This paper describes a mathematical model for use in analyzing single case replication series. First, a mathematical model of two adjacent single subject design phases is developed with some mathematical rigor. Then, a comparative data analysis is performed, comparing the information produced by a classical pretest-posttest design analysis, a classical single subject visual analysis, and an analysis employing components of the mathematical model developed in the first part of the paper. The results suggest that the use of classical group comparison methods in the controlled execution of single subject replication series may well be, at this time, the most powerful approach to explicating the functional relationship between a treatment and dependent variable.