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(MASS)

n   <- 150
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('y', 'c')

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

(yc <- cor.test(d$y, d$c))

## 
##  Pearson's product-moment correlation
## 
## data:  d$y and d$c
## 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(yc$p.value < 0.05, '有意', '有意でない')

## [1] "有意"

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