- Thread starter Igor K
- Start date

I wonder if anyone can share her/his opinion as to whether results of the significance tests for r with small sample size should be distrusted too? Thank you.

Small simulation example to exemplify:

Code:

```
rr <- double(10000)
for(i in 1:10000){
a<-rnorm(3)
b<-rnorm(3)
rr[i]<-cor(a,b)
}
> sum(abs(rr)>.9)/10000
[1] 0.2804
```

So, if anything, a large correlation with a small sample size should make you distrust said result (and associated p-value) MORE and not less.

Code:

```
n <- 10000
m <- 3
rr <- double(n)
p <- double(n)
for(i in 1:n){
a<-rnorm(m)
b<-rnorm(m)
rr[i]<-cor(a,b)
p[i] <- cor.test(a, b)$p.value
}
hist(p)
```

If we are going to distrust the results it should be on the basis that it's difficult to assess whether the assumptions of the tests are met.

Thank you for your clear, helpful explanations. You are right, the r=0.999 was unnaturally high, because the correlation example was purely hypothetical (for educational purposes). In fact, when a chi-square test for association is applied for the same example, as a conservative non-parametric alternative, the p-value is 0.2.