This paper investigates certain statistical problems arising in the determination of the ``best'' of $k$ categories when comparing $k - 1$ experimental categories with a standard or control. The discussion is limited to the case of a single stage sampling procedure with an equal number of observations on each of the $k$ categories. Results both of an exact and of an approximate nature are obtained when (a) the observations with each category are normally distributed, and (b) the observations with each category have a binomial distribution.