rank correlation

(noun)

Any of several statistics that measure the relationship between rankings of different ordinal variables or different rankings of the same variable.

Related Terms

Examples of rank correlation in the following topics:

  • Rank Correlation

    • A rank correlation is a statistic used to measure the relationship between rankings of ordinal variables or different rankings of the same variable.
    • An increasing rank correlation coefficient implies increasing agreement between rankings.
    • This means that we have a perfect rank correlation and both Spearman's correlation coefficient and Kendall's correlation coefficient are 1.
    • This graph shows a Spearman rank correlation of 1 and a Pearson correlation coefficient of 0.88.
    • Define rank correlation and illustrate how it differs from linear correlation.

  • Rank Correlation

    • A rank correlation is any of several statistics that measure the relationship between rankings.
    • Spearman developed a method of measuring rank correlation known as Spearman's rank correlation coefficient.
    • There are three cases when calculating Spearman's rank correlation coefficient:
    • This formula for d that occurs in Spearman's rank correlation formula.
    • Evaluate the relationship between rankings of different ordinal variables using rank correlation

  • Comparing Two Populations: Independent Samples

    • Nonparametric independent samples tests include Spearman's and the Kendall tau rank correlation coefficients, the Kruskal–Wallis ANOVA, and the runs test.
    • Nonparametric methods for testing the independence of samples include Spearman's rank correlation coefficient, the Kendall tau rank correlation coefficient, the Kruskal–Wallis one-way analysis of variance, and the Walk–Wolfowitz runs test.
    • Spearman's rank correlation coefficient, often denoted by the Greek letter $\rho$ (rho), is a nonparametric measure of statistical dependence between two variables.
    • If the agreement between the two rankings is perfect (i.e., the two rankings are the same) the coefficient has value $1$.
    • If the disagreement between the two rankings is perfect (i.e., one ranking is the reverse of the other) the coefficient has value $-1$.

  • Rank Randomization for Association (Spearman's ρ)

    • The rank randomization test for association is equivalent to the randomization test for Pearson's r except that the numbers are converted to ranks before the analysis is done.
    • Table 2 shows these same data converted to ranks (separately for X and Y).
    • The approach is to consider the X variable fixed and compare the correlation obtained in the actual ranked data to the correlations that could be obtained by rearranging the Y variable.
    • The correlation of ranks is called "Spearman's ρ. "
    • Therefore, there are five arrangements of Y that lead to correlations as high or higher than the actual ranked data (Tables 2 through 6).

  • When to Use These Tests

    • "Ranking" refers to the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
    • In statistics, "ranking" refers to the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
    • In these examples, the ranks are assigned to values in ascending order.
    • Some kinds of statistical tests employ calculations based on ranks.
    • Some ranks can have non-integer values for tied data values.

  • Distribution-Free Tests

    • Order statistics, which are based on the ranks of observations, are one example of such statistics.
    • Spearman's rank correlation coefficient: measures statistical dependence between two variables using a monotonic function.
    • Squared ranks test: tests equality of variances in two or more samples.
    • Wilcoxon signed-rank test: tests whether matched pair samples are drawn from populations with different mean ranks.
    • Non-parametric statistics is widely used for studying populations that take on a ranked order.

  • Descriptive and Correlational Statistics

    • Research has shown that alcohol dependence correlates with depression.
    • Correlation does not necessarily prove causation.
    • A correlational study can only describe or predict behavior, but cannot explain the behavior.
    • As an example of a correlational study, research has shown that alcohol dependence correlates with depression.
    • If the data set is an odd number, then it is the middle value once the data values are ranked.

  • The Bottom Line: Family Background

    • Student achievement is highly correlated with family characteristics, including household income and parental educational attainment.
    • What's more, because colleges want to maintain their rankings in various college ranking systems (e.g., U.S.

  • Setting Objectives and Standards

    • If any of these are not complete or correlative, management must redefine and re-think what the company stands for.
    • The items listed may be organized in a hierarchy of means and ends and numbered as follows: Top Rank Objective (TRO), Second Rank Objective, Third Rank Objective, etc.
    • From any rank, the objective in a lower rank answers the question "How?
    • " and the objective in a higher rank answers the question "Why?"
    • The exception is the Top Rank Objective (TRO): there is no answer to the "Why?"

  • Properties of Pearson's r

    • State the relationship between the correlation of Y with X and the correlation of X with Y
    • A correlation of -1 means a perfect negative linear relationship, a correlation of 0 means no linear relationship, and a correlation of 1 means a perfect positive linear relationship.
    • Pearson's correlation is symmetric in the sense that the correlation of X with Y is the same as the correlation of Y with X.
    • For example, the correlation of Weight with Height is the same as the correlation of Height with Weight.
    • For instance, the correlation of Weight and Height does not depend on whether Height is measured in inches, feet, or even miles.