  We develop a Bayesian highest-density interval (HDI) for use in
within-subject designs. This credible interval is based on a standard
noninformative prior and a modified posterior distribution that conditions on
both the data and point estimates of the subject-specific random effects.
Conditioning on the estimated random effects removes between-subject variance
and produces intervals that are the Bayesian analogue of the within-subject
confidence interval proposed in Loftus and Masson (1994). We show that the
latter interval can also be derived as a Bayesian within-subject HDI under a
certain improper prior. We argue that the proposed new interval is superior to
the original within-subject confidence interval, on the grounds of (a) it being
based on a more sensible prior, (b) it having a clear and intuitively appealing
interpretation, and (c) because its length is always smaller. A generalization
of the new interval that can be applied to heteroscedastic data is also
derived, and we show that the resulting interval is numerically equivalent to
the normalization method discussed in Franz and Loftus (2012); however, our
work provides a Bayesian formulation for the normalization method, and in doing
so we identify the associated prior distribution.
