Assessing Spearman’s Rank After a Monotonic Transformation
A researcher is investigating the relationship between advertising expenditure and sales figures. The original data is provided as follows: Advertising spend (in thousands): 10, 50, 30, 20, 40 Sales (in thousands): 85, 95, 80, 70, 90 Due to skewness in the advertising data, a logarithmic transformation is applied using the function \(f(x)=\ln(x)\). Proceed with the […]
Compute ρ from survey ranks
In a study assessing public opinion on a new public transportation system, 20 individuals were surveyed and asked to rank their satisfaction with service punctuality and user satisfaction using a 5-point Likert scale. The ranks for a subset of 5 respondents are given below: Respondent A: Punctuality = 1, Satisfaction = 3 Respondent B: Punctuality […]
Evaluating Spearman’s Rank Correlation Coefficient
Given paired data for two variables along with their rank orders, calculate Spearman’s rank correlation coefficient. Suppose we have 5 observations with rank orders for variable X: [1, 2, 3, 4, 5] and for variable Y: [2, 1, 4, 3, 5]. Compute the coefficient using the formula \(r_s = 1 – \frac{6 \sum d_i^2}{n(n^2-1)}\).