Question

A psychologist would like to examine the effects of three different testing methods on the final performance of college students. One group gets regular quizzes, one group gets three large exams, and the third group only gets a final exam. A separate sample of 10 students were assigned in each testing method condition. At the end of the course, the psychologist interviews each student to get a measure of the student’s overall knowledge of the material. Do these data indicate any significant differences among the three methods? Test with α = .05.

*Partial information is provided for you in the ANOVA summary table for the problem*

Source | SS | df | MS | F |

Between | 16 | |||

Within | - | |||

Total | 70 | - | - |

State the null and alternative hypothesis ?

b. Compute dfB, dfW, and dfT ?

c. Determine the boundary (critical) value of rejection region under alpha level equal to .05 ?

d. Compute SSW (2 pt) e. Compute MSB and MSW ?

f. Compute the F test statistic ?

g. Complete the ANOVA summary table (copy the numbers you computed to the following summary table) ?

Source | SS | df | MS | F |

Between | ||||

Within | - | |||

Total | - | - |

h. What is your statistical decision on your test of hypothesis? And your conclusion based on your test ?

i. Compute the effect size of the ANOVA analysis you just conducted.

Answer #1

H0: µ1 = µ2 = µ3 : There is no significant difference among the three testing methods

H1: There is significant difference among the three testing methods

n=10

k =3 (no. of treatments)

b) dfT = 10-1=9

dfB = k-1 =3-1=2

dfW = n-k = 10-3 =7

c) Critical F (Using Excel F.INV.2T(probability, dfB, dfW)) = F.INV.2T(0.05,9,2) = 4.73

d) SSW = TSS-SSB = 70-16 = 54

e) MSB = SSB/dfB = 16/2 = 8

MSW = SSW/dfW = 54/7 = 7.71

f) F statistic = MSB/MSW = 8/7.71 = 1.04

g) ANOVA Table

Source of Variation | SS | df | MS | F |

Between Groups | 16.00 | 2 | 8.00 | 1.04 |

Within Groups | 54.00 | 7 | 7.71 | |

Total | 70.00 | 9 |

h) Since test statistic (1.04) is less than critical value (4.73), we do not reject the null hypothesis and conclude that there is no significant difference among the three testing methods.

i) Effect size of ANOVA = SSB/TSS = 16/70 = 0.23

A psychologist would like to examine the effects of sugar
consumption on the activity level of preschool children. Three
samples of children are selected with n = 5 in each sample. One
group gets no sugar, one group gets a small dose, and the third
group gets a large dose. The psychologist records the activity
level for each child. The data from this experiment are presented
below.
No Sugar
Small Dose
Large Dose
M=3
SS=16
M=4
SS=12
M=5
SS=20
1)....

Show full work and write in complete sentences
A psychologist would like to examine the effects of a new drug
on the activity level of animals. Three samples of rats are
selected with n = 4in each sample. One group gets no drug, one
group gets a small dose, and the third group gets a large dose. The
psychologist records the activity level for each animal. The data
from this experiment are presented below. Test with alpha = .05. Do...

2) An ANOVA is computed for the effects of five different diets
on the energy level of test animals. Eight animals are given each
of the diets for a total of 40 animals. The f summary table below
is partially completed. Fill in the remaining parts of the table
and evaluate the F value for statistical significance. Make sure to
indicate the critical value that you are using in your
evaluation.
Source
SS
df
MS
F
Between
Within ...

A researcher conducts a two-way ANOVA test with interaction and
provides the following ANOVA table.
a.
Find the missing values in the
ANOVA table. (Round your answers to 2 decimal
places.)
ANOVA
Source of
Variation
SS
df
MS
F
p-value
F
crit
Sample
766.98
2
MSB
=
Ffactor B =
0.0109
3.885
Columns
12,122.69
1
MSA
=
Ffactor A =
0
4.747
Interaction
57.60
2
MSAB
=
FInteraction =
0.6148
3.885
Within
682.14
12
MSE
=
Total
13,629.41
17

3. Refer to the following ANOVA Summary Table
to answer the questions listed below it.
SOURCE
SS
df
MS
F
Between
23.57
3
.
Within
24
.95
Total
46.43
Answer each of these questions concerning this ANOVA
Summary Table:
What is SS within?
Your Answer:
.
What is MS between?
Your Answer:
.
What is df total?
Your Answer:
.
What is the observed...

Complete the following ANOVA summary table for a model, where
there are four levels of factor A selected at random and three
levels of factor B selected at random. Each cell of the design
includes 20 students (α = .05).
Also, in statistical language (symbols) what is the most
appropriate null and alternative hypothesis for each factor
(effect) for the model?
Source
SS
DF
MS
F
CriticalValue
Decision
η2
ω2
A
12
B
22
AB
Within
114
Total
172

Complete the following ANOVA summary table for a model, where
there are four levels of factor A selected at random and three
levels of factor B selected at random. Each cell of the design
includes 20 students (α = .05).
Also, in statistical language (symbols) what is the most
appropriate null and alternative hypothesis for each factor
(effect) for the model?
Source
SS
DF
MS
F
CriticalValue
Decision
η2
ω2
A
12
B
22
AB
Within
114
Total
172

Chapter 12 WebAssign
An educator wants to evaluate four different methods aimed at
reducing the time children spend "off task" in the classroom. To
test these methods, she implements one method in each of four
similar classrooms and records the time spent off task (in minutes)
in each classroom. The results are given in the table.
Classroom
Method
A
B
C
D
2
0
0
0
1
5
3
5
3
0
3
4
1
3
4
3
4
1...

An educator wants to evaluate four different methods aimed at
reducing the time children spend "off task" in the classroom. To
test these methods, she implements one method in each of four
similar classrooms and records the time spent off task (in minutes)
in each classroom. The results are given in the table.
Classroom Method
A B C D
2 4 3 2
5 5 4 5
4 0 3 4
4 3 6 4
2 4 5 3
1...

An educator wants to evaluate four different methods aimed at
reducing the time children spend "off task" in the classroom. To
test these methods, she implements one method in each of four
similar classrooms and records the time spent off task (in minutes)
in each classroom. The results are given in the table.
Classroom Method
A. B. C. D
2 4 3 2
5 5 4 5
4. 0. 3 4
4 3 6 4
2 4 5 3
1...

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