Quito Quito <[EMAIL PROTECTED]> wrote: >> Dear readers:
>> Suppose I have computed that the 95% confidence interval for the >> difference, (u1 - u2), of means from two populations is (-3.2, 5.1) >> which contains the value 0, can I say that u1 and u2 are equal to each >> other? If so, what is the confidence level I can have to say so? (later similar questions snipped) Simple answer: No. More complex answer: The definition of a confidence interval is (from The Cambridge Dictionay of Statistics, by B.S. Everitt) "A range of values, calculated from the sample observations, that are believed, with a particular probablity, to contain the true parameter value. A 95% CI, for example, implies that were the estimation process repeated again and again, then 95% of the calculated intervals would be expected to contain the true parameter value. Note that the stated probablity level refers to properties of the interval and not to the parameter itself, which is not considered a random variable....." Unless you get the entire population, you cannot say that the population means are equal. In any case, exact equality is rarely (if ever) of interest. Say, e.g. we do something silly and try to predict weight based on social security number (odd vs. even). If we got the weight and SSN of everyone in the USA, the two averages would not be identical (although they'd probably be close). Say the average weight of people with odd SSNs is 125.2939 pounds, and that for those with even SSNs is 125.2937 pounds. These are not equal. Unless we got a huge sample, however, the CI would include 0. Looking at it another way, a CI, no matter how calculated, does not allow you to accept the null hypothesis of no difference, it only allows you to fail to reject it (e.g. "Based on this study, we cannot conclude that there is a difference" rather than "Based on this study, we conclude that there is no difference" HTH 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) . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
