Statistical significance for ecological correlations With the advent of Covid-19, attempts are springing up to look for correlations across geographical and/or political areas between the rate of infection, hospitalization, death etc. and other ecological variables.
When we are looking at the 50 states, N = 50 (51, if DC is included). An online calculator gives .28 as the minimum value of Pearson’s r for significance at the .05 level (for both N = 50 and N = 51), which I still recall from some work I did on state-level correlations about a decade ago.
At the time, I recall reading somewhere that significance levels do not apply in this case, because they have to do with inferences from a sample to a population. However, in this case there is no such inference, because the sample is the population.
Another interpretation is that there is such an inference, the states being a sample from a hypothetical population, so significance levels are relevant.
Which of these two interpretations is correct, or does it depend on context?
 A: Description of a population. Correlation can be a useful descriptive statistic for a population. For example, one might have data on population density and Covid-19 hospitalizations during March '20 for the 50 US states + DC. The population is the 51 US jurisdictions.  
Then along with mean pop density and mean hospitalization rate, one might look at the Pearson correlation $\rho.$ No inference need be involved. The three numbers are descriptive of the population.
Inference from a sample to a population. With less assurance of meaningful accuracy, you might get these same numbers for a randomly chosen 15 of the 51. 
Then you might wonder what CI for the correlation of the 51 you might get from data on the 15. That is inference.
About correlation. Many of the inferences about
Pearson's $r$ are based on the assumption that both variables are normal. This may not be the case for variables like population density and Covid-19 hospitalizations.
Then you might use bootstrapping to get an idea how
well $rho$ (population correlation) is predicted by
$r$ (correlation for a random sample of $n.$
Below is a simulated population of $n=51$ pairs $(X_i,Y_i),$ with $\rho = 0.766.$ 
One style of 95% bootstrap confidence interval
$(0.0833, 0.9226)$ for $\rho$ is computed.
# Simulated Population
set.seed(2020)
x = rexp(51, .01) + 100
y = x^.7 + runif(51, -30,30) + 50
par(mfrow=c(1,2))
plot(x,y)
rho = cor(x,y);  rho
[1] 0.766022

# Bootstrap CI
set.seed(414)
n = 15;  B = 10^5;  r =numeric(B)
for(i in 1:B) {
 j = sample(1:51, n, rep=T)
 r[i] = r.re = cor(x[j],y[j]) }
mean(r)
[1] 0.6858627
CI = quantile(r, c(.025,.975)); CI
      2.5%      97.5% 
0.08325656 0.92260831 
hist(r, prob=T, br = 50, col="skyblue2", 
     main="Bootstrap Dist'n of Correlation")
  abline(v = rho)
  abline(v = mean(r),col="red")
  abline(v = CI, col="red", lty="dashed")
par(mfrow=c(1,1))

The following plots show the population and the
bootstrap distribution of $r$ for samples of
size $n=15.$

