How to calculate critical values for R for a large dataset I have gone through various formulas but all were used for a small data set like 100, 200 rows, but I want to know how to calculate critical values of r for a large data set containing >5000 rows. 
I have calculated using T.INV(1-alpha/2,df)/((sqrt(T.INV(1-alpha/2)^2+df)), but this formula is for small data sets, when I used it for a large data set, mentioned above, I got results which were not expected.
 A: The t-statistic for testing whether a correlation coefficient differs from 0 is
$$t = \frac{r}{\sqrt{1-r^2}} \,\sqrt{n-2}$$
Squaring both sides:
$$t^2 = \frac{r^2}{1-r^2} \cdot (n-2)$$
$$\qquad = \frac{1}{1/r^2-1} \cdot (n-2)$$
so
$$ 1/r^2 = \frac{n-2}{t^2}+1 $$
or
$$r^2=\frac{t^2}{(n-2)+t^2}$$
i.e.
$$|r|=\frac{t}{\sqrt{t^2+(n-2)}}$$
Then if $\text{df}=n-2$ the critical value for $|r|$ should be correctly given by your formula (except you seem to be missing a ",df" in the second call to t.inv).
In a near-repost of this question you clarified that you felt that with $n>5000$ a correlation of $0.149$ should not be significant but that impression is incorrect. 
Even if we take $n=5000$, the t-statistic exceeds 10.5; this is vastly beyond what you could reasonably get with uncorrelated variables at that sample size.
Here's a simulation of a million correlations (assuming independent Gaussian variates) at n=5000:

We see that at n=5000 a sample correlation of 0.149 is far larger than we could reasonably get if the population correlation were 0. This is what statistical significance is about - it tells us that the null hypothesis value of 0 is not consistent with the data.
It may be that 0.149 is not practically important in some circumstances, but statistical significance does not imply practical importance.
To show that the distribution doesn't matter much at large sample sizes, I did similar (if smaller) simulations for 5000 pairs of uniform random variates, $t_3$ variates and exponential variates and for pairs where one was exponential and the other was $t_3$. All gave very similar distributions to the one above (there was a some variation in the very largest $|r|$ value but the overall shape, means and standard deviations were essentially identical). 
