The problem of investigating compatibility of an assumed model with the dat
a is investigated in the situation when the assumed model has unknown param
eters. The most frequently used measures of compatibility are p values, bas
ed on statistics T for which large values are deemed to indicate incompatib
ility of the data and the model. When the null model has unknown parameters
. ?, values are not uniquely defined. The proposals for computing a p value
in such a situation include the plug-in and similar p values on the freque
ntist side, and the predictive and posterior predictive p values on the Bay
esian side. We propose two alternatives, the conditional predictive p value
and the partial posterior predictive p value, and indicate their advantage
s from both Bayesian and frequentist perspectives.