A data scientist is analyzing the relationship between two continuous variables. A scatter plot reveals a clear pattern: as one variable increases, the other consistently increases, but the relationship is distinctly non-linear (curved). The calculated coefficients are a Pearson correlation of 0.2 and a Spearman correlation of 0.9. Which statement provides the MOST accurate explanation for this significant difference in the coefficient values?
The presence of significant outliers is suppressing the Pearson correlation, while the rank-based Spearman correlation is unaffected.
Spearman correlation is only appropriate for ordinal data, and its application to continuous data has artificially inflated its value.
Pearson correlation's low value reflects the lack of a linear relationship, while Spearman correlation's high value accurately captures the strong monotonic trend.
The data likely violates the normality assumption required for Pearson correlation, leading to an inaccurate result.
The correct answer is that Pearson correlation's low value reflects the lack of a linear relationship, while Spearman correlation's high value accurately captures the strong monotonic trend. Pearson correlation specifically measures the strength and direction of a linear association between two variables. If the relationship is strong but not linear (e.g., curved), the Pearson coefficient will be low. Spearman correlation, on the other hand, measures the strength and direction of a monotonic relationship. A monotonic relationship is one where the variables tend to move in the same direction, but not necessarily at a constant rate. Since the described relationship is consistently increasing (monotonic) but curved (non-linear), Spearman's rank-based method correctly identifies a strong relationship (0.9), while Pearson's method correctly identifies a weak linear relationship (0.2).
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What is the main difference between Pearson and Spearman correlation?
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What is a monotonic relationship, and why is it important for Spearman correlation?
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Why does Pearson correlation require a linear relationship to yield a strong result?