The Spearman's Correlation Bundle: all questions and answers

 

Spearman's Correlation Bundle:

Bundle items:
Applying spearman's correlation - Theme

Applying spearman's correlation - Theme

What does the Speaman Correlation measure?

  • The Spearman correlation (denoted as p (rho) or rs) measures the strength and direction of association between two ranked variables.
  • It is most commonly used to measure the degree and direction of a linear relation between two variables that are of the ordinal type.

What are the assumptions of the Spearman Correlation test?

  • two variables that are either ordinal, interval or ratio (note: if the data are interval or ratio, normally you would use a Pearson correlation test)
  • the relationship between the variables is monotonic, or (curvi)linear
Spearman's Correlation

Spearman's Correlation

Spearman's Correlation

Table of content

  • When to use the Spearman Correlation test
  • What does the Speaman Correlation measure?
  • What are the assumptions of the Spearman
  • Spearman Correlation formula
  • What is the definition of the Spearman Correlation test?
  • Example: how to calculate Spearman Correlation?
Example: how to calculate Spearman Correlation?

Example: how to calculate Spearman Correlation?

Sample question

The scores for nine students in history and algebra are as follows:

  • History: 35, 23, 47, 17, 10, 43, 9, 6, 28
  • Algebra: 30, 33, 45, 23, 8, 49, 12, 4, 31

Compute the Spearman rank correlation.

Answer

  1. Step 1: rank each student
Student #History ScoreHistory RankAlgebra ScoreAlgebra Rank
1353305
2235333
3471452
4176236
510788
6432491
798127
86949
9284314
  1. step 2: calculate difference between the ranks (d) and square d
Student #History ScoreHistory RankAlgebra ScoreAlgebra Rankdd2
135330524
223533324
347145211
417623600
51078811
643249111
79812711
8694900
928431400
  1. step 3: sum (add up) all the d2 scores
  • Σ d2 =
......read more
Activities abroad, study fields and work areas: 
Spearman Correlation formula

Spearman Correlation formula

What is the definition of the Spearman Correlation test?

\[\rho = r_s = 1 - \frac{6\sum{d^2_i}}{n(n^2-1)}\]

  • p : Spearman correlation
  • rs : Spearman correlation
  • di : rg(Xi) - rg(Yi): difference between the two ranks of each observation (for example, one can have the second best score on variable X, but the ninth on variable Y.)
  • n : number of scores

Note: if there are tied ranks, the following method can be used to calculate the Spearman Correlation:

\[\rho = \frac{\sum_i (x_i - \bar{x})(y_i - \bar{y})}{\sqrt {\sum_i (x_i - \bar{x})^2 \sum_i (y_i - \bar{y})^2}}\]

  • x : value of x
  • x̄ : mean of x
  • y : value of y
  • ȳ : mean of y
...read more
Activities abroad, study fields and work areas: 
Wat houden de Spearman Correlation & Kendall’s Tau in? (34)
When to use the Spearman Correlation test

When to use the Spearman Correlation test

What does the Speaman Correlation measure?

  • The Spearman correlation (denoted as p (rho) or rs) measures the strength and direction of association between two ranked variables.
  • It is most commonly used to measure the degree and direction of a linear relation between two variables that are of the ordinal type.

What are the assumptions of the Spearman Correlation test?

  • two variables that are either ordinal, interval or ratio (note: if the data are interval or ratio, normally you would use a Pearson correlation test)
  • the relationship between the variables is monotonic, or (curvi)linear
...read more
Activities abroad, study fields and work areas: 
Statistics: summaries and study assistance - Theme
Supporting content & Crossroads:
Statistics: summaries and study assistance - Theme
Access: 
Public
Check all content related to:
Follow the author: Statistics Supporter
Contributions, Comments & Kudos

Add new contribution

CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Image CAPTCHA
Enter the characters shown in the image.
Statistics
98