Analytic means that the experimenter has shown a clear cause-and-effect relationship between what they changed (independent variable) and the behavior they observed (dependent variable).
Example
A behavior analyst is testing if providing praise increases a student’s on-task behavior. They first observe the student’s behavior without giving praise, then start praising the student when they stay on task. If the student’s on-task behavior increases only when praise is given, the analyst has demonstrated a functional relation between praise (independent variable) and on-task behavior (dependent variable), showing the study is analytic.