A simple LSD (least significant difference) rule is presented for simultaneously testing the differences betweenntreatments considered in all possible pairs. This rule is a simpler, fully completed, version of the Bayes rule presented for special cases in Duncan [4]. It is based on the same multiple decision theory model except for a modified and extended use of a conjugate chi-square density in the prior. The new rule has the same intuitively appealing dependence on the between-treatmentFratio, varying from a sensitive comparisonwise-α-like rule whenFis large or moderate, to a conservative experimentwise-α-like rule whenFis small. Tables oftfor computing the LSD are presented for three choices of a type-1 to type-2 error-seriousness ratio,k= 50, 100 and 500 (analogous to the usual choices of α = .10, .05 and .01 in testing a single difference), and for full ranges ofFand its degree of freedomqandf.