Circular mean of clock times in decimal hours

Computes the mean of times on the 0-24 h clock using the unit-circle method: convert each time to a unit-vector angle, average the sin and cos components, and back-project via atan2. This correctly handles midnight wrap (e.g. times at 23:30 and 00:30 average to 00:00, not 12:00).

Usage

circ_mean_h(x)

Arguments

x

numeric. Decimal hours in [0, 24). NA values are silently dropped.

Value

A single numeric in [0, 24), or NA_real_ if x is empty after NA removal.

Details

The older threshold approach (shift values >= 12 h by -24 h before averaging) produces badly biased estimates when times straddle noon – critically for sleep offset in late sleepers – and is superseded by this function (Fix 20 in the JRSV pipeline, ICC for sleep offset 0.502 -> 0.897 on N=404).

References

Pewsey, A., Neuhauser, M., & Ruxton, G. D. (2013). Circular Statistics in R. Oxford University Press.

Examples

circ_mean_h(c(23.5, 0.5))   # midnight wrap -> 0
#> [1] 24
circ_mean_h(c(23.0, 1.0))   # -> 0
#> [1] 0
circ_mean_h(c(7.0, 9.0))    # -> 8
#> [1] 8