Some define Statistics as the field that focuses on turning information into knowledge. The first step in that process is to summarize and describe the raw information - the data. In this lab, you will gain insight into public health by generating simple graphical and numerical summaries of a data set collected by the Centers for Disease Control and Prevention (CDC). As this is a large data set, along the way you’ll also learn the indispensable skills of data processing and subsetting.

Getting started

The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey of 350,000 people in the United States. As its name implies, the BRFSS is designed to identify risk factors in the adult population and report emerging health trends. For example, respondents are asked about their diet and weekly physical activity, their HIV/AIDS status, possible tobacco use, and even their level of healthcare coverage. The BRFSS Web site (http://www.cdc.gov/brfss) contains a complete description of the survey, including the research questions that motivate the study and many interesting results derived from the data.

We will focus on a random sample of 20,000 people from the BRFSS survey conducted in 2000. While there are over 200 variables in this data set, we will work with a small subset.

We begin by loading the data set of 20,000 observations into the R workspace. After launching RStudio, enter the following command.

source("more/cdc.R")

The data set cdc that shows up in your workspace is a data matrix, with each row representing a case and each column representing a variable. R calls this data format a data frame, which is a term that will be used throughout the labs.

To view the names of the variables, type the command

names(cdc)
## [1] "genhlth"  "exerany"  "hlthplan" "smoke100" "height"   "weight"  
## [7] "wtdesire" "age"      "gender"

This returns the names genhlth, exerany, hlthplan, smoke100, height, weight, wtdesire, age, and gender. Each one of these variables corresponds to a question that was asked in the survey. For example, for genhlth, respondents were asked to evaluate their general health, responding either excellent, very good, good, fair or poor. The exerany variable indicates whether the respondent exercised in the past month (1) or did not (0). Likewise, hlthplan indicates whether the respondent had some form of health coverage (1) or did not (0). The smoke100 variable indicates whether the respondent had smoked at least 100 cigarettes in her lifetime. The other variables record the respondent’s height in inches, weight in pounds as well as their desired weight, wtdesire, age in years, and gender.

  1. How many cases are there in this data set? How many variables? For each variable, identify its data type (e.g. categorical, discrete).
dim(cdc)
## [1] 20000     9
sapply(cdc, class)
##   genhlth   exerany  hlthplan  smoke100    height    weight  wtdesire 
##  "factor" "numeric" "numeric" "numeric" "numeric" "integer" "integer" 
##       age    gender 
## "integer"  "factor"

The datatypes for each variable are: genhealth: categorical, ordinal; exerany: categorical, nominal; hlthplan: categorical, nominal; smoke100: categorical, nominal; height: numerical, discrete; weight: numerical, discrete; wtdesire: numerical, discrete; age: numerical, discrete; gender: categorical, nominal

Summaries and tables

  1. Create a numerical summary for height and age, and compute the interquartile range for each. Compute the relative frequency distribution for gender and exerany. How many males are in the sample? What proportion of the sample reports being in excellent health?
summary(cdc$height)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   48.00   64.00   67.00   67.18   70.00   93.00
summary(cdc$age)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   18.00   31.00   43.00   45.07   57.00   99.00
IQR(cdc$height)
## [1] 6
IQR(cdc$age)
## [1] 26
table(cdc$gender)
## 
##     m     f 
##  9569 10431
prop.table(table(cdc$gender))
## 
##       m       f 
## 0.47845 0.52155
table(cdc$exerany)
## 
##     0     1 
##  5086 14914
prop.table(table(cdc$exerany))
## 
##      0      1 
## 0.2543 0.7457
prop.table(table(cdc$genhlth))
## 
## excellent very good      good      fair      poor 
##   0.23285   0.34860   0.28375   0.10095   0.03385
mosaicplot(table(cdc$gender,cdc$smoke100))

We could have accomplished this in two steps by saving the table in one line and applying mosaicplot in the next (see the table/barplot example above).

  1. What does the mosaic plot reveal about smoking habits and gender?

A3: The mosaic plot reveals that more males have smoked 100 cigarettes in their lifetime than females.

Interlude: How R thinks about data

  1. Create a new object called under23_and_smoke that contains all observations of respondents under the age of 23 that have smoked 100 cigarettes in their lifetime. Write the command you used to create the new object as the answer to this exercise.
under23_and_smoke <- subset(cdc, age < 23 & smoke100 == 1)

Quantitative data

bmi <- (cdc$weight / cdc$height^2) * 703
boxplot(bmi ~ cdc$genhlth)

Notice that the first line above is just some arithmetic, but it’s applied to all 20,000 numbers in the cdc data set. That is, for each of the 20,000 participants, we take their weight, divide by their height-squared and then multiply by 703. The result is 20,000 BMI values, one for each respondent. This is one reason why we like R: it lets us perform computations like this using very simple expressions.

  1. What does this box plot show? Pick another categorical variable from the data set and see how it relates to BMI. List the variable you chose, why you might think it would have a relationship to BMI, and indicate what the figure seems to suggest.

5A: The above box plot of BMI vs general health shows a trend that as BMI increases the persons general health is more likely to be worse. Below I have created a box plot that displays BMI vs exerany variable. I chose this because exercise is a proven method to reduce a persons weight and if someone reported that they have exercised in the past month they might have a lower BMI than someone who does not exercise. The below figure seems to confirm my hypothesis, although not definitively, because the median and box show a lower BMI for respondants that have exercised.

boxplot(bmi ~ cdc$exerany)

On Your Own

plot(cdc$wtdesire~cdc$weight)

The above scatter plot shows that the majority of respondants desire a weight between 100 and 250 pounds and desire a weight less than their current weight. We also can see there are a couple outliers where the respondants current weight is quite high or that their desired weight is extremely high.

wdiff <- cdc$weight - cdc$wtdesire

wdiff is a discrete numerical data type where a value of 0 indicates the respondant was currently at their desired weight. If wdiff is positive that indicates that the respondant would like to lose weight; if it is negative it indicates that the respondant would like to gain weight

summary(wdiff)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -500.00    0.00   10.00   14.59   21.00  300.00
boxplot(wdiff)

hist(wdiff, breaks = 30)

Looking at the summary, boxplot and histogram we can see that there are outliers that are far away from the median of 10. The boxplot is fairly hard to see as the spread is so large and the majority of respondants within the interquartile range are near 0. Looking at a histogram with 30 bins, it is a bit easier to see that most respondants are satisfied with their weight but more would like to lose a little weight than gain weight.

summary(wdiff)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -500.00    0.00   10.00   14.59   21.00  300.00
boxplot(wdiff ~ cdc$gender)

sd(cdc$weight)
## [1] 40.08097
mean(cdc$weight)
## [1] 169.683
sub <- subset(cdc, weight < (mean(cdc$weight) + sd(cdc$weight)) & weight > (mean(cdc$weight) - sd(cdc$weight)))
nrow(sub)/nrow(cdc)
## [1] 0.7076

This is a product of OpenIntro that is released under a Creative Commons Attribution-ShareAlike 3.0 Unported. This lab was adapted for OpenIntro by Andrew Bray and Mine Çetinkaya-Rundel from a lab written by Mark Hansen of UCLA Statistics.