In: Statistics and Probability
You are running correlation analysis on a data set with 11 items. You calculate the correlation coefficient to be 0.845.
What is the critical value?
The formula for the test statististic is :-
where r = correlation coefficient
n = sample size
So,  
, the value of the test statistic.
This , 
 distribution.
let, the level of significance be 
. Then, if your test is a two sided test ( i.e, 
 ) then, the critical value formula is :

otherwise ( i.e for  
or  
) ,  the critical value formula is :   
  
Suppose, 
 and the test is a two sided test. Then, critical value :

for one sided test , the critical value is :
  