Question

Practice Exercise 13: One -way Analysis of Variance (ANOVA)

1. When is it appropriate to use a one-way ANOVA to analyze data?

2. What letter is use the designate the test statistic used in the one-way ANOVA?

3. What are the two types of variance that are examined when conducting an analysis of variance?

4. Which type of variance is related to the effect of a treatment?

5. Does the analysis of variance test differences between two specific groups?

Use the One-way ANOVA function in SPSS to answer the questions based on the following scenario. (Assume a critical level of significance of .05).

A researcher is interested in determining if participation in extracurricular activities affects academic performance.

High school students are randomly assigned to one of three conditions: no activities, some activities, many activities.

The data from the scores are as follows:

No activities: 75 74 66 79 62 68 59 73 76 69

Some activities: 78 85 85 77 81 76 90 85 73 80

Many activities: 58 70 58 59 62 55 58 63 67 59

6. Write an appropriate null hypothesis for this analysis.

7. What is the observed or computed value of F?

8. How would you explain the procedure for determining the degrees of freedom for the Between Groups variance (numerator)?

9. How would you explain the procedure for determining the degrees of freedom for the Within Groups variance (denominator)?

10. What is the value of the Between Groups degrees of freedom?

11. What are the value for the Within Groups degrees of freedom?

12. What is the reported level of significance?

13. Based on the reported level of significance, would you reject the null hypothesis?

14. Based on the reported level of significance, would you conclude that there was a statistically significant difference among the three groups?

15. Write a statement as it might appear in an article that reports the results of the one-way ANOVA.

Help! This is due today!

Answer #1

A one-way analysis of variance was conducted on 5 groups. The
total standard devation was calculated to be 2. The total degrees
of freedom was found to be 18 and the resulting p-value was found
to be 0.25. Use the given information to fill out the rest of the
ANOVA table.
What is the number of treatment degrees of
freedom?
What is the denominator degrees of freedom for the test
statistic?
How many total observations were there?
What is the...

Explain how a one-way analysis of variance works. How do you use
between-and within-group variability? ** Your answer should
indicate that a one-way ANOVA compares the relative size
of…..Between-groups variability comes from….while within-groups
variability comes from….The F ratio ratio divides….When the I.V.
has no effect, the F ratio is about….etc.

A researcher performs an “ANOVA (Analysis of Variance)”
statistical test when the variable data s/he is working with are
characterized by which scale of measurement? Please identify the
scale of measurement for the IV and the scale of measurement for
the DV.
i. What is the difference between a t-test and a One-Factor (or
one-way) ANOVA?
ii. What is the difference between a One-Factor (or one-way)
ANOVA and a Two-Factor (or two-way) ANOVA?
iii. What is the main difference between...

A one-way analysis of variance experiment produced the following
ANOVA table. (You may find it useful to reference
the q table).
SUMMARY
Groups
Count
Average
Column 1
3
0.66
Column 2
3
1.24
Column 3
3
2.85
Source of Variation
SS
df
MS
F
p-value
Between Groups
8.02
2
4.01
4.09
0.0758
Within Groups
5.86
6
0.98
Total
13.88
8
a. Conduct an ANOVA test at the 5% significance
level to determine if some population means differ.
Do not reject...

1. A “one-way” between-subjects ANOVA is conducted when data are
recorded in one group.
True
False
2. Post hoc tests control for the total alpha level for a series
of tests conducted on the same data.
True
False
3. All post hoc tests control for the effect size of a
significant result.
True
False
4. A one-way between-subjects ANOVA is conducted to test for
mean differences between the levels of two or more factors.
True
False
5. A researcher conducts...

A one-way analysis of variance experiment produced the following
ANOVA table. (You may find it useful to reference
the q table).
SUMMARY
Groups
Count
Average
Column 1
6
0.71
Column 2
6
1.43
Column 3
6
2.15
Source of Variation
SS
df
MS
F
p-value
Between Groups
10.85
2
5.43
20.88
0.0000
Within Groups
3.86
15
0.26
Total
14.71
17
SUMMARY
Groups
Count
Average
Column 1
6
0.71
Column 2
6
1.43
Column 3
6
2.15
ANOVA
Source of Variation...

1. In one-way ANOVA, involving three groups, the alternative
hypothesis would be considered correct if, in the population,
a. all means were equal
b. two means are equal but the third is different
c. all three means have different values
d. either (b) or (c) above is true
QUESTION 2 When Null is true for a one-way ANOVA, variation of
the group means is a reflection of
a. inherent variation
b. differential treatment effects
c. nondifferential treatment effects
d. a...

#1. Which type of ANOVA would you use for each
of the studies below?
One-way between subjects (independent groups)
One-way within subjects (repeated measures)
Two-way between subjects
Measure the self-esteem of the same group of college students
at the beginning, middle and end of their freshman year.
Compare math skills for three different professional groups:
physicians, attorneys and psychologists.
Measure Body Mass Index (BMI) for persons who take Supplement X
vs. a placebo and who either exercise regularly or don’t....

Consider the One-Way ANOVA table (some values are intentionally
left blank) for the amount of food (kidney, shrimp, chicken liver,
salmon and beef) consumed by 50 randomly assigned cats (10 per
group) in a 10-minute time interval.
H0: All the 5 population means are equal
H1: At least one population mean is
different.
Population: 1 = Kidney, 2 = Shrimp, 3 = Chicken Liver, 4 =
Salmon, 5 = Beef.
ANOVA
Source of Variation
SS
df
MS
F
P-value
F...

Exercise 16.037
{Exercise 16.37}
The following exercises require the use of a
computer and software.
Use a 5% significance level for all tests of
hypotheses.
Dataset:
Income
Food
53
188.24
47
304.89
59
304.99
44
283.99
87
316.21
56
263.32
62
315.87
60
201.52
70
295.5
85
318.53
63
278.78
57
254.34
59
253.79
64
310.97
45
215.79
62
248.34
63
299.66
55
220.72
77
319.58
52
280.96
72
259.73
64
254.5
68
181.99
54
256.8
63
258.54
57
203.91...

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