Calculate the rank correlation coefficient of the given problem

In summary, the conversation discusses a problem and solution related to correlation, specifically Spearman's rank correlation coefficient. The formula for this coefficient is questioned for its validity and there is a request for proofs and alternative solutions. It is also mentioned that the expression ##m^3-m## is derived from properties of the Uniform Distribution. The conversation concludes with a mention of other measures for rank correlation and a request for notes on the provided links.
  • #1
chwala
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Homework Statement
See attached.
Relevant Equations
Spearman's rank correlation coefficient.
Find the problem and solution here; I am refreshing on this topic of Correlation.

1659967128371.png


The steps are pretty much clear..my question is on the given formula ##\textbf{R}##. Is it a generally and widely accepted formula or is it some form of improvised formula approach for repeated entries/data? How did they arrive at... ##m^3-m?## ... Any proofs? Supposing ##9## entries are repeated and ##1## entry is different would the formula still hold?
Are there other different ways of solving this particular problem?

Cheers...
 
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  • #2
chwala said:
Homework Statement:: See attached.
Relevant Equations:: Spearman's rank correlation coefficient.

Find the problem and solution here; I am refreshing on this topic of Correlation.

View attachment 305574

The steps are pretty much clear..my question is on the given formula ##\textbf{R}##. Is it a generally and widely accepted formula or is it some form of improvised formula approach for repeated entries/data? How did they arrive at... ##m^3-m?## ... Any proofs? Supposing ##9## entries are repeated and ##1## entry is different would the formula still hold?
Are there other different ways of solving this particular problem?

Cheers...
This just measures the degree to which the two rankings agree. There are other such measures:

https://en.wikipedia.org/wiki/Rank_correlation

https://en.wikipedia.org/wiki/Rank_correlation/Spearman%27sSpearman's ##\rho## as a particular caseEdit: I think the expression ##m^3 -m## comes from properties of the Uniform Distribution

Edit 2 : Per the article linked, this is the case, i.e., the expression ##m^3-m ## ad others are derived from the Uniform Distribution:
Ranks are just elements of permutations
of ##S_n## , the group of permutations of the elements in ##\{ 1,2,3,..n\} ##
 
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  • #3
Thanks...let me look at the links and make some short notes. Cheers.
 
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Related to Calculate the rank correlation coefficient of the given problem

1. What is the rank correlation coefficient?

The rank correlation coefficient, also known as Spearman's rank correlation coefficient, is a statistical measure that evaluates the strength and direction of the relationship between two ranked variables.

2. How is the rank correlation coefficient calculated?

The rank correlation coefficient is calculated by first assigning ranks to the data points for each variable. Then, the difference between the ranks for each pair of data points is squared and summed. Finally, the coefficient is calculated by dividing the sum of squared differences by the total number of pairs of data points.

3. What does a rank correlation coefficient of 0 indicate?

A rank correlation coefficient of 0 indicates that there is no correlation between the two variables. This means that there is no relationship between the ranks of the data points for each variable.

4. How do I interpret the value of the rank correlation coefficient?

The rank correlation coefficient can range from -1 to 1. A value of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other decreases. A value of 1 indicates a perfect positive correlation, meaning that as one variable increases, the other also increases. A value of 0 indicates no correlation.

5. Can the rank correlation coefficient be used for non-linear relationships?

Yes, the rank correlation coefficient can be used to measure the strength and direction of any type of relationship between two variables, whether it is linear or non-linear. This makes it a useful tool for analyzing data that does not follow a linear pattern.

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