Description
Objectives
1. Understand logical statements and subsetting
2. Reinforce knowledge on visualization techniques
3. Compute z-scores and understand the Empirical Rule
Collaboration Policy
In Lab you are encouraged to work in pairs or small groups to discuss the concepts on the
assignments. However, DO NOT copy each other’s work as this constitutes cheating. The work
you submit must be entirely your own. If you have a question in lab, feel free to reach out to
other groups or talk to the TA if you get stuck.
Intro Logical Statements/Relational Operators
Logical Expressions: Type ?Comparison to see the R documentation on the list of all relational
operators you can apply. Many logical expressions in R use these relational operators.
Try running the lines of code below that use the relational operators >, >=, <=, ==, !=. We can
also use the conditions & and | to combine relational operators. Try running these examples:
4 > 3 # Is 4 greater than 3?
c(3,8) >= 3 # Is 3 or 8 greater than or equal to 3?
c(3,8) <= 3 # Is 3 or 8 less than or equal to 3?
c(1,4,9) == 9 # Is 1, 4, or 9 exactly equal to 9?
c(1,4,9) != 9 # Is 1, 4, or 9 not (exactly) equal to 9?
c(1,2,4,7) < 5 & c(1,2,4,7) > 1 #Which of 1,2,4,7 is less than 5 and greater than 1?
c(1,2,4,7) < 5 | c(1,2,4,7) > 1 #Which of 1,2,4,7 is less than 5 or greater than 1?
Notice that the output is a logical vector (i.e., uses TRUE and FALSE) that has the length of the
vector on the left of the relational statement.
Applications of logical statements: calculations
We can perform certain calculations on logical vectors because R reads TRUE as 1 and FALSE
as 0. Create the NCbirths object from last lab and try these examples:
sum(NCbirths$weight > 100) #the number of babies that weighed more than 100 ounces
mean(NCbirths$weight > 100) #the proportion of babies that weighed more than 100 ounces
mean(NCbirths$Gender == “Female”) #the proportion of female babies
mean(NCbirths$Gender != “Male”) #again gives the proportion of female babies
Applications of logical statements: subsets
We can combine logical statements with square brackets to subset data based on conditions.
Examples with NCbirths:
fem_weights <- NCbirths$weight[NCbirths$Gender == "Female"]
With the line above we created a vector called fem_weights that contains the weights of all the
female babies.
Good coding practices:
1. Use the pound symbol (#) often to comment on different code sections. Consider using
them to label your exercise numbers and question parts, and to help describe what your
code does.
2. Use good spacing. Adding a space between arguments and inside of functions makes
your code easier to read. You can also skip lines for clarity
3. Create as many objects as you like to make it easier to follow. For example, consider my
line above creating the fem_weights object. An alternative way to code this using best
practices is below:
## Create an object with the baby weights from NCbirths
baby_weight <- NCbirths$weight
## Create an object with the baby genders from NCbirths
baby_gender <- NCbirths$Gender
## Create a logical vector to describe if the gender is female
is_female <- baby_gender == "Female"
## Create the vector of weights containing only females
fem_weights <- baby_weight[is_female]
Exercise 1
We will be working with lead and copper data obtained from the residents of Flint, Michigan
from January-February, 2017. Data are reported in PPB (parts per billion, or µg/L) from each
residential testing kit. Remember that “Pb” denotes lead, and “Cu” denotes copper. You can
learn more about the Flint water crisis at https://en.wikipedia.org/wiki/Flint_water_crisis.
a. Download the data from CCLE and read it into R. When you read in the data, name your
object “flint”.
b. The EPA states a water source is especially dangerous if the lead level is 15 PPB or greater.
What proportion of the locations tested were found to have dangerous lead levels?
c. Report the mean copper level for only test sites in the North region.
d. Report the mean copper level for only test sites with dangerous lead levels (at least 15 PPB).
e. What proportion of the lead observations are above zero, but also less than the dangerous
level?
f. Report the mean lead and copper levels.
g. Create a box plot with a good title for the lead levels.
h. Based on what you see in part (g), does the mean seem to be a good measure of center for the
data? Report a more useful statistic for this data.
Exercise 2
The data here represent life expectancies (Life) and per capita income (Income) in 1974 dollars
for 101 countries in the early 1970’s. The source of these data is: Leinhardt and Wasserman
(1979), New York Times (September, 28, 1975, p. E-3). They also appear on Regression
Analysis by Ashish Sen and Muni Srivastava. You can access these data in R using:
life <- read.table("http://www.stat.ucla.edu/~nchristo/statistics12/countries_life.txt",
header=TRUE)
a. Construct a scatterplot of Life against Income. Note: Income should be on the horizontal axis.
How does income appear to affect life expectancy?
b. Construct the boxplot and histogram of Income. Are there any outliers?
c. Split the data set into two parts: One for which the Income is strictly below $1000, and one for
which the Income is at least $1000. Come up with your own names for these two objects.
d. Use the data for which the Income is below $1000. Plot Life against Income and compute the
correlation coefficient. Hint: use the function cor()
Exercises continue on the next page
Exercise 3
Use R to access the Maas river data which contains the concentration of lead and zinc in ppm at
155 locations at the banks of the Maas river in the Netherlands. Read the data in R as follows:
maas <- read.table("http://www.stat.ucla.edu/~nchristo/statistics12/soil.txt", header=TRUE)
a. Compute the summary statistics for lead and zinc using the summary() function. What is the
interquartile range (IQR) for zinc?
b. Plot two histograms: one of lead and one of log(lead).
c. Plot log(lead) against log(zinc). What do you observe?
d. The level of risk for surface soil based on lead concentration in ppm is given on the table
below:
Mean concentration (ppm) Level of risk
Below 150 Lead-free
Between 150-400 Lead-safe
Above 400 Significant environmental lead hazard
Use techniques similar to last lab to give different colors and sizes to the lead concentration at
these 155 locations. You do not need to use the maps package create a map of the area. Just plot
the points without a map.
Exercise 4
The data for this exercise represent approximately the centers (given by longitude and latitude)
of each one of the City of Los Angeles neighborhoods. See also the Los Angeles Times project
on the City of Los Angeles neighborhoods at: http://projects.latimes.com/mappingla/neighborhoods/. You can access these data at:
LA <- read.table("http://www.stat.ucla.edu/~nchristo/statistics12/la_data.txt", header=TRUE)
a. Plot the data point locations. Use good formatting for the axes and title. Then add the outline
of LA County by typing:
map("county", "california", add = TRUE)
b. Do you see any relationship between income and school performance? Hint: Plot the variable
Schools against the variable Income and describe what you see. Ignore the data points on the plot
for which Schools = 0. Use what you learned about subsetting with logical statements to first
create the objects you need for the scatter plot. Then, create the scatter plot. Alternate methods
may only receive half credit.
c. Let’s say we have a new observation of a $100,000 income. Compute the z-score for this
observation using the LA Income data. What does this z-score tell us?
d. Determine the proportion of LA Income observations that are within 1SD, 2SD, and 3SD of
the average. How do these results compare with the empirical rule?
