Understanding Spearman’s Correlation Coefficient for Assessing Relationships Between Quantitative Variables

Spearman

proposed that general intelligence (g) is linked to many clusters that can be analyzed by factor analysis

Spearman is a statistical measure of correlation that assesses the strength of the relationship between two variables. It is particularly relevant when we want to determine if there is a relationship between two quantitative or continuous variables. Spearman’s correlation coefficient, also known as rho, ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

Spearman’s correlation coefficient is based on the ranks of the observations rather than the actual values of the observations. This is advantageous when the variables being studied are not normally distributed or when there are outliers present in the data.

To calculate Spearman’s correlation coefficient, we must first rank the values of each variable from smallest to largest. We then assign each value its rank, with the smallest value receiving a rank of 1, the second-smallest value receiving a rank of 2, and so on. Next, we calculate the difference between the ranks of each pair of observations, square those differences, and sum them up. Finally, we use the following formula to calculate the correlation coefficient:

Spearman’s rho = 1 – (6Σd^2)/(n(n^2-1))

where d is the difference between the ranks of each pair of observations, Σ represents the sum of those differences, and n is the number of observations.

Spearman’s correlation coefficient can be used to answer research questions such as: Is there a significant relationship between age and income? Is there a significant relationship between body mass index (BMI) and blood pressure?

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