- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 8. Hypothesis Testing
- Subject 11. Tests Concerning the Equality of Two Variances (F-Test)

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**CFA Practice Question**

Which of the following statements least accurately describes the interpretation of a F-statistic?

A. The F-statistic will increase as the sample size increases.

B. The F-statistic may be found as the ratio of the variance of the regression to the variance that is accounted for by the error terms.

C. The F-statistic may be found using the components of an ANOVA.

**Explanation:**The F-statistic is independent of the sample size. It's simply a ratio of two variances.

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**User Contributed Comments**
11

User |
Comment |
---|---|

ThePessimist |
C is wrong too, because you need to take the MSR and MSE, not the full variance. |

PhiWong |
Agree. I picked C as well. When N increases, the MSE should be reduced accordingly (DF=n-k-1) and accordingly make F-statistic increase. |

volkovv |
PhiWong, I used the same logic and picked C as well. But now looking more at it, I think B is correct, meaning that statement B is false. If you look at an F-Table, you see that for an F-statistic, F(k,n-k-1), the larger the n, the lower the F-value. |

creativemny |
Ok volkovv but the question doesn't ask about F critical it asks about the F statistic ((SSR/k)/(SSE/n-k-1)). All else equal the F Statistic would increase as MSE decreased. |

Kostanm |
totally agree with creativemny |

tom1980 |
C is right simply due to the possibility that K=N-K-1 therefore 2k=N-1, for example,if k=8 and n=17. and B is wrogn becasue SSE may increase more than the increase in N as a result of a possible decrease in F statistic. Hopefully that should explain |

mazen1967 |
variance |

shiva5555 |
uh, What is ANOVA? |

daverco |
Analysis of variance |

chriswwu |
Yes, I still think C is the right answer. |

sumeetb |
Error is deviation and squared error is variance..So F stat being ratio of squared errors is a ratio of variances |