What particular measure of correlation would be most appropriate for use with two variables measured at an ordinal level?
a. Spearman’s Rho
B. Pearson’s r
C. Contingency Coefficient
D. Chi Square
d. chi square
When dealing with variables measured at an ordinal level, Spearman's Rho would be the most appropriate measure of correlation.
To understand why Spearman's Rho is the appropriate choice, let's briefly explain what an ordinal level of measurement means.
In statistics, variables can be classified into different levels of measurement: nominal, ordinal, interval, and ratio. Ordinal level variables have properties of the nominal level (categories), but with the added feature that the categories can be ordered or ranked. For example, a variable like "Satisfaction Level" with categories such as "Very Satisfied," "Satisfied," "Neutral," "Dissatisfied," and "Very Dissatisfied" would be considered ordinal.
Now, let's discuss why Spearman's Rho is the appropriate measure for correlating ordinal variables.
Spearman's Rho is a non-parametric measure of correlation that assesses the relationship between two variables based on the ranks or orders of their values. It is designed to capture monotonic relationships, meaning that as the rank of one variable increases, the rank of the other variable tends to increase (or decrease).
Pearson's r and the Contingency Coefficient, on the other hand, are designed to measure the strength and direction of the linear relationship between two continuous or categorical variables, respectively, but not specifically for ordinal variables.
Chi Square is used to test the independence of two categorical variables, so it is not a measure of correlation.
Therefore, in the case of variables measured at an ordinal level, Spearman's Rho would be the most suitable measure to assess the correlation between them.