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u07a1 – ANOVA
Complete the following problems within this Word document. (Do not submit other files.) Show your work for
problem sets that require calculations. Ensure that your answer to each problem is clearly visible. (You may
want to highlight your answer or use a different type color to set it apart.)
Submit the document to your instructor by Sunday, 11:59 p.m. central time.
Problem Set 7.1: Critical Value
Criterion:
Explain the relationship between
k
and power based on calculated
k
values.
Instructions:
Read the following and answer the question.
Work through the following and write down what you see in the
F-
table. This will help familiarize you with the
table.
The
F-
table.
The degrees of freedom for the numerator (
k
− 1) are across the columns; the degrees of freedom
for the denominator (
N
−
k
) are across the rows in the table. A separate table is included for a .05 and .01 level
of significance.
Increasing the levels of the independent variable (
k
):
1.
Suppose we have a sample size of 24 participants (
N
= 24). Record the critical values given the
following values for
k
:
.05
.01
k
= 2
k
= 4
k
= 6
k
= 8
2-1=1;
4.30
4-1=3;
3.10
6-1=5;
2.77
8-1=7;
2.66
24-2=22;
7.95
24-4=20;
4.94
24-6=18;
4.25
24-8=16;
4.03
2.
As
k
increases (from 1 to 8), does the critical value increase or decrease? Based on your answer,
explain how
k
is related to power.
As k increases, the critical value decreases. As k increases, the power increases.
Problem Set 7.2: Interpret ANOVA Results
Criterion:
Interpret the results of an ANOVA.
Instruction:
Read the following and answer the question.
Data:
Life satisfaction among sport coaches.
Drakou et al. (2006) tested differences in life satisfaction among
sport coaches. They tested differences by sex, age, marital status, and education. The results of each test in
the following table are similar to the way in which the data were given in their article.
1
Independent Variables
Life Satisfaction
M
SD
F
p
Sex
0.68
.409
Men
3.99
0.51
Women
3.94
0.49
Age
3.04
.029
20s
3.85
0.42
30s
4.03
0.52
40s
3.97
0.57
50s
4.02
0.50
Marital status
12.46
.000
Single
3.85
0.48
Married
4.10
0.50
Divorced
4.00
0.35
Education
0.82
.536
High school
3.92
0.48
Postsecondary
3.85
0.54
University degree
4.00
0.51
Masters
4.00
0.59
1.
Which factors were significant at a .05 level of significance?
Age and marital status were significant at a
.05 level of significance.
2.
State the number of levels for each factor.
Sex: 2 levels, Age: 4 levels, Marital Status: 3 levels,
Education: 4 levels.
Problem Set 7.3: One-way ANOVA in JASP
Criterion:
Calculate an ANOVA in JASP.
Data:
Use the Stress data set. This data set is a record of the amount of fat (in grams) consumed in a buffet-
style lunch among professional bodybuilders under conditions of high, moderate, and low stress.
Instructions:
Complete the steps below.
1.
Download Stress data set. Double-click the icon to open the data set in JASP.
2.
In the
Toolbar
, click
ANOVA.
In the menu that appears, under
Classical,
select
ANOVA.
3.
Select
Fat grams consumed
and then click the upper
Arrow
to send it over to the
Dependent
Variable
box.
4.
Select
Stress level
and then click the lower
Arrow
to send it over to the
Fixed factors
box.
5.
Check the
Descriptive statistics
box.
6.
Copy and paste the output below.
ANOVA
2
ANOVA - Fat Grams Consumed
Cases
Sum of Squares df Mean Square
F
p
Stress
Level
15.600
2
7.800 1.773 0.212
Residuals
52.800 12
4.400
Note.
Type III Sum of Squares
Descriptives
Descriptives - Fat Grams Consumed
Stress Level N Mean
SD
SE
Coefficient of variation
High
5 8.600 2.408 1.077
0.280
Low
5 6.200 1.924 0.860
0.310
Moderate
5 6.800 1.924 0.860
0.283
Problem Set 7.4: One-way ANOVA in Excel
Criterion:
Calculate an ANOVA in Excel.
Instructions:
Use the data from the table below to complete the following steps:
a. Open
Excel
to an empty sheet.
b.
Enter the data from
this table:
Stress Levels
High
Moderate
Low
10
9
9
7
4
4
8
7
6
12
6
5
6
8
7
c. In
Row 1
, enter High in cell A1, Moderate in cell B1, and Low in cell C1.
d.
In the toolbar, click
Data Analysis
, select
Anova: Single Factor,
and click
OK.
e. In
Input Range
: $A$1:$C$6, put a check next to
Labels in First Row
, click
OK.
f.
Results will appear in a new sheet to the left, copy and paste the input below.
Anova: Single Factor
3
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SUMMARY
Groups
Count
Sum
Average
Variance
High
5
43
8.6
5.8
Moderate
5
34
6.8
3.7
Low
5
31
6.2
3.7
ANOVA
Source of
Variation
SS
df
MS
F
P-value
F crit
Between Groups
15.6
2
7.8
1.772727
0.211576
3.885294
Within Groups
52.8
12
4.4
Total
68.4
14
Problem Set 7.5: One-way ANOVA Results in APA Style
Criterion:
Report ANOVA results in APA format.
Data:
Use the results from Problem Set 7.4.
Instructions:
Complete the following:
a.
State the null hypothesis.
The null hypothesis is that there is no difference in the stress levels
.
.
Report your results in APA format (as you might see them reported in a journal article).
A one-way
ANOVA examined the relationship between fat consumption and stress levels. The following one-way
ANOVA results show an insignificant relationship between fat consumption and stress levels F(2,12) =
1.773, p=.212.
Problem Set 7.6: Tukey HSD Test in JASP
Criterion:
Calculate post hoc analyses in JASP.
Data:
Use Stress data set from Problem Set 7.3.
Instructions:
Complete the steps below. (Note: The first 7 steps below are repeated from Problem Set 7.3.).
1.
Download Stress data set. Double-click the icon to open the data set in JASP.
2.
In the
Toolbar
, click
ANOVA.
In the menu that appears, under
Classical,
select
ANOVA.
3.
Select
Fat grams consumed
and then click the upper
Arrow
to send it over to the
Dependent
Variable
box.
4.
Select
Stress level
and then click the lower
Arrow
to send it over to the
Fixed factors
box.
5.
Check the
Descriptive statistics
box.
6.
Select Post-Hoc Tests. In the menu that appears, select
Stress level
and then click the
Arrow
to move
it from the left to the right box.
7.
Check
Standard
and
Tukey
and uncheck any other boxes in the Post-Hoc area.
8.
Copy and paste the output below.
4
Post Hoc Tests
Standard
Post Hoc Comparisons - Stress Level
Mean Difference
SE
t
p
tukey
Hig
h
Low
2.400 1.327 1.809 0.208
Moderat
e
1.800 1.327 1.357 0.393
Low
Moderat
e
-0.600 1.327 -0.452 0.894
Note.
P-value adjusted for comparing a family of 3
Problem Set 7.7: Tukey HSD Interpretation
Criterion:
Interpret Tukey HSD results from JASP output.
Data:
Use your output from Problem Set 7.6.
Instructions:
Identify where significant differences exist at the .05 level between the stress levels.
There are no significant differences that exist.
Problem Set 7.8 Variables for Week 9 Assignment
Criterion:
Define your two variables for the Week 9 Assignment.
Instructions:
In this section you need to define the two specific variables you selected from the Grades data
file for use in the Week 9 assignment and you need to define them in the following ways: (1) variable name and
definition, (2) scale of measurement (nominal, ordinal, interval, or ratio) which ties into WHICH type of
statistical analysis you can use (Privitera, 2018).
Variable 1: Extra Credit (DV)
Variable 2: Year (IV)
Variable Definition
Completing extra credit
opportunities
The amount of years the
participant has been in high
school (Freshman-1, sophomore-
2, junior-3, or senior-4)
Scale of Measurement
Nominal Scale
Ordinal Scale
Statistical Analysis that should be used:
Difference of proportion (z score)
Reference
Privitera, G. J. (2018).
Statistics for the behavioral sciences
(3rd ed.). Sage.
5
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Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman