Page 386 - DMTH404_STATISTICS

Statistics Richa Nandra, Lovely Professional University

Notes Unit 28: F-distribution

CONTENTS

Objectives
Introduction
28.1 Snedecor's F- Distribution
28.2 Summary

28.3 Keywords
28.4 Self Assessment
28.5 Review Questions
28.6 Further Readings

Objectives

After studying this unit, you will be able to:
 Define F - distribution

 Discuss F - distribution examples
Introduction

In the last unit you studied about samples distribution and T - Distribution. This unit provides
you information related to F - distribution.

28.1 Snedecor's F- Distribution

Let there be two independent random samples of sizes n and n from two normal
1 2
1 2
2
2
2
populations with variances s and s respectively. Further, let s = å (X - X ) and
1 2 1 1i 1
n - 1
1
1 2
2
s = å (X - X 2 ) be the variances of the first sample and the second samples respectively.
2i
2
n - 1
2
Then F - statistic is defined as the ratio of two c 2 - variates. Thus, we can write
c 2 n - 1 s 2 s 2
1 1
n - ( 1 ) 1 / n - ) 1 1
n - 1 s 2 ( 1 s 2
F = 1 2 = 1 2 = 1 2
c (n - 1 s s
n - 2 ) 2 ( / n - ) 1 2
2 1
n - 1 s 2 2 2 s 2 2
2

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