Which non-parametric statistic assesses monotonic relationships between two ordinal variables?

Which non-parametric statistic assesses monotonic relationships between two ordinal variables?

• A. Pearson correlation
• B. Chi-square
• C. Spearman correlation
• D. ANOVA

Answer: (C)

The idea is to quantify a monotonic association between two ordinal variables using a rank-based statistic. Spearman correlation does this by converting each variable to ranks and then measuring the correlation between those ranks. Because it works with ranks rather than the actual values, it does not assume equal intervals or a linear relationship, only that the variables tend to move in the same (positive) or opposite (negative) direction as one increases. This makes it ideal for two ordinal variables or data that don’t meet normality assumptions. If there are ties in the data, they’re handled with a correction, but the overall interpretation remains: values close to 1 indicate a strong increasing monotonic relationship, values close to -1 indicate a strong decreasing monotonic relationship, and values around 0 suggest little to no monotonic association. In contrast, Pearson correlation requires interval/ratio data and a linear relationship, Chi-square examines association between categorical counts, and ANOVA compares group means—none of these specifically measure monotonic relationships between two ordinal variables.

The idea is to quantify a monotonic association between two ordinal variables using a rank-based statistic. Spearman correlation does this by converting each variable to ranks and then measuring the correlation between those ranks. Because it works with ranks rather than the actual values, it does not assume equal intervals or a linear relationship, only that the variables tend to move in the same (positive) or opposite (negative) direction as one increases. This makes it ideal for two ordinal variables or data that don’t meet normality assumptions. If there are ties in the data, they’re handled with a correction, but the overall interpretation remains: values close to 1 indicate a strong increasing monotonic relationship, values close to -1 indicate a strong decreasing monotonic relationship, and values around 0 suggest little to no monotonic association. In contrast, Pearson correlation requires interval/ratio data and a linear relationship, Chi-square examines association between categorical counts, and ANOVA compares group means—none of these specifically measure monotonic relationships between two ordinal variables.