For which of the following situation the 'Rank-correlation coefficient' is most suitable ?

Question

Accepted Answer

The correct option is 2:

The Rank-correlation coefficient, most famously attributed to Spearman's Rank Correlation, is a statistical measure designed to assess the relationship between two variables when the data is qualitative or ordinal, meaning it can only be arranged in order (ranked), but cannot be measured precisely on an interval or ratio scale. A **Beauty contest** is the classic example where this method is most suitable because the judges do not assign absolute numerical scores (like marks or length); rather, they assign ranks (1st, 2nd, 3rd, etc.) based on subjective qualitative criteria (beauty, poise, etc.). Since the core data gathered in a beauty contest is inherently ranked, Spearman's coefficient is the appropriate tool to find the degree of agreement or correlation between the rankings assigned by different judges.

The incorrect option is 1:
"Obtained marks of students" are quantitative data, measured on a ratio scale. The correlation between two sets of marks (e.g., Math and Science) is typically calculated using the standard Pearson's Product-Moment Correlation coefficient, which requires interval or ratio data for accurate results.

The incorrect option is 3:
"Length" is a physical measure and is quantitative data, measured on a ratio scale. If a researcher were correlating a person's height with their shoe size, for instance, they would use Pearson's coefficient, as both variables are capable of precise measurement.

The incorrect option is 4:
"Weight" is also a physical measure, which is quantitative and measured on a ratio scale. Calculating the correlation between two sets of weights (e.g., weight at birth and weight at age 5) should ideally be done using Pearson's correlation because precise numerical values are available.