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# How to Calculate One, Two Tailed P-Value Correlation - Definition, Formula, Example

## How to Calculate One, Two Tailed P-Value Correlation - Tutorial

##### Definition:

'r', its value varies between -1 and 1, 1 means perfect correlation, 0 means no correlation, positive values means the relationship is positive, negative values mean the relationship is negative. Also called correlation coefficient.

#### Formula:

t =                r                √[(1—r2)/(N—2)] df  = N-2 P (one and two tailed) = [ 1/ ( (√df) Β(1/2,df/2) ) ] lt->-t to t ∫ ( 1+ x²/df)(-(v+1)/2) .dx Where, t  = True Correlation r  = Observed (Pearson Correlation Coefficient) Value N = Sample Size df = Degrees of Freedom x  = t Value
##### Example :

If the sample test size is 12 and observed value is 0.8, calculate the r to P value.

##### Given :

Sample Size       = 12 Observed value = 0.8

r to P Value

##### Solution :
###### Step 1:

Let us first calculate the value of true correlation.

 t =              0.8 √[(1 - (0.8)2)/(12 - 2)] =              0.8 √[(0.36)/(10)] t = 4.216
###### Step 2:

Degrees of freedom Calculation: df = 10

###### Step 3:

P (one and two tailed) Calculation: P    = [ 1/ ( (√10) Β(1/2,10/2) ) ] lt->-t to 4.216 ∫ ( 1+ 4.216²/10)(-(v+1)/2) .4.216 one tailed = 0.000891 two tailed = 0.001782

##### Result :

P value one tailed = 0.000891 and two tailed = 0.001782