Confidence intervals are not betworthy. Our mystery user is correct, although s/he is not expressing him/herself as clearly as s/he might, which is not to say I'll do any better.
A confidence interval is an interval generated by a process that has the property that the resulting interval will contain the parameter(s) of interest in the specified proportion of cases. Let X1, X2 be i.i.d. U(theta-1, theta+1), that is, uniform over (theta-1, theta +1). There is a 25% chance that both X1 and X2 will lie below theta. There is a 25% chance that both X1 and X2 will lie above theta. Therefore, there is a 50% chance that theta will lie between them. Then (Y1=min(x1,x2), Y2=max(x1,x2)) is a 50% confidence interval because it covers theta 50% of the time. However, when Y2-Y1 is greater than 1, it MUST contain theta, even though (Y1,Y2) is a 50% CI! . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
