If we want to know covariance from 2*2 Table, how many samples are needed at least.
Thanks a lot [EMAIL PROTECTED] (Donald Burrill) wrote in message news:<[EMAIL PROTECTED]>... > On 22 Aug 2003, Eric Bohlman wrote in part: > > > But mathematically, that's nonsensical; zero correlation implies a > > roughly circular pattern of points > > While a circular pattern implies zero correlation, the converse is not > true. A horizontal (or vertical) line also implies zero correlation. > So, for that matter, does the symmetrical center section of a parabola. > and any number of other patterns: think of all the patterns described > by a set of orthogonal polynomials. "Zero correlation" of itself does > not imply ANYthing about the pattern described by the bivariate space, > except that the sum of products of deviations from the means of the two > variables is zero -- which can happen in an infinite number of ways, > arising from an infinite number of possible patterns. > > > (I like Stephen Jay Gould's heuristic that correlation measures the > > "skinniness" of a scatterplot), > > Which is true enough for the usual rather amorphous scatterplot that > the term "scatterplot" conjures up in one's mind, AND where the > "skinniness" in question is tilted (NOT horizontal, NOT vertical). > > > and it's rather obvious that if you simply interchange axes, there's > > no difference between the two situations. > > Precisely. > > > I think this is a case where we're encountering what Sir Francis > > Bacon called an "idol," a prejudice of thought that distorts our > > view of reality. We want to believe that correlation is defined for > > any pair of random variables, but in fact it's meaningless if one of > > those RVs has all its density concentrated at a single point. We > > somehow expect that because we call it a random "variable" it has to > > *vary*, but the definition of a random variable is merely "a > > function whose domain is a probability space" and constants meet > > that definition. > > More than that, though: correlation is defined whether the variables in > question are random or not. > > ----------------------------------------------------------------------- > Donald F. Burrill [EMAIL PROTECTED] > 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 > > . > . > ================================================================= > 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/ . =================================================================
