On 15 Mar 2004 19:58:03 -0800, [EMAIL PROTECTED] (Alexei) wrote: > > I have a very simple question related to the combination of two > results that can, in general, be correlated. > > It's natural to assume that combination C of two measurements A and B > must be within the interval between the values A and B. Is this always > true?
What is the definition of "combination"? It is certainly not true about the simplest combination, A+B . I don't think a version of a generalized mean of two numbers would be acceptable, if it popped up a value outside the interval. > On the other hand, two measurements A and B can be the values that are > higher than the true value T. Then if the process of combination > reduces the error or uncertainty of the measurement, the combined > value C will get more close to the true value T and even may get > outside the interval of the values between A and B. If you take the average of independent biased estimates, sharing the same bias, the precision of the estimate will improve. But *precision* is not *accuracy*. It will get no closer to T. (Increasing a sample size may reduce the bias of a biased estimator, such as, the variance estimated by dividing by N. But that was not the question.) You are mis-interpreting something; or you are reading something written badly; or your text is grossly wrong. This is a distinction between 'reliability' (where measures are reproducible) and 'validity' (where measures are right). > > So which statement is the correct one? > I would really appreciate any help on this problem. > Thank you. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html - I need a new job, after March 31. Openings? - . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
