F Test Example

F Test is generally defined as ratio of the variances of the given two set of values. First calculate standard deviation and variation of the given set of values. The formula used to calculate SD is,
Standard Deviation Formula

The standard deviation is represented by the symbol ᵟ and variance is square of the standard deviation.
The formula used to calculate F Test is,
F Test Formula


For Example:
Calculate F Test for given 10,20,30,40,50 and 5,10,15,20,25.
For 10, 20,30,40,50:

Calculate Variance of first set

Total Inputs (N) =(10,20,30,40,50)
Total Inputs (N)=5
Mean (xm)= (x₁+x₁+x₂...x_n)/N
Mean (xm)= 150/5
Means(xm)= 30
SD=sqrt(1/(N-1)*((x₁-xm)²+(x₂-x_m)²+..+(x_n-x_m)²))
=sqrt(1/(5-1)((10-30)²+(20-30)²+(30-30)²+(40-30)²+(50-30)²))
=sqrt(1/4((-20)²+(-10)²+(0)²+(10)²+(20)²))
=sqrt(1/4((400)+(100)+(0)+(100)+(400)))
=sqrt(250)
=15.8114
Variance=SD²
Variance=15.8114²
Variance=250

Calculate Variance of second set
For 5, 10,15,20,25:
Total Inputs(N) =(5,10,15,20,25)
Total Inputs(N)=5
Mean (xm)= (x1+x2+x3...xN)/N
Mean (xm)= 75/5
Means (xm)= 15
SD=sqrt(1/(N-1)*((x₁-x_m)²+(x₂-x_m)²+..+(x_n-x_m)²))
=sqrt(1/(5-1)((5-15)²+(10-15)²+(15-15)²+(20-15)²+(25-15)²))
=sqrt(1/4((-10)²+(-5)²+(0)²+(5)²+(10)²))
=sqrt(1/4((100)+(25)+(0)+(25)+(100)))
=sqrt(62.5)
=7.9057
Variance=SD²
Variance=7.9057²
Variance=62.5

To calculate F Test
F Test = (variance of 10, 20,30,40,50) / (variance of 5, 10, 15, 20, 25)
= 250/62.5
= 4.

The F Test value is 4.


The above worksheet help you to understand how to compute F Test calculation. When you try such calculations on your own, use this F Test calculator to verify your results.