AR(1) mean precision multiplier
Compute the finite-series variance inflation of an equally weighted mean under an AR(1) correlation model.
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Use an integer series length from 2 to 10,000 and lag-one correlation strictly between −1 and 1. The underlying process must be stationary with equal marginal variance.
The starting values are hypothetical. Results update as you edit. Use aggregate or synthetic inputs only.
Calculation results
- Mean variance multiplier
- 2.8000002
- Effective n for mean variance
- 7.1428567
- SE multiplier
- 1.6733201
How to interpret the output
Variance multiplier is 1+2×sum((1−lag/n)×rho^lag). Effective n=n/multiplier matches the variance of the mean, not an actual independent sample count. Negative correlation can produce effective n above n. The assumed rho is treated as known; trend, irregular spacing and estimated-correlation uncertainty are excluded.
Method referenceSource checked 2026-11-06. Read the reproducible calculator validation report.