##This file contains R code for performing statistical tests on ring data presented in the manuscript.
##For specific independence tests, the data is provided in Supplemental Table 1 and the excel file Ring_Data_SEARCH.


library(readxl)

setwd("~[set path to file]")


##Statistical Tests on Averaged Values (by density cluster group)

##Friedman Test on difference between identified and known ring sites
ring_matrix <- matrix(c(64, 57, 32,
                        86, 77, 60,
                        35, 27.5, 18,
                        33, 27, 215),
                      nrow = 4,
                      byrow = TRUE)



friedman.test(ring_matrix)
SC_ring_matrix <- matrix(c(64, 57, 32,
                        35, 27.5, 18,
                        33, 27, 15),
                      nrow = 3,
                      byrow = TRUE)

friedman.test(SC_ring_matrix)

ring_dist_matrix <- matrix(c(549.1037, 31.22222222, 24.33333333, 11, 2.555556,
                             691.5765, 41.9375, 32, 20.375, 2.750000,
                             749.6754, 39.94736842, 30.63157895, 19.15789474, 2.421053,
                             1394.4871, 43.85714286, 29.14285714, 16.14285714, 1.714286),
                           nrow = 4,
                           byrow = TRUE)


friedman.test(ring_dist_matrix)


Arc_dist_matrix <- matrix(c(549.1037, 2.555556,
                            691.5765, 2.750000,
                            749.6754, 2.421053,
                            1394.4871, 1.714286),
                           nrow = 4,
                           byrow = TRUE)


wilcox.test(Arc_dist_matrix)

shapiro.test(ring_group$DIST_M_mean)
cor.test(ring_group$DIST_M_mean, ring_group$Arc_height_mean, method = c("kendall"))

elev_dist_matrix <- matrix(c(549.1037, 7.855713,
                             691.5765, 4.252152,
                             749.6754, 2.972602,
                             1394.4871, 1.608039),
                           nrow = 4,
                           byrow = TRUE)

wilcox.test(elev_dist_matrix)               

vol_dist_matrix <- matrix(c(549.1037, 1314.157,
                            691.5765, 1756.283,
                            749.6754, 1813.906,
                            1394.4871, 1271.953),
                          nrow = 4,
                          byrow = TRUE)

wilcox.test(vol_dist_matrix)

volrat_dist_matrix <- matrix(c(549.1037, 0.7731943,
                            691.5765, 0.5898152,
                            749.6754, 0.6419694,
                            1394.4871, 0.4314737),
                          nrow = 4,
                          byrow = TRUE)

wilcox.test(volrat_dist_matrix)



##Statistical tests on individual rings##

rings <- read_excel("~[add path]/Ring_data_SEARCH.xls")     #data used for analysis is found in supplemental table 1


wilcox.test(rings$MSH_DIST_M, rings$MAX_DIAM, alternative = "two.sided")

wilcox.test(rings$MSH_DIST_M, rings$MIN_DIAM, alternative = "two.sided")

wilcox.test(rings$MSH_DIST_M, rings$PLAZA_DIAM, alternative = "two.sided")

wilcox.test(rings$MSH_DIST_M, rings$Arc_height, alternative = "two.sided")

wilcox.test(rings$MSH_DIST_M, rings$VOL_M, alternative = "two.sided")

wilcox.test(rings$MSH_DIST_M, rings$`VOL/AREA_M`, alternative = "two.sided")

wilcox.test(rings$MSH_DIST_M, rings$SUIT_R1, alternative = "two.sided")


wilcox.test(rings$DIST_M, rings$MAX_DIAM, alternative = "two.sided")

wilcox.test(rings$DIST_M, rings$MIN_DIAM, alternative = "two.sided")

wilcox.test(rings$DIST_M, rings$PLAZA_DIAM, alternative = "two.sided")

wilcox.test(rings$DIST_M, rings$Arc_height, alternative = "two.sided")

wilcox.test(rings$DIST_M, rings$VOL_M, alternative = "two.sided")

wilcox.test(rings$DIST_M, rings$`VOL/AREA_M`, alternative = "two.sided")