T Test Calculator

T test calculator is used to calculate a statistical hypothesis test where the test statistic follows a students t distribution. This is done only when the null hypothesis is supported. t = (mean(x1) – mean(x2)) / √ (s1²/n1 + s2²/n2)

= difference between means of 2 samples/ (variance / sample size). 


Example 1: Using t test calculator solve the following;

X1 = 2,4,6,8 ; X2 = 3,6,9,12

Mean of x1 = 2+4+6+8/4= 20/4=5

Mean of x2= 3+6+9+12/4= 30/4 =7.5

Standard deviation for x1

1.      Sum (x1-mean x1)² = (2-5)²+(4-5)²+(6-5)²+(8-5)²= 9+1+1+9= 20

2.      Sum (x2-mean x2)² = (3-7.5)²+(6-7.5)²+(9-7.5)²+(12-7.5)²= 20.25+2.25+2.25+20.25= 45

3.      Standard deviation x1= s1²= 20/4= 5

4.      Standard deviation x2= s2²= 45/4=11.25

T critical value

T = (mean(x1) – mean(x2))/√(s1²/n1 + s2²/n2)

5-7.5/√/(5/4+ 11.25/4) = -2.5/√16.25/4=  -2.5/2.015 = - 1/0.4 = -1.240



Example 2: Using t test calculator  solve following;

X1 = 4,5.5,2.5 ; X2 = 4.5,14

 Mean of x1 = 4+5.5+2.5= 12/3=4

Mean of x2= 4.5+14/2= 18.5/2 =9.25

Standard deviation for x1

1.      Sum (x1-mean x1)² = (4-4)²+(5.5-4)²+(2.5-4)²= 0+2.25+6.25= 8.5

2.      Sum (x2-mean x2)² = (4.5- 9.25)²+(14 -9.25)²= 22.5625+22.5625= 45.125

3.      Standard deviation x1= s1²= 8.5/3= 2.83

4.      Standard deviation x2= s2²= 45.125/2=22.5625

T = (mean(x1) – mean(x2))/√(s1²/n1 + s2²/n2)

4-9.25/√/(2.83/3+ 22.5625/2) = -5.25/√10.33825=  -5.25/3.215= - 1.632970