Question at position 3 An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correlation coefficient was found to be γ\gamma = 0.86. A reader of the study concluded that more sleep causes employees to perform better. Why is such a conclusion not correct? 4STM17An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correlation coefficient was found to be γ\gamma = 0.86. A reader of the study concluded that more sleep causes employees to perform better. Why is such a conclusion not correct? 4STM17The correlation value should be negative for such a conclusion.The correlation value should equal 1 for such a conclusion.The correlation value implies that less than 75% of the variability in job performance can be explained by sleep.The sample was not representative of the population.Causation cannot be determined from an observational study.题目解析单项选择题
A
The correlation value should be negative for such a conclusion.
B
The correlation value should equal 1 for such a conclusion.
C
The correlation value implies that less than 75% of the variability in job performance can be explained by sleep.
D
The sample was not representative of the population.
E
Causation cannot be determined from an observational study.

Question

Question at position 3 An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correlation coefficient was found to be γ\gamma = 0.86. A reader of the study concluded that more sleep causes employees to perform better. Why is such a conclusion not correct? 4STM17An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correlation coefficient was found to be γ\gamma = 0.86. A reader of the study concluded that more sleep causes employees to perform better. Why is such a conclusion not correct? 4STM17The correlation value should be negative for such a conclusion.The correlation value should equal 1 for such a conclusion.The correlation value implies that less than 75% of the variability in job performance can be explained by sleep.The sample was not representative of the population.Causation cannot be determined from an observational study.题目解析单项选择题

A

The correlation value should be negative for such a conclusion.

B

The correlation value should equal 1 for such a conclusion.

C

The correlation value implies that less than 75% of the variability in job performance can be explained by sleep.

D

The sample was not representative of the population.

E

Causation cannot be determined from an observational study.

BlackTom AI · Accepted Answer

Restating the question and answer options: An observational study found that the amount of sleep an employee gets each night is associated with job performance, with a correlation coefficient of γ = 0.86. A reader concluded that more sleep causes better performance. Why is this not correct?
Option 1: The correlation value should be negative for such a conclusion. This is incorrect because a positive correlation (0.86) simply indicates that as sleep increases, performance tends to increase as well; it does not imply causation or negate the possibility of a positive association. The sign of the correlation does not by itself determine causality.
Option 2: The correlation value should equal 1 for such a conclusion. A correlation of 1 indicates a perfect linear relationship, which is extremely rare in real-world data. A value of 0.86 indicates a strong but not perfect association, but this alone does not establish causation.
Option 3: The correlation value implies that less than 75% of the variability in job performance can be explained by sleep. Interpreting the exact proportion of variance explained requires computing R-squared (0.86^2 ≈ 0.7396, about 74%). This statement would be roughly true if claimed as an R-squared interpretation, but it does not address causation directly and is somewhat imprecise in conveying the issue of causality from correlation alone. Moreover, explaining ~74% of variability does not by itself confirm causation; the relation could be due to confounding factors.
Option 4: The sample was not representative of the population. While a nonrepresentative sample is a valid concern in general, this option does not directly address the fundamental issue of inferring causation from an observational study. It could contribute to biased results, but it does not explain why correlation does not imply causation as a general principle.
Option 5: Causation cannot be determined from an observational study. This statement correctly identifies the central reasoning: observational studies reveal associations but cannot establish that one variable causes another due to potential confounding variables, reverse causation, and other biases. This is the key reason the reader’s conclusion is not justified.

In summary, the core flaw in concluding causation from this observational correlation is that correlation does not equal causation (Option 5). The other options either misinterpret the meaning of the correlation coefficient, misstate statistical norms, or address study design issues that are relevant but not the fundamental rule about causation. The strongest, most direct critique is that causation cannot be determined from an observational study, which is exactly what Option 5 asserts.