Dittenberger then examined Plato’s use of comparative particles (ὥσπερ and καθάπερ), but the results are fuzzy at best (pp. 19-20). B. tries (p. 19) to make them more precise by noting a decreasing rate, counted as uses per page, from Euthd., Meno, Gorg., Crat., Phdo., Symp., Lysis (0.80) to Phdr., Rep., Theaet. (0.61), and thence to Parm., Phil., Soph., Pol., Tim., Crit., and Laws (0.40). In … comparing the three numbers [B.] claims a clear trend but he fails to determine whether it is in fact statistically significant. Briefly the uncertainty σ for each ratio would be respectively 0.80 ± 0.15, 0.61 ± 0.08, and 0.40 + 0.07, and the level of significance of the pairwise differences would be z = 1.1 (73 % ) and z = 2.0 (95 %).

Clearly there can be no doubt of the direction of the trend.

z1 <- (0.8 - 0.61) / sqrt( 0.15^2 + 0.08^2) # 1.1
z2 <- (0.61 - 0.4) / sqrt( 0.08^2 + 0.07^2) # 1.97

pnorm(abs(z1), lower.tail = F) * 2 # 27%
pnorm(abs(z2), lower.tail = F) * 2 # 5%

That is, those are the probabilities that the difference is significant—and most statisticians would consider anything less than 95% (I and most physicists prefer 99%) as insignificant. B. calculates (pp. 21-2) various ratios, which suffer from the same defect.

library(stylo)
library(dendextend)

data("galbraith")
data <- as.data.frame.matrix(galbraith)[c(1,2, 9, 10, 16, 17),c(1:30)]
distmx <- dist(scale(data))

d1 <- as.dendrogram(hclust(distmx, method ="average")) %>% set("labels_col", value = c("skyblue", "orange", "grey40"), k=3) %>% set("branches_k_color", value = c("skyblue", "orange", "grey40"), k = 3)

d2 <- as.dendrogram(hclust(distmx, method ="ward.D2")) %>% set("labels_col", value = c("skyblue", "orange", "grey40"), k=3) %>% set("branches_k_color", value = c("skyblue", "orange", "grey40"), k = 3)

dlist <- dendlist(d1, d2)

par(family = "Arial Bold")
tanglegram(dlist, common_subtrees_color_lines = FALSE, highlight_distinct_edges  = TRUE, highlight_branches_lwd=FALSE, margin_inner=10, lwd=2, axes=FALSE, main_left = "Cредняя", main_right = "Уорд", lab.cex = 1.3)

Under the FEATURES tab, users can define the minutes of the MFW division and sampling procedure, using the increment, the minimum and maximum parameters. For minimum = 100, maximum = 3000, and increment = 50, stylo will run subsequent analyses for the following frequency bands: 100 MFW, 50–150 MFW, 100–200 MFW, ..., 2900–2950 MFW, 2950–3000 MFW.

library(stylo)
library(ape)
library(purrr)

data("galbraith")
df <- as.data.frame.matrix(galbraith)[c(1,2, 9, 10, 16, 17),]

get_tree <- function(df) {
  X <- df[ , sample(3000, replace = T, size = 100)]
  distmx <- dist(scale(X))
  tr <- as.phylo(hclust(distmx))
  tr
  }

set.seed(123)
result <- map(1:4, ~get_tree(df))

# отдельные деревья
par(mfrow = c(2, 2), mar = c(1,1,1,1))
map(1:4, ~print(plot(result[[.]])))