Which of the following values of Pearson’s r indicates the strongest association between two variables?

Question

BlackTom AI · Accepted Answer

Question restatement: Which of the following values of Pearson’s r indicates the strongest association between two variables? Note: The provided answer indicates r = -.97, but the answer options are not present here, so we will reason about the concept.

Key concept: The strength of a linear relationship in Pearson’s r is determined by the magnitude (absolute value) of r, not its sign. Values near 1 or -1 indicate a strong relationship, while values near 0 indicate a weak or no linear relationship.

Option analysis (conceptual, since actual options are missing):
- If a value has an absolute value close to 1 (e.g., |r| = 0.95, 0.97, or 0.99), that represents a very strong linear association, positive if the sign is positive, negative if the sign is negative.
- A value like r = 0.3 or r = -0.2 would indicate a weak to moderate association, far from the strongest possible relationship.
- A value of r = 0 or r = -0 would indicate no linear relationship.
- Between two values with different signs but similar magnitudes, the sign only tells the direction, not the strength; for strength, compare magnitudes.

Reasoning about the specific candidate r = -.97: A correlation of -0.97 has a large magnitude (|r| = 0.97), which is very close to 1 in absolute terms, indicating a very strong linear association despite the negative direction. In typical comparison with other plausible r-values (e.g., -0.8, -0.5, 0.6), -0.97 has the greater absolute value and thus the strongest relationship.

Common misconceptions to watch out for: 
- Mistaking the sign for strength: a positive and a negative correlation can be equally strong if their magnitudes are the same. Here, magnitude is the key for strength.
- Thinking that a larger numeric value always means stronger strength without considering the absolute value; -0.95 is about as strong as 0.95 in magnitude, just opposite in direction.
- Assuming that a value near zero indicates strength; in fact, near zero means weak or no linear association.

Summary: Strength is tied to how close |r| is to 1. A value like r = -.97, having |r| = 0.97, represents a very strong linear relationship, stronger in magnitude than many other common r-values, regardless of sign.

PSYC20009_2025_SM2 Quiz for Correlation: Part 2

Which of the following values of Pearson’s r indicates the strongest association between two variables?

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类似问题

Of the following, the correlation coefficient that indicates the weakest relationship between the two variables being measured is ______________.

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