The error of closure is a blunder detector, nothing more. The surveyor should be familiar with the instrument specifications to determine the standard error (theorical uncertainty) of the measurements - no measurements are absolute.
For example, if the surveyor were to traverse an equal sided figure of four 400' legs with an theoretical uncertainty (tu) of 0.03' (one sigma-68%) per setup for four setups. The math would be the square root of 0.03 squared x 4 = 0.06' x 2 (two sigma) = 0.12' theoretical uncertainty. Total traverse length is 400'x 4 = 1600'/0.12' tu is a relative error of closure of 1:13k.
The relative error of closure is a range from 0.00' to 0.12' (two sigma means there is 5% outlier that will not fit in the range.) Think of a spinning a wheel or throwing a dart at a board with a numerical range of 0.00' to 0.12'. The traverse closure is just as likely to be 0.00' or 0.12' or any other number in between. Restated, the error closure 1600'/0.01 = 1:160,000 is the same/likely as 1600'/0.12' = 1:13,000 - or any number in between - are the same closure. The surveyor only concerns him/herself if the number is less than 1:13k as the survey exceeded the instrument specification - indicating a possible blunder.
In closing, the 1:60k, 1:40k, 1:15k are all equal and meaningless as to the accuracy or precision of the work. A 1:8k or similar is the only meaningful number as it indicates a blunder.
If this post was intended to clown the crowd, I fell for it.
Do not take my word for it. See Brown, Curtis M., Robillard, Walter G., Wilson, Donald A., pgs. 282-284, "Evidence and Procedures for Boundary Location", 1981.
For those that do not have the book "The value has very little to do with the closure, except that the experienced discrepancy should fall within the expected range. It is just as likely for a closure to be zero as for it to be any other number within the expected range." (pages 283-284).
DWoolley
