With
Homogeneity of Variance
Used
to compare two sample means. The independent
variable is nominal level data and the dependent variable is interval/ratio level.
Problem:
You have obtained the number of years of education from one random sample of 38 police
officers from City A and the number of years of education from a second random sample of
30 police officers from City B. The average years of education for the sample from City A
is 15 years with a standard deviation of 2 years. The average years of education for the
sample from City B is 14 years with a standard deviation of 2.5 years. Is there a
statistically significant difference between the education levels of police officers in
City A and City B?
Assumptions
Random
sampling
Independent
samples
Interval/ratio
level data
Organize
data
City
A (labeled sample 1)
City
B (labeled sample 2)
State
Hypotheses
Ho:
There is no statistically significant difference between the mean education level of
police officers working in City A and the mean education level of police officers working
in City B.
For
a 2tailed hypothesis test
Ha:
There is a statistically significant difference between the mean education level of police
officers working in City A and the mean education level of police officers working in City
B.
For
a 1tailed hypothesis test
Ha:
The mean education level of police officers working in City A is significantly greater
than the mean education level of police officers working in City B.
Set
the Rejection Criteria
Determine
the degrees of freedom (df) = (n1+n2)2
df
= 38+302=66
Determine
level of confidence  alpha
(1 or 2tailed test)
Use
the tdistribution
table to determine the critical value
If
using 2tailed test
Alpha.05,
tcv= 1.997
If
using 1tailed test
Alpha.05,
tcv= 1.668
Compute
Test Statistic
Standard
error
Test
Statistic
Decide
Results
If
using 2tailed test
There
is no statistically significant difference between the mean years of education for police
officers in City A and mean years of education for police officers in City B. (note: the
test statistic 1.835 does not meet or exceed the critical value of 1.997 for a 2tailed
test.)
If
using 1tailed test
Police
officers in City A have significantly more years of education than police officers in City
B. (note: the test statistic 1.835 does exceed the critical value of 1.668 for a 1tailed
test.)
Software Output Example
