Homework #7:
ANOVA
Due Date: 12:00 p.m. on November 7, 2019 (via Canvas)
Directions: Answer each question below in its entirety. Submit your answers through Canvas by the
due date. Your submission should be a Word document and named with the following structure:
LASTNAME_hw7.doc. Be sure to show your work and to list the names of any students with whom
you worked on this assignment. Please round to the nearest hundredth in your calculations.
Part I: ANOVA
1.) Which of the following partitioned distributions has the statistically significant F-ratio? How
do you know? Explain.
2.) A researcher is examining whether or not systolic blood pressure readings vary across age
groups in the U.S. adult population. They ran an ANOVA test and presented the output
below. They also provided some descriptive statistics for the systolic blood pressure variable,
computed separately for each age group. Using this information, answer the following
questions:
a. What is your null hypothesis? What is your alternative hypothesis?
b. What is the F-ratio (i.e., the F-statistic), and what is its interpretation?
c. What is the critical F-value, assuming an a = .01 (hint: you’ll need your textbook—
or some copy of the F-distribution—for this one).
XXXXXXXXXX
y
XXXXXXXXXX
x
Group 1 Group 2
Group 3 Group 4
Group 5
XXXXXXXXXX
y
XXXXXXXXXX
x
Group 1 Group 2
Group 3 Group 4
Group 5
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d. Do you reject or fail to reject your null hypothesis? What is your interpretation of the
results?
ANOVA Results:
> summary(aov(nhanes$bpsystol ~ nhanes$agegrp))
Df Sum Sq Mean Sq F value Pr(>F)
nhanes$agegrp XXXXXXXXXX605.9 Residuals XXXXXXXXXX
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Descriptive Statistics:
Age groups | Summary of systolic blood pressure
1-6 | Mean Std. Dev. Freq.
------------+------------------------------------
age20-29 | XXXXXXXXXX 2320
age30-39 | XXXXXXXXXX 1621
age40-49 | XXXXXXXXXX 1270
age50-59 | XXXXXXXXXX 1289
age60-69 | XXXXXXXXXX 2852
age 70+ | XXXXXXXXXX 985
------------+------------------------------------
Total | XXXXXXXXXX 10337
3.) The researcher from question #7 claims that they can simply compare the descriptive
statistics presented just above the ANOVA table to determine which age groups are
significantly different from one another. Explain to them why this is not a good idea.
Part II: ANOVA in R
4.) I use a sample of a dataset quite frequently in this class called NHANES—the National
Health and Nutrition Examination Survey. I have provided this sample data as part of this
assignment. Download the “nhanes_data.rds” file and move it to your working directory.
Once it is there, continue with the prompt below.
You are a medical sociologist who studies racial-ethnic inequalities in health outcomes. You
ask the following research question: “Are there racial-ethnic disparities in average vitamin C
levels in the U.S. adult population?” Looking at the data, you see two relevant variables. The
first variable, “vitaminc,” lists each respondent’s vitamin C serum levels (in mg/dL). The
second variable, “race,” is a nominal variable listing each respondent’s racial-ethnic group.
The categories on the race variable are white, black, and other.
Carry out an ANOVA test in R to answer this question. You will want to carry out the
following commands (once the RDS file is in your working directory):
nhanes
summary(aov(A ~ B))
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where the A indicates where you’ll need to specify the dataset (or “object,” in R lingo) and
the dependent variable name, and B indicates where need to again specify the dataset and the
independent variable name.
Copy and paste the R output showing the ANOVA test into your write-up. After you do
that, please interpret the output. Why did you run an ANOVA test instead of an
independent samples z-test or t-test?
Bonus (not required)
A school has three after-school programs that are meant to bolster participating students’ math test
grades. The principal wants to know if there is a meaningful difference between these programs in
terms of how much they impact math scores. They take a random sample of 21 students and
document their most recent math test grade along with the after-school program to which they were
assigned. The principal arranged the information in the following dataset:
grade program
99 1
86 3
77 2
89 2
93 3
79 1
73 3
85 2
88 1
88 2
94 3
99 3
72 2
76 3
80 1
81 2
84 1
85 1
95 2
85 1
90 3
Use this information to conduct an ANOVA test by hand and interpret your results. Be sure to
show all of your work.