The authors present a method that ensures control over the Type I error rate for those who visually analyze the data from response-guided multiple-baseline designs. The method can be seen as a modification of visual analysis methods to incorporate a mechanism to control Type I errors or as a modification of randomization test methods to allow response-guided experimentation and visual analysis. The approach uses random assignment of participants to intervention times and a data analyst who is blind to which participants enter treatment at which points in time. The authors provide an example to illustrate the method and discuss the conditions necessary to ensure Type I error control. (Contains 1 figure.)