Calculate P value for the correlation coefficient I would like to understand how people add the P value on a figure for means (Y axis) by age, volume or any other variable (x axis). How did they calculate the P value here?
Please check the following figure:  
 
(They draw scatter plot for FA by age in figure one and they have two P values for the control and for ASD). In those figures we have two P values? why and how?)
 A: The following is an excerpt from Miles and Banyard's (2007) "Understanding and Using Statistics in Psychology --- A Practical Introduction" on "Calculating the exact significance of a Pearson correlation in MS Excel": 

Inconveniently, this is not completely straightforward - Excel will
  not give us the exact p-value for any value of r. However, it will
  give the exact $p$-value for any value of $t$, and it’s not too hard to
  convert $r$ to $t$. The formula you need is this one:



And then you use the tdist() function in Excel. So, we have a value of
  $r = 0.44$, and $N = 19$. We can use Excel to turn the $r$ into $t$, so in the
  Excel sheet (at Cell A1, let’s say) we type: 

=(0.44 * sqrt(19 – 2))/(sqrt(1-0.44^2)) 

This gives a value of $t = 2.02$. We then use the
  tdist() function to find the associated $p$. We need to tell Excel 3
  things. First, the value of $t$, second, the degrees of freedom, which
  are equal to $N – 2 = 17$, and third, the number of tails – either 1 or
  2, and we always use 2 tails. If the value from the first calculation
  is stored in cell A1, we can write:
  =tdist(A1, 17, 2) Which gives a result of $p = 0.059$.
Should you ever want to calculate a critical value for a Pearson
  correlation, the process is reversed. You first calculate the critical
  value for $t$, and then you convert this into $r$. Let’s say we wanted to
  know the critical value for a correlation for $p = 0.05$. We first find
  the value of $t$ that gives a $p$ of $0.05$. We use the excel function
  tinv(). We need to tell Excel two things, the probability that we
  are interested in, and the degrees of freedom. Into cell A1 We type:
  =tinv(0.05, 17) Excel tells us that the answer is $2.11$. We then need
  to turn that into a value of r. The formula is the reverse of the one
  above, which takes a bit of algebra, so we’ll tell you what it is:



We type the formula into Excel =A1/(SQRT(A1 * A1 + 19 - 2 )) And we
  get the answer that the critical value is 0.0456.

References:


*

*"Understanding and Using Statistics in Psychology: A Practical Introduction" Google Books 

*How to Calculate the P-Value & Its Correlation in Excel ehow 
