Which correlation measure is appropriate for ordinal data or non-linear but monotonic relationships?

Which correlation measure is appropriate for ordinal data or non-linear but monotonic relationships?

• A. Point-Biserial Correlation
• B. Phi-Coefficient
• C. Pearson Correlation
• D. Spearman Correlation

Answer: (D)

Spearman correlation measures the strength and direction of a monotonic relationship by ranking the data. For ordinal data, you can’t assume equal distances between categories, but you can order them; converting to ranks preserves that order and allows you to assess whether, as one variable increases, the other tends to increase or decrease, regardless of whether the relationship is straight-line or curved. Because it works on ranks, it doesn’t rely on normal distributions or equal intervals, and it’s robust to outliers. If the relationship is non-linear but monotonic, Spearman will still show a strong association, whereas Pearson would miss it because it looks for a linear relationship. The other measures are designed for different types of data—one for a binary and a continuous variable, another for two binary variables—so they aren’t appropriate for ordinal data or non-linear monotonic patterns.

Spearman correlation measures the strength and direction of a monotonic relationship by ranking the data. For ordinal data, you can’t assume equal distances between categories, but you can order them; converting to ranks preserves that order and allows you to assess whether, as one variable increases, the other tends to increase or decrease, regardless of whether the relationship is straight-line or curved. Because it works on ranks, it doesn’t rely on normal distributions or equal intervals, and it’s robust to outliers. If the relationship is non-linear but monotonic, Spearman will still show a strong association, whereas Pearson would miss it because it looks for a linear relationship. The other measures are designed for different types of data—one for a binary and a continuous variable, another for two binary variables—so they aren’t appropriate for ordinal data or non-linear monotonic patterns.