# How to utilize Spearman Rho coefficient

The dataset below presents the ranking of different multicriteria methods. My idea is to generate a final ranking based on the multicriteria methods for all alternatives, but it can be seen that in some cases both methods presented the same results as is the case for the alternative with 2 clusters. For the alternative with 5 clusters, they presented different rankings. I spoke to an expert on this and he said the following: "My advice to you is this: Compare the MCDM ranking results you find statistically with a third party. In this sense, you can use the Spearman Rho coefficient".

Do you know how I can use this coefficient in R in this dataset below?

df1<-structure(list(nclusters = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25), Promethee = c(1L,
6L, 4L, 5L, 2L, 3L, 23L, 24L, 22L, 21L, 20L, 19L, 17L, 18L, 9L,
10L, 11L, 12L, 13L, 14L, 15L, 16L, 8L, 7L), WSM = c(1, 24, 20,
19, 18, 17, 23, 22, 21, 16, 15, 14, 13, 12, 7, 6, 5, 4, 11, 10,
9, 8, 3, 2), TOPSIS = c(1L, 24L, 20L, 21L, 18L, 19L, 22L, 23L,
17L, 16L, 15L, 14L, 12L, 13L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L,
3L, 2L), VIKOR = c(1L, 24L, 19L, 20L, 17L, 18L, 22L, 23L, 21L,
16L, 15L, 14L, 12L, 13L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 3L,
2L)), class = "data.frame", row.names = c(NA, -24L))

> df1
nclusters Promethee WSM TOPSIS VIKOR
1          2         1   1      1     1
2          3         6  24     24    24
3          4         4  20     20    19
4          5         5  19     21    20
5          6         2  18     18    17
6          7         3  17     19    18
7          8        23  23     22    22
8          9        24  22     23    23
9         10        22  21     17    21
10        11        21  16     16    16
11        12        20  15     15    15
12        13        19  14     14    14
13        14        17  13     12    12
14        15        18  12     13    13
15        16         9   7      4     4
16        17        10   6      5     5
17        18        11   5      6     6
18        19        12   4      7     7
19        20        13  11      8     8
20        21        14  10      9     9
21        22        15   9     10    10
22        23        16   8     11    11
23        24         8   3      3     3
24        25         7   2      2     2

• I'm not sure what your expert meant by "third party". Possibly he meant showing the original criteria values (not shown above) to an subject area expert, asking the expert to rank the cluster counts from best to worst, then computing the Spearman correlation between the subject area expert's ranking and each of your computed rankings ... though to what end is again unclear.
– prubin
Feb 25, 2022 at 17:45
• Crossposted on Math.SE: How to utilize Spearman Rho coefficient Mar 16, 2022 at 22:44