無相関検定

演習課題

d <- data.frame(
  u = c(7, 4, 6, 2, 9, 3, 8, 1, 6, 3),
  v = c(3, 6, 5, 8, 3, 4, 2, 9, 2, 6),
  w = c(6, 3, 4, 9, 1, 8, 4, 2, 5, 7))

library(DT)

datatable(d)

x <- c(1, 2, 3, 5)
y <- c(0, 3, 3, 6)

cor(x, y)

## [1] 0.9561829

cor(d$u, d$v)

## [1] -0.851136

cor(d$u, d$v, method = 'spearman')

## [1] -0.836927

cor(d$u, d$v, method = 'kendall')

## [1] -0.7059312

r <- cor(d)
r

##            u          v          w
## u  1.0000000 -0.8511360 -0.4151543
## v -0.8511360  1.0000000  0.1015166
## w -0.4151543  0.1015166  1.0000000

library(kableExtra)
kable(round(r, 2), caption = '相関表') |> kable_classic('striped', full_width = F)

相関表

	u	v	w
u	1.00	-0.85	-0.42
v	-0.85	1.00	0.10
w	-0.42	0.10	1.00

library(psych)

pairs.panels(d)

cor.plot(d)

library(corrplot)

## corrplot 0.92 loaded

corrplot.mixed(r, lower = 'ellips', upper = 'number')

library(plotly)

kyokasho <- list(size = 11, color = 'blue', family = 'UD Digi Kyokasho NK-R')

plot_ly(x = rownames(r),
        y = colnames(r),
        z = as.matrix(r),
        text = paste(r),
        type = 'heatmap') |>
  layout(font = kyokasho,
         title = '主タイトル',
         xaxis = list(title = 'x軸カテゴリラベル'),
         yaxis = list(title = 'y軸カテゴリラベル'))

(uv <- cor.test(d$u, d$v))

## 
##  Pearson's product-moment correlation
## 
## data:  d$u and d$v
## t = -4.586, df = 8, p-value = 0.001788
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.9641022 -0.4772863
## sample estimates:
##       cor 
## -0.851136

ifelse(uv$p.value < 0.05, '有意', '有意でない')

## [1] "有意"

(uw <- cor.test(d$u, d$w))

## 
##  Pearson's product-moment correlation
## 
## data:  d$u and d$w
## t = -1.2907, df = 8, p-value = 0.2329
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.8282759  0.2903733
## sample estimates:
##        cor 
## -0.4151543

ifelse(uw$p.value < 0.05, '有意', '有意でない')

## [1] "有意でない"

(vw <- cor.test(d$v, d$w))

## 
##  Pearson's product-moment correlation
## 
## data:  d$v and d$w
## t = 0.28862, df = 8, p-value = 0.7802
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.5641701  0.6872176
## sample estimates:
##       cor 
## 0.1015166

ifelse(vw$p.value < 0.05, '有意', '有意でない')

## [1] "有意でない"

library(Hmisc)

rcorr(as.matrix(d))

##       u     v     w
## u  1.00 -0.85 -0.42
## v -0.85  1.00  0.10
## w -0.42  0.10  1.00
## 
## n= 10 
## 
## 
## P
##   u      v      w     
## u        0.0018 0.2329
## v 0.0018        0.7802
## w 0.2329 0.7802

library(MASS)

n   <- 100
rho <- 0.2 

set.seed(5)

m <- mvrnorm(n = n, mu = c(10, 5),
             Sigma = rbind(c(1, rho),
                           c(rho, 1)))

d <- as.data.frame(m) 

colnames(d) <- c('u', 'v')

library(DT)
datatable(round(d, 2))