Matakuliah : I0134/Metode Statistika
Tahun
: 2007
Pengujian Hipotesis Varians dan Kesamaan Varians
Pertemuan 22
Developing the F Test
• Hypotheses
– H0 : s 1 2 = s 2 2
– H1: s12 s22
• Test Statistic
– F = S12 /S22
–
–
Reject H0
Reject H0
a/2
Two Sets of Degrees of Freedom
• df1 = n1 - 1; df2 = n2 - 1
Critical Values: FL(
n1 -1, n2 -1
0
FL
a/2
FU
n1 -1 , n2 -1
) and FU(
FL = 1/FU* (*degrees of freedom switched)
Bina Nusantara
Do Not
Reject
)
F
F Test: An Example
Assume you are a financial analyst for Charles Schwab. You want to
compare dividend yields between stocks listed on the NYSE & NASDAQ.
You collect the following data:
NYSE
NASDAQ
Number
21
25
Mean
3.27
2.53
Std Dev
1.30
1.16
Is there a difference in the
NYSE
NASDAQ at the a=0.05 level?
Bina Nusantara
variances between the
&
© 1984-1994 T/Maker Co.
F Test: Example Solution
• Finding the Critical Values for a = .05
–
df1 = n1  1 = 21  1 = 20
–
df 2 = n2  1 = 25  1 = 24
FL 20,24 = 1/ FU  24,20 = 1/ 2.41 = .415
FU  20,24 = 2.33
Bina Nusantara
F Test: Example Solution
Test Statistic:
H0 : s 1 2 = s 2 2
H1 : s 1 2  s 2 2
a = .05
df1 = 20 df2 = 24
2
1
2
2
2
S
1.30
F=
=
= 1.25
2
S
1.16
Critical Value(s):
Reject
.025
Reject
.025
0 0.415
Bina Nusantara
Decision:
Do not reject at a = 0.05.
2.33
1.25
F
Conclusion:
There is insufficient
evidence to prove a
difference in variances.
F Test in PHStat
• PHStat | Two-Sample Tests | F Test for Differences in Two Variances
• Example in Excel Spreadsheet
Bina Nusantara
F Test: One-Tail
H0: s12  s22
H1: s12 <s22
or
a = .05
FL n1 1,n2 1 =
Reject
H0: s12  s22
H1: s12 > s22
1
FU  n2 1,n1 1
Reject
a =.05
a =.05
0
Bina Nusantara
Degrees of
freedom
switched
F
FL n1 1,n2 1
0
FU  n1 1,n2 1
F