It is difficult to ensure the numeric stability of all possible calculations made by any software that uses floating-point arithmetic. To guard against the loss of precision during ANOVA computation, Xynk assumes that
your data is well-conditioned (i.e., that the magnitude of individual data points are similar),
neither extremely small nor extremely large values are included in the data set, and
the total number of data points is not too great.
Xynk takes the following precautions to avoid the most common errors in floating-point arithmetic.
If you require higher precision or have a very large number of data points with high dynamic range, we recommend you use a more sophisticated package, e.g., software that uses exact precision numbers or symbolic calculation.
In accordance with the Apple Style Guide and common usage, we use data as a singular collective noun. Insisting that data are plural may be on your agendum, but I will continue to read a magazine while a panini is prepared. My stamina is not great enough to argue.
Goldberg, David (March 1991), What every computer scientist should know about floating-point arithmetic., ACM Computing Surveys 23 (1): 5–48, doi:10.1145/103162.103163
Chan, Tony F.; Golub, Gene H.; LeVeque, Randall J. (1979), Updating Formulae and a Pairwise Algorithm for Computing Sample Variances, Technical Report STAN-CS-79-773, Department of Computer Science, Stanford University.
Chan, Tony F.; Golub, Gene H.; LeVeque, Randall J. (1983). Algorithms for Computing the Sample Variance: Analysis and Recommendations. The American Statistician 37, 242-247. https://www.jstor.org/stable/2683386
Higham, Nicholas (2002). Accuracy and Stability of Numerical Algorithms (2 ed) (Problem 1.10). SIAM.
Pebay, P.; Terriberry, T.B.; Kolla, H. ;Bennett, J. Formulas For The Computation of Higher-Order Central Moments
Manning, E. Floating-point Summation Dr. Dobbs September 01, 1996