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F-Test Calculator

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F-Test Calculator

F-Test Calculator is a tool that evaluates the F-test value using the value of two data sets. It finds the mean, standard deviation, and variance of the given sets to find the result. 

What is meant by F-value?

The F-test value is a statistical test that compares the variances of two or more groups or populations. It determines if the differences in variances are significant enough to reject the null hypothesis of equal variances. The F-test uses the F-statistic which is the ratio of two variances and follows an F-distribution.

Formula:

F-Test value = (variance of dataset x )/(variance of dataset y)

S.D of x = σ = (√ {∑ (x - x̄)2 )/(n – 1)}

S.D of y = σ = (√ {∑ (y – y )2 )/(n – 1)}

Variance of x = σ2 = {∑ (x - x̄)2 )/(n – 1)}

Variance of y = σ2 = {∑ (x - x̄)2 )/(n – 1)}

Where “ȳ” and “ x̄  ” are the means of the data respectively.

How to solve F-test problems?

Example 1:

If the value of two data sets is given as {2, 4, 6, 8, 10} and {4, 7, 6, 5, 9} then calculate the F-value.

Solution:

Step 1:

Write the given data from the question carefully.

For Dataset x

Input Data = {2, 4, 6, 8, 10}

Total Numbers = 5

For Dataset y

Input Data = {4, 7, 6, 5, 9}

Total Numbers = 5

Step 2:

Write the formula of the F-test value.

F-Test value = (variance of dataset x) / (variance of dataset y)

Step 3:

First, we calculate the value of the variance of “x” for this we find the mean of x that is “x̄”.

x̄ = (Sum of all values of data set x)/ Total Number

x̄ = (2+4+6+8+10)/5

x̄ = 30/5

x̄ = 6

Use the mean in the below formula and evaluate for the standard deviation of “x”.

∑ (x - x̄)2 = ( 2 - 6 )2 + ( 4 - 6 )2 + ( 6 - 6 )2 + ( 8 - 6 )2 + ( 10 - 6 )2

∑ (x - x̄)2 = ( -4.00 )2 + ( -2.00 )2 + ( 0.00 )2 + ( 2.00 )2 + ( 4.00 )2

∑ (x - x̄)2 = 40

Put the values from the above data.

S.D of x = σ = √{ ∑ (x - x̄)2 )/(n – 1)}

S.D of x = σ = √{ (40)/(5 – 1)}

S.D of x = σ = √{ (40)/(4)}

S.D of x = σ = √10

S.D of x = σ = 3.16228

Put the value of “S.D of x” in the below formula to evaluate the variance of “x”.

Variance of x = σ2

Variance of x = (3.16228)2

Variance of x = 10

Step 4:

Now, for the variance of the data set “Y”, we calculate the mean of “y”.

y = (Sum of all values of data set y)/ (total Number)

y  = (4+7+6+5+9)/5

y  = (31)/5

y = 6.2

∑ (y -  y )2 = ( 4 - 6.2 )2 + ( 7 - 6.2 )2 + ( 6 - 6.2 )2 + ( 5 - 6.2 )2 + ( 9 - 6.2 )2

∑ (y -  y )2 = ( -2.20 )2 + ( 0.80 )2 + ( -0.20 )2 + ( -1.20 )2 + ( 2.80 )2

∑ (y – y )2 = 14.8

S.D of y = σ = √ {∑ (y – y )2 )/(n – 1)}

S.D of y = σ = √ {(14.8) /  (5 – 1)}

S.D of y = σ = √{ (14.8)/(4)}

S.D of y = σ = √3.7

S.D of y = σ = 1.92

Put the value of “S.D of y” in the below formula to evaluate the variance of “y”.

Variance of y = σ2

Variance of y = (1.92)2

Variance of y = 3.7

Step 5:

Now we have to put variances of both datasets in the formula of the F-test value.

Variance of x = 10, Variance of y = 3.7

F-Test value = (variance of dataset x) / (variance of dataset y)

F-Test value = 10/ 3.7

F-Test value = 2.7027

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