The esteemed Dr. Bookworm has just completed a study in which he found a +1.0 correlation between the number of cups of coffee his students drank right before class and the scores they earned on his final exam. This correlation means that:
A. the less coffee the students drank, the higher they scored on the exam.
B. the more coffee the students drank, the lower they scored on the exam.
C. the more coffee the students drank, the higher they scored on the exam.
D. there was absolutely no correlational relationship between coffee consumption and exam scores
My conclusion was D.
Your conclusion is incorrect. The correct answer is C. The more coffee the students drank, the higher they scored on the exam.
To understand this correlation, let's first explain what a correlation coefficient represents. In this case, the correlation coefficient is +1.0, which indicates a perfect positive correlation. A correlation coefficient ranges from -1.0 to +1.0, where -1.0 indicates a perfect negative correlation, 0 indicates no correlation, and +1.0 indicates a perfect positive correlation.
In this study, a positive correlation between the number of cups of coffee consumed and the exam scores means that as the number of cups of coffee increases, the scores also increase. In other words, the more coffee the students drank, the better they performed on the exam.
To arrive at this answer, Dr. Bookworm likely gathered data on the number of cups of coffee consumed by his students before the exam, as well as their corresponding scores. By comparing the two variables, he calculated the correlation coefficient of +1.0, indicating a strong positive relationship between coffee consumption and exam scores.
It's important to note that correlation does not imply causation. While this study found a positive correlation between coffee consumption and exam scores, it does not necessarily mean that drinking coffee directly causes higher exam scores. There could be other factors at play that contribute to this observed relationship.