) in .

• In any case, is very important because it allows an easy criterion for the goodness of fit.

• Thus, if value of is many (say >2) standard deviations away from its mean, then the theoretical form is in doubt.

• The usual maximum likelihood method does not have this advantage:

• Remember, L was unnormalized and so value had no significance for the goodness of fit. This is quite a difficult problem.