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:

student t test statistics formula sample variance 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:
Step 1:
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

sample variance

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

Step 3:
Calculate the test statistic
student t test statistics formula

t= (3.25-8) / √(2.678571429 2 x (1/4 + 1/5)) t= -4.3265

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