Ex-Gaussian decomposition of reaction times

Split an RT distribution into a normal body and an exponential tail: mu and sigma describe ordinary responding, tau describes the long right tail. The attention literature treats tau as the lapse parameter — the trials where someone was, briefly, not there.

The interpretive trap this wiki met first-hand

Eusebio et al. (2022) predicted that interoception-focused yoga would reduce tau (fewer lapses). It did not: no group × time effect on tau at all, while the same participants’ no-go accuracy improved significantly. Lapse frequency was flat while errors fell.

Their proposed resolution is the trap worth recording. A long RT can be a lapse (mind gone, response late) or a deliberate pause (error noticed, engagement re-established) — Cheyne et al. (2009) and Jackson & Balota (2012) both describe post-error slowing as potentially adaptive rather than disruptive. If training converts lapse-slowing into control-slowing, tau stays put while what it means inverts. Eusebio et al. read their significant accuracy × group × time interaction on tau (β = 85.05, p = .006) as evidence of exactly that shift in meaning.

That reading may be right, but note its structure: it rescues a failed prediction by reinterpreting the dependent variable after seeing the result. The honest form is the one the authors give — a call for thought probes to establish where attention actually was on slow trials, rather than inferring it from the tail. Until someone runs that, a null on tau is uninformative rather than negative, and this page’s advice is to pair tau with a direct probe of thought content (multidimensional-experience-sampling) wherever the question is about mind-wandering rather than about slowness.