Implementing Algorithms to Measure Common Statistics

Stuart McCrary writes about ways to calculate the mean, variance, skewness, kurtosis, covariance, correlation, regression parameters, and other regression statistics.

Formulas for common statistics are generally well known, and users have access to native routines in Microsoft Excel and most programming languages to calculate many statistics. Under most circumstances and with most data, these routines provide identical results. That is, they produce identical results within the mathematical precision available in that environment. However, these algorithms can be constructed in at least three ways, and sometimes the results differ because the algorithms exceed the precision of the environment. Stated differently, the three methods place unequal demands on the precision available for the calculations. Some data also put more demands on the precision available for calculations. For most data, the choice involves convenience; for some data, choosing the right algorithm is important.