Method at a glance
- Modality: analytic (applies to any RT distribution)
- Measures: Separates a reaction-time distribution into a Gaussian body (mu = mean, sigma = SD) and an exponential right tail (tau), so that ordinary responding and rare extreme-slow responses are estimated as distinct parameters rather than averaged into one mean.
- Procedure: Fit the convolution of a Gaussian and an exponential to correct-trial RTs within block and within session (e.g. the timefit function of the R retimes package). Yields mu, sigma and tau per participant per block.
- Also called: ex-Gaussian, tau, mu sigma tau, ex-Gaussian RT modelling
Strengths
- Mean RT confounds a shift of the whole distribution with a handful of very slow trials. These have different psychological meanings and ex-Gaussian fitting separates them.
- Tau is a validated index of distraction and mind-wandering (Gmehlin et al. 2014; Tamm et al. 2012; McVay & Kane 2012), giving an implicit lapse measure that does not ask the participant whether their mind wandered.
- Cheap: no extra trials, no extra instrument — it re-analyses data a task already produced.
Limitations
- Descriptive, not mechanistic. Tau is where slow responses live, not an explanation of why they are slow; ‘lapse’, ‘distraction’ and ‘strategic pause’ all deposit trials in the same tail.
- Fits need substantial trial counts per cell to be stable; block-level fits in small samples are noisy, and the noise is largest in exactly the tail parameter of interest.
- The interpretation of tau can change between conditions without the parameter changing — see below, which is why a null on tau is hard to read.
Connections
- Key studies: Eusebio et al. (2022)
- Related methods: Sustained Attention to Response Task (SART)
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 (MDES)) wherever the question is about mind-wandering rather than about slowness.