What do you mean by 'combination'? Clearly, the mean of two values is between those two (unless they are equal), but other versions of combination are not (e.g, the sum never is).
If 'combination' = 'mean' then it is not necessarily true that the combination is closer to the true value than either of the values that make up the mean; you seem to be confusing error and bias. But even if the measurements are unbiased, with only two, it's easily possible for them to both be too low or too high. If each meansurement is TRUE + ERROR, and error is ~ N(0, sigmasq) then 1/4 of the time both will be low, 1/4 of the time both will be high, 1/2 the time one will be high and one low. In the last case, obviously, the combination is closer to the true value than either of the components; in the first two cases, it is not. HTH Peter Peter L. Flom, PhD Assistant Director, Statistics and Data Analysis Core Center for Drug Use and HIV Research National Development and Research Institutes 71 W. 23rd St www.peterflom.com New York, NY 10010 (212) 845-4485 (voice) (917) 438-0894 (fax) >>> [EMAIL PROTECTED] 3/15/2004 10:58:03 PM >>> Hi, 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? 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. So which statement is the correct one? I would really appreciate any help on this problem. Thank you. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
