Spearman’s Rank Correlation
SPEARMAN’S RANK CORRELATION
BY
NILOY MAJUMDAR
Table of Contents
1. INTRODUCTION 2. BIVARIATE DATA 3. ASSOCIATION AND CORRELATION 4. DEFINITION AND CALCULATION 5. RELATED QUANTITIES 6. INTERPRETATION 7. EXAMPLE 8. PEARSON’S PRODUCT-MOMENT CORRELATION COEFFICIENT 9. DETERMINING SIGNIFICANCE 10. CORRESPONDENCE ANALYSIS BASED ON SPEARMAN’S rho 11. REFERENCES
1. Introduction
Rank correlation is used quite extensively in school subjects other than mathematics, particularly geography and biology. There are two accepted measures of rank correlation, Spearman’s and Kendall’s; of these, Spearman’s is the more widely used.
In statistics, Spearman 's rank correlation coefficient or Spearman 's rho, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a non-parametric measure of statistical dependence between two variables. It assesses how well the relationship between two variables can be described using a monotonic function. If there are no repeated data values, a perfect Spearman correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other.
Spearman 's coefficient can be used when both dependent (outcome; response) variable and independent (predictor) variable are ordinal numeric, or when one variable is a ordinal numeric and the other is a continuous variable. However, it can also be appropriate to use Spearman 's correlation when both variables are continuous.
2. Bivariate Data
The data referred to in this paper are all bivariate. So each data item is reported in terms of the values of two attributes. These could, for example, be the heights and weights of 11-year old girls. In keeping with common convention, the two variables are referred to separately as X, with sample values , and Y, with sample values , or together as the bivariate distribution(X,Y) with sample values . A general
BY
NILOY MAJUMDAR
Table of Contents
1. INTRODUCTION 2. BIVARIATE DATA 3. ASSOCIATION AND CORRELATION 4. DEFINITION AND CALCULATION 5. RELATED QUANTITIES 6. INTERPRETATION 7. EXAMPLE 8. PEARSON’S PRODUCT-MOMENT CORRELATION COEFFICIENT 9. DETERMINING SIGNIFICANCE 10. CORRESPONDENCE ANALYSIS BASED ON SPEARMAN’S rho 11. REFERENCES
1. Introduction
Rank correlation is used quite extensively in school subjects other than mathematics, particularly geography and biology. There are two accepted measures of rank correlation, Spearman’s and Kendall’s; of these, Spearman’s is the more widely used.
In statistics, Spearman 's rank correlation coefficient or Spearman 's rho, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a non-parametric measure of statistical dependence between two variables. It assesses how well the relationship between two variables can be described using a monotonic function. If there are no repeated data values, a perfect Spearman correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other.
Spearman 's coefficient can be used when both dependent (outcome; response) variable and independent (predictor) variable are ordinal numeric, or when one variable is a ordinal numeric and the other is a continuous variable. However, it can also be appropriate to use Spearman 's correlation when both variables are continuous.
2. Bivariate Data
The data referred to in this paper are all bivariate. So each data item is reported in terms of the values of two attributes. These could, for example, be the heights and weights of 11-year old girls. In keeping with common convention, the two variables are referred to separately as X, with sample values , and Y, with sample values , or together as the bivariate distribution(X,Y) with sample values . A general
References: 1. Jmp For Basic Univariate And Multivariate Statistics: A Step-by-step Guide. Ann Lehman. 2. Myers, Jerome L.; Well, Arnold D. (2003), Research Design and Statistical Analysis (2nd ed.), Lawrence Erlbaum. 3. Maritz. J.S. (1981) Distribution-Free Statistical Methods, Chapman & Hall. ISBN 0-412-15940-6. 4. Yule, G.U and Kendall, M.G. (1950), "An Introduction to the Theory of Statistics", 14th Edition (5th Impression 1968). Charles Griffin & Co. 5. Piantadosi, J.; Howlett, P.; Boland, J. (2007) "Matching the grade correlation coefficient using a copula with maximum disorder", Journal of Industrial and Management Optimization.