Identify the direction and all possible interpretations of each of the following correlations. Be sure to identify each example as positive, negative, or zero (not correlated). Then give all possible causal interpretations for the results.
Many students in Professor Handel’s class express that they want a review session. Professor Handel agrees to hold an open review session for two hours the day before the exam. He then has his TA write down when each student arrives at the session and when they depart. When the exams are graded, Professor Handel announces there will be no more review sessions. The longer students spent at the review session the lower their score on the exam.
this is what I think:
negative correlation
interpretation that the longer the students reviewed impacted their exam grade
It is negative, but why would longer reviews reduce exam grades (causes)? Fatigue factor for students or teacher? Less intelligent students require more review time? Is there a grading bias against the students who attended longer? Something else?
To identify the direction and possible interpretations of correlations, we can first calculate the correlation coefficient between two variables, and then analyze the relationship based on the results.
In this case, we have two variables: the amount of time students spent at the review session and their score on the exam. We are told that the longer students spent at the review session, the lower their exam score. This suggests a negative correlation between the two variables.
To calculate the correlation coefficient, you would need the actual data points of the time spent at the review session and the corresponding exam scores for each student. Once you have the data, you can use statistical software or a calculator to calculate the correlation coefficient.
Assuming there is a negative correlation between the time spent at the review session and the exam scores, here are some possible interpretations for the results:
1. Causal interpretation: The review session was not helpful or effective in preparing the students for the exam. Spending more time at the review session may have led to confusion or lack of focus, resulting in lower exam scores.
2. Reverse causality: The students who performed poorly on the exam felt the need to spend more time at the review session, hoping to improve their understanding. However, their attempts were not successful, leading to lower scores.
3. Confounding factor: There might be a third factor that influences both the time spent at the review session and the exam scores. For example, students who were less prepared for the exam might have spent more time at the session and subsequently scored lower on the exam.
It's important to note that correlation does not imply causation, and further research or analysis could be needed to confirm any causal interpretations.