Researcher: Results indicate that the higher their educational level, the better are students' mathematical skills
These results do not prove that education improves mathematical skills, however, since it is possible that students who have better mathematical skills to start with are the students who reach higher educational levels
Results from competition indicate that professional athletes outperform amateur athletes. These results do not prove that becoming a professional athlete improves one's athletic performance, since it is possible that the athletes who become professionals are those whose performance is better to begin with.