Jay Warner writes: > But when we get to negative sums of squares, I think we have a > very serious issue on our hands. Mathematically negative sums > of squares are impossible, so we have an issue of digital > execution to deal with. This is what Excel is _supposed_ to do well. > > Would someone post a sample dataset that produces this > error? Can we have a discussion of what properties of this dataset > lead to the errors? What should a user, forced or allowed to live > with Excel, look out for to avoid falling into the same trap?
I have a benchmark data set that examines ANOVA calculations. Assessing the accuracy of ANOVA calculations in statistical software. S.D. Simon, J.P. Lesage. Computational Statistics and Data Analysis 1990: 8(3); 325-332. It is an artificial data set, but it has a lot of flexibility to test for both cancellation error and accumulation error. I describe the benchmark data set on my web pages at http://www.childrens-mercy.org/stats/ask/accuracy.asp One of the values for the benchmark data set causes Excel to compute -4096 for the sums of squares for treatment. In fairness to Excel, this data set is very extreme as it uses numbers like 1,000,000,000.4 and 1,000,000,000.3. It is unlikely that any real world data set would cause problems this serious. And note in my original publication that other software (SAS, SPSS, and BMDP) also had difficulty with this data. That was back in 1990. I suspect that SAS and friends now screen for data that is nearly constant, but I haven't had the time recently to test them to be sure. It's okay to fail with a data set this extreme. But the software should fail in a graceful way by either refusing to analyze the data, or by setting one of more of the sums of squares equal to zero. I think that some of the other things that Jon Cryer points out about Microsoft Excel are far more serious, but since you asked, it is not hard to get Excel to produce negative sums of squares. Steve Simon, [EMAIL PROTECTED], Standard Disclaimer. The STATS web page has moved to http://www.childrens-mercy.org/stats. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
