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T Critical Value Calculator - Online Calculator - Tutorpace

# T Critical Value Calculator

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T Critical Value calculator is used to calculate the critical values for a given area for one and two tailed probabilities. It also tells degrees of freedom. This calculates as a hypothesis of statistics test and it follows a normal distribution if the values follow the t distribution.

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

Example 1: Using t critical value calculator  solve following;

X1 = 1,2,3,4,5 ; X2 = 3,4,5,6,7

Mean of x1 = 1+2+3+4+5/5= 15/5=3

Mean of x2= 3+4+5+6+7/5= 25/5 =5

Standard deviation for x1

1.      Sum (x1-mean x1)2 = (1-3)2+(2-3)2+(3-3)2+(4-3)2+(5-3)2 = 4+1+0+1+4= 10

2.      Sum (x2-mean x2)2 = (3-5)2+(4-5)2+(5-5)2+(6-5)2+(7-5)2 = 4+1+0+1+4= 10

3.      Standard deviation x1= s12= 10/5= 2

4.      Standard deviation x2= s22= 10/5=2

T critical value

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

3 -5/√/(2/5+ 2/5) = -2/√4/5=  -2/0.8= - 1/0.4= - 2.5

Example 2: Using t critical value calculator  solve following;

X1 = 5,22,3 ; X2 = 2,6

Mean of x1 = 5+22+3/3= 30/3=10

Mean of x2= 2+6/2= 8/2 =4

Standard deviation for x1

1.      Sum (x1-mean x1)2 = (5-10)2+(22-10)2+(3-10)2= 25+144+49= 218

2.      Sum (x2-mean x2)2 = (2-4)2+(6-4)2= 4+4= 8

3.      Standard deviation x1= s12= 218/3= 72.67

4.      Standard deviation x2= s22= 8/2=4

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

10-4/√/(72.67/3+ 4/2) = -6/√26.2=  -6/5.12= - 1.171875