A Remark on the Interpretation of Pooling Results

A multinomial distribution (-1, π₁), (0, π₂), (1, π₃), π₁ + π₂ + π₃ = 1 is observed. Suppose that n₁ values -1, n₂ values 0 and n₃ values 1 (n = n₁ + n₂ + n₃) were observed. The construction of the confidence region for the vector (π₁, π₂, π₃) is given. Theoretical considerations are illustrated by an example of the results of a pool.