Fast Variance Calculation and Its Difference from Welford’s Method

Summary

The document describes a variance calculation intended to avoid repeated loops after initial values are established, making it potentially useful where execution speed matters. It contrasts this approach with Welford’s method, which processes observations in a single pass but still uses a loop. No formula, implementation details, timing measurements, or test results are provided, so the claimed speed advantage is qualitative rather than demonstrated.

The main caveat is that the two methods use different variance conventions: the described approach does not apply sample correction, while Welford’s method does. The document says the resulting difference is small in typical comparisons, and suggests matching the calculation to the convention used by built-in indicators. For data with widely varying values, it recommends Welford’s method. The guidance is brief and does not define what counts as unusually variable data or explain numerical stability, so researchers should verify the calculation against their own data and intended variance definition.

Key ideas

• The described variance method aims to avoid loops after initialization.
• Welford’s method uses a single pass but still iterates through observations.
• The methods differ because the described approach omits sample correction.
• The document recommends Welford’s method for data with widely varying values.
• No benchmark or detailed implementation is supplied to substantiate the speed claim.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.