11.1. While a  t  test is used to compare  two  means ,  the one - way ANOV A  c a n be used to simultaneously compare ____ groups.  11.2. An ANOV A is considered to be an extension of the  t  test  f o r  independent samples because both investigate differences bet w een ______. 11.3. By conducting a one-way ANOVA test to compare multiple (more than 2) group means  simultaneously  instead of conducting a series of  t  tes ts  to compare these means ,  the potential level of ____ is reduced .  11.4. In order to appl y  the ANOV A test ,  the data should be measured on a (n)  _____  or  ______ scale .  • 11.5. The one-way ANOV A is used when there is/are ____indepe n d ent  variable(s).  11 . 6 .  With 3 groups ,  the null h y pothesis  (H o ) in  ANOV A  is : __________. 11.7. The  total  (or  grand)  mean in ANOV A can be thought of as the mean o f ____. 11.8. The SSw  (within - group s  sum of squares) and the SSg  (betwee n - groups  sum of squares) are equal to thesum of squares.  11.9. To find the MS g ,  we divide the SSg by _________. 11.10. To compute the  F  ratio, we divide the ______ mean squar e  b y t he  _________  mean square.  11.11 .  Factorial ANOVA is commonly used when there are at lea s t ______ independent variables.  Circle the  correct  answer:  11 . 12. The following is an example of a(n)  null/alternative  h y pothesi s i n  AN O VA:  Mean one does not equal mean 2 and/or mean one does not equal mean 2 and/or mean 2 does not equal mean 3 11.13 .  Post hoc comparisons should be conducted in cases  w here the  F  ra t io   is/is not  statistically significant.  11 . 14 .  The  F  ratio is likely to be statistically significant when the differenc es  be tw e en  the group means are  small/large . .  11.15 .  The  F  ratio is more likely to be statistically significant when it is used  t o  anal y ze scores from groups that are  homogenous/heterogeneous in regar d t o the characteristic or behavior being measured. 11 . 16. An ANOVA procedure is used to analyze data from a study comparin g  s cores of three  groups .  Following are the obtained mean squares and  t he appropr i at e  critical  values  for the  F  ratio at  p=.05  and  p=.01  F crit (. 05 , 2 ,2 0)  = 3.49 and  F c r i t ( . O1,2 , 20)  = 5.85  Compute the  obtained F  ratio.  Determine whether the results are statistically significan t .  Report your conclusions.  1 1 .17. Three different age groups of consumers (ages 18-25 ,  26-35 ,  36 -45) in two  different regions of the country (Midwest , South) were sur v e y ed  a b out the i r  likelihood of buying a new product. Following are the means a n d  st and ard  deviations obtained by the three age groups in each of the two regions :  Means  Standard Deviations  Ages  Ages  Ages  Ages  Ages  Age s  Region  18-25  26-35  36-45  18-25  26-35  3 6 -45  Midwest  50.2  52.8  53.3  2. 5  3.1  2. 7  South  41.0  48.5  55.9  2. 7  3. 2  2. 8  Two  separate  one-way ANOVA procedures are conducte.

1. 11.1. While a
t
test is used to compare
two
means
,
the one
-
way ANOV
A
c
a
n be used to simultaneously compare ____ groups.
11.2. An ANOV A is considered to be an extension of the
t
test
f
o
r
independent samples because both investigate differences bet
w
een ______.
11.3. By conducting a one-way ANOVA test to compare
multiple (more than 2) group means
simultaneously
instead of conducting a series of
t
tes
ts
to compare these means
,
the potential level of ____ is reduced
.
11.4. In order to appl

2. y
the ANOV A test
,
the data should be measured on a
(n)
_____
or
______
scale .
•
11.5. The one-way ANOV A is used when there is/are
____indepe
n
d
ent
variable(s).
11
.
6
.
With 3 groups
,
the null h
y
pothesis
(H
o
) in
ANOV
A
is
: __________.
11.7. The
total
(or
grand)

3. mean in ANOV A can be thought of as the mean o
f ____.
11.8. The SSw
(within
-
group
s
sum of squares) and the SSg
(betwee
n
-
groups
sum of squares) are equal to thesum of squares.
11.9. To find the MS
g
,
we divide the SSg by _________.
11.10. To compute the
F
ratio, we divide the ______ mean squar
e
b
y t
he
_________
mean square.
11.11
.
Factorial ANOVA is commonly used when there are at lea
s
t ______ independent variables.
Circle the
correct
answer:

4. 11
.
12. The following is an example of a(n)
null/alternative
h
y
pothesi
s i
n
AN
O
VA:
Mean one does not equal mean 2 and/or mean one does not
equal mean 2 and/or mean 2 does not equal mean 3
11.13
.
Post hoc comparisons should be conducted in cases
w
here the
F
ra
t
io
is/is not
statistically significant.
11
.
14
.
The
F
ratio is likely to be statistically significant when the differenc
es
be
tw
e

5. en
the group means are
small/large
.
.
11.15
.
The
F
ratio is more likely to be statistically significant when it is
used
t
o
anal
y
ze scores from groups that are
homogenous/heterogeneous
in regar
d t
o the characteristic or behavior being measured.
11
.
16. An ANOVA procedure is used to analyze data from a study
comparin
g
s
cores of three
groups
.
Following are the obtained mean squares and
t
he appropr
i
at

6. e
critical
values
for the
F
ratio at
p=.05
and
p=.01
F
crit
(.
05
,
2
,2
0)
= 3.49 and
F
c
r
i
t
(
.
O1,2
,
20)
= 5.85
Compute the
obtained F
ratio.
Determine whether the results are statistically significan
t
.

7. Report your conclusions.
1
1
.17. Three different age groups of consumers (ages 18-25
,
26-35
,
36
-45) in two
different regions of the country (Midwest
,
South) were sur
v
e
y
ed
a
b
out the
i
r
likelihood of buying a new product. Following are the means a
n
d
st
and
ard
deviations obtained by the three age groups in each of the two
regions
:

8. Means
Standard Deviations
Ages
Ages
Ages
Ages
Ages
Age
s
Region
18-25
26-35
36-45
18-25
26-35
3
6
-45
Midwest
50.2
52.8
53.3
2.
5
3.1
2.
7
South
41.0
48.5
55.9
2.
7

9. 3.
2
2.
8
Two
separate
one-way ANOVA procedures are conducted
to
test
whet
h
er the
differences between the three means of the three age groups
i
n
e
ach
of
th
e two
regions are statistically significant.
Estimate
which
F
ratio w
o
uld be
l
arge
r: The
one resulting from analyzing the survey results obtained
fr
o

10. m
th
e t
hre
e ag
e groups in the Midwest or the one from analyzing the surv
ey re
s
u
l
t
s ob
t
ain
ed by
the three age groups in the South explain your answer.
11.18. Three statistics classes at University A took the same
t
est a
s d
i
d 3 other
statistics classes at College B. Following are the means and s
t
andard de
viation
s of the 3 classes in each of the two schools
:
Means
Standard Dev
i

11. ations
SCHOOL
Stats
Stat
s
Stats
Stats
S
tats
S
t
a
t
s
Class I
Class 2
Class 3
Class I
Class 2
Cla
ss 3
University A
71.4
78
.
8
90.2
3.2
4.3
4.8
Colle
ge B
72.1
78.6

12. 89.3
9.3
6.6
8
.
7
Two
separate
one-way ANOVA procedures are used to tes
t wh
eth
er the
differences between the means in each of the two schools
a
r
e s
ta
tistically
significant.
Estimate
which
F
ratio would be larger
:
the one
resu
lt
i
n
g from
analyzing the test scores obtained by the three groups at Univ
er
s
ity A or the one
resulting from analyzing the test scores of the three groups
at Coll

13. e
ge B
.
Explain your answer.
11.19
.
Each of the two figures below (Figure A and Figure
B
)
depicts
a set of 3
distributions. Two
separate
one-way AN OVA analyses ar
e
per
f
o
r
m
e
d
to tes
t whether there are statistically significant differences between
th
e
three me
ans in
each set and two
F
ratios are computed. Estimate which of the
tw
o
F
ra
t

14. ios is
likely to be higher and explain your answer.
11.20. In a study comparing means of 4 groups, the
F
ratio was significant at the
p<.0
5
level
.
The 4 means are Mean 1=13
.
12; Mean 2=9.31; Mean 3=13.65
;
and Me
an
4
=
11.34. Tukey's post hoc comparison is used to test which means
statisticall
y
differ from each other. The
obtained
HSD value at the
p=.05
level is 3
.
74
.
Which means are statistically significantly different from each
other? Expla
i
n

15. .
11.21. A pilot-test marketing research study comparing two new
models of
w
idgets was conducted in two companies (Company A and
Company B)
.
In each of
t
he two companies, one manufacturing plant used one new
widget and the other plant used the other new widget
.
At the end of the year, the employees using the new widgets in
their jobs completed a questionnaire assessing their satisfaction
with the widgets. Following is a table listing the mean scores of
the two plants questionnaire scores for each of the two
companies (those that used new widge
t
1 and those that used new widget 2). Study the data in the
table.
(Note
:
Do no
t
attempt to compute the F ratios or the exact level of significanc
e i
n order
to
answer the questions below
.
)
Means of
Means of
Company

16. Employees Using
Employees Using
Widget 1
Widget 2
Company A
55
53
Company B
50
48
a.Are there differences in questionnaire scores as a result of the
using the two widgets? Explain.
b.Are there differences in questionnaire scores between the two
companies?
Explain.