A psychology professor wants to examine the relation between amount of sleep and test performance. The professor asks the students to write down how long they had slept the night before the final exam. The results showed a correlation of -.70 between the amount of sleep students reported and their exam scores. Which of the following best describes the results of the study?
The less students slept, the higher their exam scores were.
The correlation of -.70 indicates a strong negative relationship between the amount of sleep and exam scores, meaning that as the amount of sleep decreases, the exam scores tend to increase. This suggests that students who reported less sleep performed better on the exam, revealing an inverse relationship.
This statement is incorrect because a correlation of -.70 indicates a significant negative relationship between the variables. A correlation of zero would suggest no relationship at all, whereas the negative correlation shown here demonstrates a clear inverse association.
This choice is also incorrect as correlations can indeed be negative, which is what the -.70 value indicates. Negative correlations are a valid statistical outcome and suggest that as one variable increases, the other decreases.
This option misinterprets the correlation coefficient. While a correlation of -.70 indicates a strong relationship, to determine the percentage of variance accounted for, one would square the correlation coefficient. Squaring -.70 yields approximately 49%, not 70%, so this statement is inaccurate.
In summary, the strong negative correlation of -.70 reveals that less sleep is associated with higher exam scores among students. This study highlights the essential understanding of how sleep may affect academic performance, indicating that lower amounts of sleep could be linked to better outcomes in this specific context, despite common intuitions about sleep and performance.
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