what is the study called where the same people are tested repeatedly at different ages?

The study you are referring to is called a longitudinal study. In a longitudinal study, a group of individuals is followed over an extended period of time, and data is collected from them at multiple points or "waves" of assessment. This allows researchers to observe how certain variables or characteristics change or remain stable as individuals age. To find more information about longitudinal studies, you can try searching for academic articles or books about longitudinal research methods in psychology, sociology, or other social sciences. Online academic databases such as Google Scholar or PubMed are great resources for finding relevant studies and publications in this field. Additionally, you can consult websites or resources from reputable research institutions or universities that specialize in longitudinal studies.