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I have a set of data described by two qualitative variables. The data can therefore be analysed as a matrix, showing the intersections of the two variables' levels that have many (or few) occurrences.

I am looking for a measure to express the difference between two of such matrices  : the first, in which all intersections of the two variables are equally populated (uniform distribution), and the second, in which some intersections are much more (or much less) populated than others.

These are two matrices like the ones I have: counts of positive integers in all cells (r code).

m1 <- matrix(c(3,3,3,3,3,3,3,3,3), nrow = 3, ncol = 3)    
 
m2 <- matrix(c(6,0,3,3,6,3,0,0,6), nrow = 3, ncol = 3)

I want to express the idea the the first matrix is more uniform than the second. Is there a measure that I can use? I believe that there should be a straightforward answer, something like a generalisation of variance for matrices. I just want to be sure to get the right one.

I have a set of data described by two qualitative variables. The data can therefore be analysed as a matrix, showing how many occurrences there are at each intersection of the two variables' levels.

I am looking for a measure to express the difference between two such matrices: the first, in which all intersections of the two variables are equally populated (uniform distribution), and the second, in which some intersections are much more (or much less) populated than others. Here are two matrices like the ones I have: they are counts of positive integers in all cells (r code).

m1 <- matrix(c(3,3,3,
               3,3,3,
               3,3,3), nrow=3, ncol=3, byrow=TRUE)    
m2 <- matrix(c(6,3,0,
               0,6,0,
               3,3,6), nrow=3, ncol=3, byrow=TRUE)

I want to express the idea the the first matrix is more uniform than the second. Is there a measure that I can use? I believe that there should be a straightforward answer, something like a generalisation of variance for matrices. I just want to be sure to get the right one.

I have a set of data described by two qualitative variables (A and B). The data can therefore be analysed as a matrix, showing the intersections of the two variables' levels that have many (or few) occurrences (for example, A1 has many occurrences while B3 just a few).

I am looking for a measure to express the difference between two of such matrices : the first, in which all intersections of the two variables are equally populated (uniform distribution), and the second, in which some intersections are much more (or much less) populated than others (so a distribution with positive and/or negative peaks).

These are two matrices like the ones I have: counts of positive integers in all cells (r code).

m1 <- matrix(c(3,3,3,3,3,3,3,3,3), nrow = 3, ncol = 3)    

m2 <- matrix(c(6,0,3,3,6,3,0,0,6), nrow = 3, ncol = 3)

I want to express the idea the the first matrix is more uniform than the second. Is there a measure that I can use? I believe that there should be a straightforward answer, something like a generalisation of variance for matrices. I just want to be sure to get the right one.

I have a set of data described by two qualitative variables. The data can therefore be analysed as a matrix, showing the intersections of the two variables' levels that have many (or few) occurrences.

I am looking for a measure to express the difference between two of such matrices : the first, in which all intersections of the two variables are equally populated (uniform distribution), and the second, in which some intersections are much more (or much less) populated than others.

These are two matrices like the ones I have: counts of positive integers in all cells (r code).

m1 <- matrix(c(3,3,3,3,3,3,3,3,3), nrow = 3, ncol = 3)    

m2 <- matrix(c(6,0,3,3,6,3,0,0,6), nrow = 3, ncol = 3)

I want to express the idea the the first matrix is more uniform than the second. Is there a measure that I can use? I believe that there should be a straightforward answer, something like a generalisation of variance for matrices. I just want to be sure to get the right one.

I have a set of data described by two qualitative variables (A and B). The data can therefore be analysed as a matrix, showing the intersections of the two variables' levels that have many (or few) occurrences (for example, A1 has many occurrences while B3 just a few).

I am looking for a measure to express the difference between two of such matrices : the first, in which all intersections of the two variables are equally populated (uniform distribution), and the second, in which some intersections are much more (or much less) populated than others (so a distribution with positive and/or negative peaks).

Is there a measure that I can use? (Matrix covariance? Determinant of covariance?)

I have a set of data described by two qualitative variables (A and B). The data can therefore be analysed as a matrix, showing the intersections of the two variables' levels that have many (or few) occurrences (for example, A1 has many occurrences while B3 just a few).

I am looking for a measure to express the difference between two of such matrices : the first, in which all intersections of the two variables are equally populated (uniform distribution), and the second, in which some intersections are much more (or much less) populated than others (so a distribution with positive and/or negative peaks).

These are two matrices like the ones I have: counts of positive integers in all cells (r code).

m1 <- matrix(c(3,3,3,3,3,3,3,3,3), nrow = 3, ncol = 3)    

m2 <- matrix(c(6,0,3,3,6,3,0,0,6), nrow = 3, ncol = 3)

I want to express the idea the the first matrix is more uniform than the second. Is there a measure that I can use? I believe that there should be a straightforward answer, something like a generalisation of variance for matrices. I just want to be sure to get the right one.