Most statistical methodology has focused on cross–sectional data (observation at one time across many people). Tools such as smartphones have allowed for the collection of repeated, within–person self–reports in the social, behavioral, and medical sciences. The analysis tools for such data, however, are still being developed. Integrating intraindividual/intragroup data with statistics, dynamical system theory, methods for analyzing repeated observations, and rich theories about intraindividual/intragroup change, we have the potential of revolutionizing our understanding of how, when, and why people change. The potential is to move beyond stereotyped inferences based on averages of people with similar characteristics, and towards being able to offer truly personalized psychological and medical resources.