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The F distribution

  • The F critical value is found from the F table
  • The are two appropriate degrees of freedom
    • One for numerator and other for denominator
  • In the F table:
    • Numerator degrees of freedom determine the row
    • Denominator degrees of freedom determine the column

   where df1 = n1 – 1 ;   df2 = n2 – 1

 

Finding the critical value
 

Example
 
You are a financial analyst for a brokerage firm.  You want to compare dividend yields between stocks listed on the Dow30 & EURO STOXX 50. You collect the following data:
 
Is there a difference in the variances between the Dow30 & EURO STOXX 50 at the α = 0.05 level?
 
Solution

Form the hypothesis test:
H0: σ21 – σ22 = 0   (there is no difference between variances)
HA: σ21 – σ22 ≠ 0     (there is a difference between variances)
 
Find the F critical value for α = 0.05
Numerator:
df1 = n1 – 1 = 30 – 1 = 29
Denominator:
df2 = n2 – 1 = 50 – 1 = 49
F0.05/2, 29, 49 = 1.881
The test statistic is:
 


F = 1.148 is not greater than the critical F value of 1.881, so we do not reject H0
 
Conclusion:  There is no evidence of a difference in variances at α = 0.05
 

 





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