Red team

Every observer on this page has, by construction, no stimulus-history effect at all. The only acceptable answer from the analysis is “nothing here”.

Five generators were used to try to manufacture serial dependence: an observer with no history; one that regresses toward the running mean of recent orientations; one attracted to cardinal orientations; one whose dial drifts toward its random start angle; and one biased toward its own previous response. Each was run 200 times on the balanced stimulus design and again on a deliberately autocorrelated one. Each simulated “experiment” resamples 24 of them and applies the primary test.

The naive lag-1 model, which is what most of the literature fits, reports serial dependence for the central-tendency observer in 100% of experiments. The adjusted primary model reports it in 5.5%.

Two different ways to fail

A rejection rate estimated by resampling from a finite pool of observers mixes two things. One is genuine estimator bias: the confound really does shift the amplitude estimate. The other is how the test behaves given the shape of the estimator’s sampling distribution. The table separates them: the bias column is the pool mean with its standard error and a t-test against zero; the calibrated rate resamples from the pool re-centred at zero. Hypothesis H6 passes only if the calibrated rate is at most 7.5% and the bias is not significant.

The adjusted model does not pass for every generator. It fails the gate for response history (bias +0.16° ± 0.06, p 0.009). The response-history leak has a known cause: the synthetic observer is biased toward its previous response relative to its own noisy percept, but the model can only condition on the observable target. That errors-in-variables gap is not closable with behavioural data alone, and it is reported as a limitation rather than tuned away.

Can model comparison find the true generator?

The complement of a false-positive test is a discrimination test: generate from a known model, fit them all, and see which one wins. Picking exactly the right model is hard — AIC does it in 81% of simulations and a single held-out split in 57%. The question that matters for a claim about perception is coarser: did the winning model contain a stimulus-history term when, and only when, the generator had one? AIC gets that verdict right in 91% of simulations overall, and held-out likelihood in 72%.