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))
(uv <- cor.test(d$u,d$v))
## 
##  Pearson's product-moment correlation
## 
## data:  d$u and d$v
## t = 1.012, df = 98, p-value = 0.3141
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.09665551  0.29227338
## sample estimates:
##       cor 
## 0.1016932
ifelse(uv$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
## u 1.0 0.1
## v 0.1 1.0
## 
## n= 100 
## 
## 
## P
##   u      v     
## u        0.3141
## v 0.3141
library(MASS)

n0   <- 150
rho0 <- 0.2

set.seed(5)

m0 <- mvrnorm(n = n0,mu = c(10,5),
             Sigma = rbind(c(1,rho0),
                           c(rho0,1)))

d0 <- as.data.frame(m0)

colnames(d0) <- c('U','V')

library(DT)
datatable(round(d0,2))
(uv0 <- cor.test(d0$U,d0$V))
## 
##  Pearson's product-moment correlation
## 
## data:  d0$U and d0$V
## t = 2.888, df = 148, p-value = 0.004459
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.07343229 0.37727185
## sample estimates:
##       cor 
## 0.2309756
ifelse(uv0$p.value < 0.05,'有意','有意でない')
## [1] "有意"
library(Hmisc)
rcorr(as.matrix(d0))
##      U    V
## U 1.00 0.23
## V 0.23 1.00
## 
## n= 150 
## 
## 
## P
##   U      V     
## U        0.0045
## V 0.0045

検定結果

# 100の場合は有意でないのに対して、150の場合は有意なので100と150では無相関検定結果は異なる