Visualizing Experimental Designs for Balanced ANOVA Models using Lisp-Stat

Abstract

The structure, or Hasse, diagram described by Taylor and Hilton (1981, American Statistician) provides a visual display of the relationships between factors for balanced complete experimental designs. Using the Hasse diagram, rules exist for determining the appropriate linear model, ANOVA table, expected means squares, and F-tests in the case of balanced designs. This procedure has been implemented in Lisp-Stat using a software representation of the experimental design. The user can interact with the Hasse diagram to add, change, or delete factors and see the effect on the proposed analysis. The system has potential uses in teaching and consulting.