  In an attempt to provide an answer to the increasing criticism against
p-values and to bridge the gap between statistical inference and prediction
modelling, we introduce the probability of improved prediction (PIP). In
general, the PIP is a probabilistic measure for comparing two competing models.
Three versions of the PIP and several estimators are introduced and the
relationships between them, p-values and the mean squared error are
investigated. The performance of the estimators is assessed in a simulation
study. An application shows how the PIP can support p-values to strengthen the
conclusions or possibly point at issues with e.g. replicability.
