The generalized NIO (gNIO) model is described by
Equation 2 in the main text. It includes four free parameters,
Display Formula (the variance of a late noise added to the difference between estimates of sample mean effective sizes),
Display Formula (the variance of an early noise added to the effective size of each item independently on each loop),
l (the number of times or “loops” an observer forms an independent estimate of the mean size using the same subarray), and
m (the maximum effective sample size of each such independent estimate). In the present experiments both
Ns and
Nt were either 1 or 8, hence yielding four spatio-temporal combinations 1:1, 8:1, 1:8, and 8:8. These are the last two digits appearing between parentheses in the left side expressions of the equations below. Since
m is the maximum effective sample size on each side of the display, it cannot exceed the total number of elements that appear on each side during a single loop. Thus, when there is at least one loop per subarray,
l ≥ 1
⇒ m ≤ Ns. However, when there is less than one loop per subarray,
m can be larger than
Ns. In the limit, when all subarrays are exposed within the same loop,
m is bound by the total number of elements on each side of the array,
l ≤ 1/
Nt⇒ m ≤ NsNt. Furthermore, we adopt the “reasonable” (Allard & Cavanagh,
2012) assumption that all estimates are based on at least one element, i.e.,
m ≥ 1. Consequently,
and