= Solution
\b[Consistent independent replications should strengthen confidence; contradictory results can weaken it.] The change depends on the actual evidence. If $k$ of $n$ studies are positive and all labels are available, the <posterior odds> are
$$
R\left(\frac{1-\beta}{\alpha}\right)^k\left(\frac{\beta}{1-\alpha}\right)^{n-k}.
$$
For the normal model, retaining the full independent statistics instead gives
$$
\boxed{\text{posterior odds}=R\exp\left(2.49\sum_{j=1}^n y_j-n\frac{2.49^2}{2}\right).}
$$
Each study multiplies the existing odds by its own <Bayes factor>. Reading a complete synthesis is therefore different from learning only that somebody obtained a positive result. <Publication bias>, dependence between studies and changes in study design must be accounted for before applying the independent-product formula.
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