Nick Ruiz
Methodology and Statistics
ANOVA Sample Exam Questions
1. What is the null hypothesis in an ANOVA experiment? What is the alternative hypothesis?
H0: All population groups have the same mean.
Ha: Not all of the population groups have the same mean.
2. Is the following statement true: "The alternative hypothesis in an ANOVA measure concludes
that all of the population groups do not have the same mean." Explain.
No; the alternative hypothesis concludes that not all of the population groups have the
same mean. Some groups may have the same mean. It is up to the experimenter to determine
which groups have a different mean and to determine the amount of variance.
3. What statistic is used to test the null hypothesis in a one-way ANOVA experiment? What
variables are used in this test? When is the null hypothesis rejected?
The null hypothesis is rejected when the F score shows that the variance between
groups (MSG) is significantly larger than the variance within groups (MSE, or the residual). The Pvalue of the F score is used to show the significance.
4. In a one-way ANOVA, how are the residual degrees of freedom calculated (DFE)?
DFE = DFT - DFG;
In other words, the DFE is the total degrees of freedom, subtracted by the degrees of freedom
within the groups.
5. A school district wants to compare the standardized test scores of 5th grade students in writing.
The district is interested in determining whether a particular school achieves higher average
scores. There are four schools within the district. The district randomly selects 50 test scores
from each school and records the results form a single test. Set up the experiment and describe
the type of analysis you would use.
In this experiment, 4 groups are being compared (each school within the district). Since
the grade of the students are held constant, as well as the subject of the standardized test and
the number of tests being performed, a one-way ANOVA experiment would be sufficient.
6. The same school district would like to analyze the effectiveness of their teaching of non-native
English speakers. The same experiment as in (5) is repeated. The following questions are being
considered: "Does being a non-native speaker affect standardized test scores in the school
district?" "Does the school of instruction affect the test scores?" Describe the experiment you
would use to answer these questions.
Since the experiment seeks to answer two simultaneous questions, a two-way ANOVA
should be used (assuming normal distributions). There will be a total of 10 groups: 2 groups for
each school to compare the performances of native and non-native English speakers in each
school.
Nick Ruiz
Methodology and Statistics
7. How does the calculation of the total sum of squares differ in a 2-way ANOVA?
In ANOVA, the total sum of squares is calculated by:
SST = SSG + SSE.
In two-way ANOVA, one must account for the variance within each group, as well as the
variance when the groups are combined. Thus,
SSG = SSA + SSB + SSAxB.
8. What are some advantages of using factorial ANOVA over n one-way ANOVAs?
 It is more efficient to study the n factors simultaneously, rather than separately.
 We reduce the residual error in our model by including additional factors to influence
the response.
 We can investigate interactions between the factors.
9. The same school district as in (6) would like to determine how adding additional educational
resources for non-native English speakers will improve their writing skills over time. Suggest how
the experiment in (6) can be modified to do a longitudinal study. How would you analyze the
test results?
A repeated measures two-way ANOVA would be used to analyze the results.
10. Assuming that the test in (9) will be performed over 3 years, what are some disadvantages to
the repeated measure design that can affect the validity of this test?
 Students may leave the school district before the analysis is complete, causing the
number of test subjects to vary between each group.
 New students may enter the district during the testing process.
 Other outside conditions can affect a student's performance/response over time.
11. How is the residual calculation different in a one-way repeated measures ANOVA from a classic
one-way ANOVA?
In standard 1-way ANOVA:
SST = SSG + SSE
In repeated measures 1-way ANOVA: SST = SSG + (SSE - SSS)
The residual variance decreases in a repeated measures ANOVA, as the sum of squares within
subjects is considered.