The work partially reported here concerned the development ot a prototype Expert System for giving advice about Statistics experiments, called ASA, and an inference engine to support ASA, called ABASE. This involved discovering what knowledge was necessary for performing the task at a satis? factory level of competence, working out how to represent this knowledge in a computer, and how to process the representations efficiently. Two areas of Statistical knowledge are described in detail: the classification of measure? ments and statistical variables, and the structure of elementary statistical experiments. A knowledge representation system based on lattices is proposed, and it is shown that such representations are learnable by computer programs, and lend themselves to particularly efficient implementation. ABASE was influenced by MBASE, the inference engine of MECHO [Bundy et al 79a]. Both are theorem provers working on typed function-free Horn clauses, with controlled creation of new entities. Their type systems and proof procedures are radically different, though, and ABASE is "conversational" while MBASE is not.