[EMAIL PROTECTED] (Robert J. MacG. Dawson) wrote in message news:<[EMAIL PROTECTED]>... > [...] > Suppose I show you a barrel that looks as if it would contain about a > million jellybeans, and you grab a handful (say, fifty) and you count > them and find that half are green. You'd be able to estimate that half > the jellybeans in the barrel are green, and you'd have some idea of how > good that estimate was - say between about 35% and 65% with about 95% > confidence. > > Now suppose I tell you - surprise - the barrel has a false bottom and > only contains 10,000 jellybeans, 1% of the number you'd assumed. Does it > seem reasonable that your estimate has just got a lot better? (People > making this mistake usually assume that a small population can be > estimated better, not worse.)
It *can* be estimated better: in this case the confidence interval is now only .99757 times as wide as it used to be. The mistake is to overstate the improvement. > Or suppose the barrel is connected to a huge underground warehouse > contianing a billion well-mixed jellybeans. Do you suddenly lose > confidence in your estimate? Yes, a little: the confidence interval is now 1.0000245 times as wide as it originally was. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
