T Critical Value Calculator

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

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