Compare rankings using the Spearman Rho coefficient

[JojoSouza]

I would like to compare the ranking results of Methods 2, 3 and 4 with Method 1. In this regard, I would like to use the Spearman Rho coefficient. I would also like to know if a significant relationship between the results of methods 2, 3 and 4 with method 1. So how to do this?

database<-structure(list( 
Method1 = c(1L, 10L, 7L, 8L, 9L, 6L, 5L, 3L, 4L, 2L), Method2 = c(1L, 
8L, 6L, 7L, 10L, 9L, 4L, 2L, 5L, 3L), Method3 = c(1L, 
10L, 7L, 8L, 9L, 6L, 4L, 2L, 3L, 5L), Method4 = c(1L, 
9L, 6L, 7L, 10L, 8L, 5L, 3L, 2L, 4L)), class = "data.frame", row.names = c(NA, 
10L))

> database
   Method1 Method2 Method3 Method4
1        1       1       1       1
2       10       8      10       9
3        7       6       7       6
4        8       7       8       7
5        9      10       9      10
6        6       9       6       8
7        5       4       4       5
8        3       2       2       3
9        4       5       3       2
10       2       3       5       4

[williaml]

You could do them individually:

cor.test(database$Method1, database$Method2, method = 'spearman')

# results -----------
# Spearman's rank correlation rho
# 
# data:  database$Method1 and database$Method2
# S = 20, p-value = 0.001977
# alternative hypothesis: true rho is not equal to 0
# sample estimates:
#       rho 
#     0.8787879