# How to Calculate Unpaired Student T Test Statistics - Tutorial

## Calculate Unpaired Student T Test Statistics - Definition, Formula, Example

##### Definition:

Unpaired student test is a method in statistic to evaluate the difference between two means.

#### Formula:  Where X1 - Group one data, X2 - Group two data, t - test statistic n1,n2 - Group values count
##### Example:

Consider the gain in weight of 10 female rats between 28 and 84 days after birth. 5 were fed on a high protein diet and 5 on a low protein diet. Calculate t test statistics.

##### Given:
Group 1Group 2
16
37
48
59
10

Group one count n1=4 Group two count n2=5

##### Solution:
###### Calculate mean value

Mean of X1 = ∑ X1/n1 = (1+3+4+5) = 13/4 = 3.25 Mean of X2 = ∑ X2/n2 = 6+7+8+9+10 = 40/5 = 8

###### Step 2:

Calculate sample variance s2 n1 ∑ (xj - X1)2 = (1-3.25)2+(2-3.25)2+(3-3.25)2+(4-3.25)2+(5-3.25)2 = 8.75 j=1 n2 ∑ (xi - X2)2 = (6-8)2+(7-8)2+(8-8)2+(9-8)2+(10-8)2 = 10 i=1 s2 = 8.75+10 / (4 + 5 - 2) = 18.75/7 = 2.678571429

###### Calculate the test statistic t= (3.25-8) / √(2.678571429 2 x (1/4 + 1/5)) t= -4.3265