On 24 Mar 2003 19:01:50 -0800, [EMAIL PROTECTED] (Gary) wrote: > SCENARIO: > --------- > If one measures a quantity x1 with an uncertainty u1 at the 95% > confidence level, and a quantity x2 with an uncertainty u2 at the 95% > confidence level.
Do you mean? - Given, mean X1 with standard error u1, and mean x2 with standard error u2. Or, you might have means, and the 95% CI of the man around each mean, based on stated N. Or, less likely, you might have the a set of measurements along with the 95% CI of the measures (not, "of their mean"). Or, the "variance" might be given along with some other statement. - Speaking in English, as we use it in statistics, we might say that we make a measurement "with error [or, accuracy] of +/- 0.05 inches [ for the 95% CI / as the Standard deviation / as the standard error of the resulting mean ]". - Does the precision describe a single measure, or a mean? - That matters as a factor of n in your eventual computations. > > QUESTION: > --------- > (a) How does one determine at the 95% confidence that x1 and x2 are > different? It is usually true, ultimately and philosophically, that x1 and x2 are "different", absolutely. No reference to 95% is needed when the philosophy is completely true. The usual question is whether x1 and x2 are different enough, that the difference is *unlikely* to owe to chance. We can conduct a "t-test" to see if the difference is zero; the p-level of the test shows how unlikely the numerical outcome was. Equivalently, we can construct a confidence interval for the difference, and note whether it overlaps zero. > (b) What is the correct definition of resolution? If English is your second language -- I can apologize that I don't follow what you are asking as (b). I can say that one of the tricky things in statistics is learning the terms well enough to state these things well. Some people memorize stereotyped statements in order to avoid mis-stating; unfortunately, sometimes the stereotyped statements are not entirely right. Google shows me that uncertainty and resolution are paired for 582 thousand hits. Neither term is a keyword in biostatistics, in English -- so you need to ask more specifically if you still want a definition. Hope this helps. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
