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We develop a Bayesian highest-density interval (HDI) for use inwithin-subject designs. This credible interval is based on a standardnoninformative prior and a modified posterior distribution that conditions onboth the data and point estimates of the subject-specific random effects.Conditioning on the estimated random effects removes between-subject varianceand produces intervals that are the Bayesian analogue of the within-subjectconfidence interval proposed in Loftus and Masson (1994). We show that thelatter interval can also be derived as a Bayesian within-subject HDI under acertain improper prior. We argue that the proposed new interval is superior tothe original within-subject confidence interval, on the grounds of (a) it beingbased on a more sensible prior, (b) it having a clear and intuitively appealinginterpretation, and (c) because its length is always smaller. A generalizationof the new interval that can be applied to heteroscedastic data is alsoderived, and we show that the resulting interval is numerically equivalent tothe normalization method discussed in Franz and Loftus (2012); however, ourwork provides a Bayesian formulation for the normalization method, and in doingso we identify the associated prior distribution.

A Better (Bayesian) Interval Estimate for Within-Subject Designs