library(MASS)
#size 100
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

#-----------------------------------------------------150--------------------------------------------------------




library(MASS)
#size 150
q<- 150 
rhoq <- 0.2 

set.seed(5)

m1 <- mvrnorm(n = q, mu = c(10, 5),
             Sigma = rbind(c(1, rhoq),
                           c(rhoq, 1)))

dq <- as.data.frame(m1) 

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

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

(uvq <- cor.test(dq$u, dq$v))

## 
##  Pearson's product-moment correlation
## 
## data:  dq$u and dq$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(uvq$p.value < 0.05, '有意', '有意でない')

## [1] "有意"

library(Hmisc)
rcorr(as.matrix(dq))

##      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の場合は判別結果が有意ではないのに対して150の場合は有意なので100と150では無相関検定結果が異なると言える