This paper discusses efficacy issues in software testing strategies through attained failure size. Failure size is the probability of finding an input that causes a failure in the input domain. As testing progresses, failure size decreases due to debugging. The failure size at the termination of testing is called the attained failure size. Using this measure, we compare the efficacies of partition testing and random testing, derive conditions that lead to the superiority of partition testing, and obtain optimal time allocations in partition testing. The core findings are presented in a decision tree to assist testers in test management.