The reversal is a property of the instrument

The margin between the two block windows under each of four rules, on three readings of the same resampled means, signed so that a positive bar is the tapered window winning. On the implied long-run variance the taper wins at the best available block length and at one estimated from the sample and loses at a length written into a protocol and at the rule of thumb — which is the reversal the earlier field's whole argument turns on, at 1.48 and 4.52 points. On the 95% point a test actually reads, the taper wins at all four, by 6.13 to 7.08 points. On the coverage the interval actually delivers, the taper wins at all four again, by 2.50 to 5.75 percentage points. Two of the four rules change sign between the first reading and the other two, and the two that change are exactly the two the earlier field's recommendation is about.

The block length that would actually have been best on each draw, for each of the two error readings, averaged over 400 samples of 120 rows. For the rectangular window the implied long-run variance wants 18.92 and the 95% point wants 16.05; for the tapered window, 21.82 against 17.74. The quantile wants a shorter block under both windows — a ratio of 0.848 and 0.813. That is the mechanism the whole field turns on: a rule for choosing a block length is a way of guessing a target, and the two instruments do not have the same target. A rule tuned to one is systematically long for the other, and the two windows do not pay the same price for being long.

Root mean squared relative error on a rectangular window at a persistence of 0.7 on 120 rows. a protocol length of 8: implied variance 45.8%, the 95% point uncentred 65.5%, the 95% point about its own mean 28.5%; the cube-root rule: implied variance 56.9%, the 95% point uncentred 68.2%, the 95% point about its own mean 35.5%; the plug-in rule: implied variance 46.4%, the 95% point uncentred 66.2%, the 95% point about its own mean 28.9%; the best length, in hindsight: implied variance 39.1%, the 95% point uncentred 53.6%, the 95% point about its own mean 23.1%.