# Calculating Spearman's Rho Value Matrix for 6x6 Matrix

• swartzism
In summary, the person is having trouble calculating the Spearman correlation matrix for a 15x6 matrix. They have found examples for calculating rho scores between two columns, but they need to replicate results from a white paper which generates a 6x6 correlation matrix T. They have tried using the Iman and Conover method, but are not sure how to produce the T matrix. They also mention that the matrix in question is not actually a Spearman's rank correlation, but rather the Pearson's coefficient matrix of R.
swartzism
So I'm interested in calculating the Spearman correlation matrix, but I am running into some issues. All of the examples I have found only calculate rho scores between two columns. I am trying to replicate results from a white paper (http://www.tandfonline.com/doi/abs/10.1080/03610918208812265?journalCode=lssp20) and they generate a 6x6 correlation matrix T for a 15x6 matrix R. I cannot figure out how they do this!

I know how to calculate Pearson's correlation coefficient in matrix form by performing R'*R and working on the resultant 6x6 matrix, but Spearman's doesn't seem clear how to produce this T matrix.

Any help on how I would go about generating this Spearman rank correlation matrix would be greatly appreciated!

The 15 x 6 matrix is matrix of sample data for 15 joint realizations of 6 random variables. The sample correlation matrix for 6 random variables is naturally 6 by 6.

I've also discovered that this is not a Spearman's rank correlation, although they claim it is. If you do the the Spearman's coefficient calculation between columns, you do not get the T matrix given. It is in fact the Pearson's coefficient matrix of R! I had a bug in my correlation calculation. I am now getting

1.00000 0.00000 0.00000 0.00000 0.00000 0.00000
0.09688 1.00000 0.00000 0.00000 0.00000 0.00000
-0.46671 -0.31292 1.00000 0.00000 0.00000 0.00000
-0.23352 0.07098 0.33767 1.00000 0.00000 0.00000
0.26142 0.48383 -0.19696 -0.04125 1.00000 0.00000
0.17479 -0.22700 0.19021 -0.02984 0.05223 1.00000

As expected.

## What is Spearman's Rho Value Matrix?

Spearman's Rho Value Matrix is a statistical method used to measure the strength of a relationship between two variables. It is based on the ranks of the data rather than the actual values and is commonly used when the data is not normally distributed.

## How does Spearman's Rho Value Matrix work?

Spearman's Rho Value Matrix is calculated by first ranking the data for each variable from lowest to highest. Then, the difference between the ranks for each pair of data points is calculated. These differences are then squared and summed to obtain a sum of ranks difference. This value is then used to calculate the Spearman's Rho value, which ranges from -1 to 1, with a value of 0 indicating no correlation and values closer to 1 or -1 indicating a stronger correlation.

## When should Spearman's Rho Value Matrix be used?

Spearman's Rho Value Matrix is typically used when the data is not normally distributed or when there are outliers present. It is also useful when the relationship between the two variables is non-linear.

## What are the advantages of using Spearman's Rho Value Matrix?

One advantage of using Spearman's Rho Value Matrix is that it is not affected by outliers as much as other correlation measures. It is also less affected by non-normal data. Additionally, it can be used for both continuous and ordinal data.

## Are there any limitations to using Spearman's Rho Value Matrix?

One limitation of Spearman's Rho Value Matrix is that it does not take into account the magnitude of the differences between the ranks, only the direction of the relationship. It also may not be as sensitive as other correlation measures in detecting a relationship.

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