A 40-item free response test on signed-number subtraction was administered to 172 eighth graders. Their responses are viewed as consisting of two different components, the sign and absolute value. Each component is scored zero for wrong or one for correct, yielding a score of one only when both components have scores of one. By taking the values of the Extended Caution Index for the absolute value component as the x-axis and those for the sign component as the y-axis, all pairs of component response patterns produced by consistent or inconsistent application of various rules or random errors are mapped into the ECI product space. A simulation study showed that the response patterns generated by changing the binary score of any one item in the response patterns of an erroneous rule cluster together. Moreover, the patterns resulting from the same kind of misconceptions fall closer together than those resulting from very different kinds. This property of the ECI product space opens up a promising way to handle large numbers of "bugs" or rules quantitatively, although the ECIs are not defined in the cases of perfect or zero scores. Typically, there are many incomplete rules. (MNS)