Very good, Donald. I appreciate the help dusting off the cobwebs... although... I'm not sure I ever did know what n before the sigma was.
Also enjoyed your comment, "no need for capital C's, it's not a title of nobility". "Donald Burrill" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > On Sat, 13 Mar 2004, John Gregory wrote: > > > In Pearson's Correlation Coefficient formula, the Greek symbol for Sum > > (backward E) has a small "n" preceeding it at half height. > > The mathematical symbol for "Sum" is the Greek letter sigma (a capital > sigma), corresponding to the capital S in the word Sum (which is why it > was chosen in the first place; the corresponding symbol for "Product" > in multiplication is a capital pi). If there is a lower-case "n" > preceding it, the value of "n" is to be multiplied by the sum, once the > sum has been obtained. > > The standard methods of indicating the range of summation, which is what > you described subsequently, are: > (1) when each individual value in the formula is indicated or implied > by a subscript (say "i"), a line of small type under the capital Sigma > reads "i = 1" and above the capital Sigma "n"; this would be read "Sum > <the following quantities> for i = 1 to n". This usage permits one to > indicate partial summations (e.g., from 7 to 31 instead of from 1 to n). > (2) when the particular quantities to be summed are obvious from the > context (e.g., for all the data in hand), the capital Sigma may be > unadorned, the implication being "for all the data" or "from 1 to n". > (3) sometimes, as shorthand for (1) above, a subscript "i" attached to > the Sigma. More commonly used when the items to be summed are indexed > in two dimensions (say "i" and "j") but the summing is to be carried out > only with respect to one of them. > > > I think it's to be read something to the effect "Sum the following and > > perform the other operations in sequence for each set of varible in > > the list you're working from; or in other words... row by row from the > > 1st to as many as there are (this "n")." > > Close. Depends on whether "the other operations in sequence" are > intended to be performed before summing or afterward. This is made > explicit by parentheses in the formula. In particular, in one of the > numerous formulas for the Pearson correlation coefficient (no need for > capital C's, it's not a title of nobility) you may have an expression > like > SUM((X_i - Xbar)(Y_i - Ybar)) > (using "_i" for the subscript "i", and "Xbar" for the sample mean of X) > in which case the algorithm implied is > subtract the mean of X from the current value of X; > subtract the mean of Y from the current value of Y; > multiply these two differences together; > and sum all such products. Or, if you have a formula part of which > reads > n SUM XY - (SUM X)(SUM Y) > the algorithm implied is > add up all the X values (= SUM X); > add up all the Y values (= SUM Y); > count the number of values (= n); > for each case, multiply X by Y (= XY) and sum all these products; > multiply this last by "n"; > subtract from this the product of the first two sums. > (This quantity will be n times as large as the result of the previous > formula, by the way.) > > > Is that how I'd express this verbally? Been a long, long time since > > I've had to deal with the formula. > > ------------------------------------------------------------ > 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/ . =================================================================
