On Sat, 21 Dec 2002, Ronny Richardson wrote: > After further experimenting, it is not a small number problem. I > took the random numbers and multiplied them times 1000 to make them > larger and got negative SS's on my third recalc. Then I tried times > 1,000,000 and it happened again.
Depends on what one means by "a small number problem". If, as I conjectured earlier, it's a problem of a small DIFFERENCE in numbers, where "small" is relative to the size of the numbers, multiplying the numbers by any large (or small) constant will not change the nature of the problem. If it takes 9 decimal digits to distinguish between the raw sum of squares (e.g.) and the sum of squared sums of the row (or column) subgroups (divided by the number of cases involved therein), and you only have 8 digits available in the single precision that Excel is almost certainly using, it will take 9 digits whether the numbers are 3.23456789 and 3.23456788 or 3234567.89 and 3234567.88. In either case, the difference is zero to the precision of your arithmetic, and will therefore be reported as some random value near zero (and unrelated to your data) for which you cannot (obviously!) even trust the sign. (I do not know what Excel's single precision actually is, in the computer you're using; the point applies for any data for which the computing formula leads to trying to estimate a tiny difference from two numbers that are so similar as to be indistinguishable from each other in the precision available.) Incidentally, the value for the total SS is probably more believable than the others; although it too is probably not precise to more than 2 digits. But in the "computing formulas" that will have been implemented by the programmer, the interaction SS will be calculated by subtraction (using the fact that SS(rows) + SS(columns) + SS(interaction) = SS(total), where SS(interaction) is what Excel reports (if I remember your earlier post correctly) as SS(Error)): thus, SS(Error) = SS(Total) - SS(Rows) - SS(Columns) and if both SS(Rows) and SS(Columns) are miscalculated as negative, the error SS will be miscalculated as distinctly larger than it really is: as you can see from the output. As the ancient proverb hath it, GIGO. Cheers! -- DFB. ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 [was: 184 Nashua Road, Bedford, NH 03110 (603) 471-7128] . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
