Normal probability analysis
This is a way to check our assumption that the observations follow a normal distribution with known standard deviation.
If the true intensity of a reflection is J and we make an unbiased measurement with a standard error s and assuming a Gaussian distribution of errors, then:-
P(I|J,s) = (1/v2p) exp [-(I-J)2/2 s2]
Since we do not know J, the best estimate to compare to Ihl is <I>others the mean of the other observations (if necessary, considering only observations in the same class, eg I+ or I-, or observations from the same crystal). Then the deviation normalised by the estimated standard deviation is
d(observed) = c = (Ihl - <I>others)/v(s2(Ihl) + s2(<I>others))
d should follow a normal distribution with mean 0.0 and standard deviation 1.0
From a set of observations Ihl we can construct a list of observed normalised deviations d (or c)