Tutorial 2: Introduction to Data
Johannes Karreth
RPOS 517, Day 2
This tutorial shows you:
- how to load and inspect a dataset
- how to summarize and describe variables
- how to create basic descriptive plots of data
- how to use Dropbox to share data with others
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 tutorial, 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.
Note on copying & pasting code from the PDF version of this tutorial: Please note that you may run into trouble if you copy & paste code from the PDF version of this tutorial into your R script. When the PDF is created, some characters (for instance, quotation marks) are converted into non-text characters that R won’t recognize. To use code from this tutorial, please type it yourself into your R script or you may copy & paste code from the source file for this tutorial which is posted on my website.
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.
First, download the dataset from my website and open it in Excel. Here, I provide a smaller version since the dataset we use in this tutorial is rather big. The link to the smaller version is http://www.jkarreth.net/files/cdc_small.csv. Save this file on your computer, then right-click it and open it in Excel. Have a look at the dataset, identify rows and columns and remember the structure of the dataset. Close the file again and delete it. (We will read the full version of the dataset into R directly from my website, so no need to store it on your computer this time.)
We begin by loading the data set of 20,000 observations into the R workspace. After launching RStudio, create a new working directory (for RPOS 517, Day 2) on your computer. In that directory, create a new script file. Click on File -> New -> R Script. This will open a blank document above the console. As you go along you can copy and paste your code here and save it. This is a good way to keep track of your code and be able to reuse it later. To run your code from this document, highlight the code and hit the Run button, or highlight the code and hit command+enter on a Mac or control+enter on a PC. You’ll also want to save this script. To do so click on the disk icon. The first time you hit save, RStudio will ask for a file name; you can name it anything you like. Once you hit save you’ll see the file appear under the Files tab in the lower right panel. You can reopen this file anytime by simply clicking on it.
Enter the usual meta-information in the script file (purpose of the script, author, etc.), then begin by loading this dataset:
cdc <- read.csv("http://www.jkarreth.net/files/cdc.csv")The data set cdc that shows up in your workspace is a data set, 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 tutorials.
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.
We can have a look at the first few entries (rows) of our data with the command
head(cdc)## genhlth exerany hlthplan smoke100 height weight wtdesire age gender
## 1 good 0 1 0 70 175 175 77 m
## 2 good 0 1 1 64 125 115 33 f
## 3 good 1 1 1 60 105 105 49 f
## 4 good 1 1 0 66 132 124 42 f
## 5 very good 0 1 0 61 150 130 55 f
## 6 very good 1 1 0 64 114 114 55 fand similarly we can look at the last few by typing
tail(cdc)## genhlth exerany hlthplan smoke100 height weight wtdesire age
## 19995 good 0 1 1 69 224 224 73
## 19996 good 1 1 0 66 215 140 23
## 19997 excellent 0 1 0 73 200 185 35
## 19998 poor 0 1 0 65 216 150 57
## 19999 good 1 1 0 67 165 165 81
## 20000 good 1 1 1 69 170 165 83
## gender
## 19995 m
## 19996 f
## 19997 m
## 19998 f
## 19999 f
## 20000 mYou could also look at all of the data frame at once by typing its name into the console, but that might be unwise here. We know cdc has 20,000 rows, so viewing the entire data set would mean flooding your screen. It’s better to take small peeks at the data with head, tail or the subsetting techniques that you’ll learn in a moment.
Summaries and tables
The BRFSS questionnaire is a massive trove of information. A good first step in any analysis is to distill all of that information into a few summary statistics and graphics. As a simple example, the function summary returns a numerical summary: minimum, first quartile, median, mean, second quartile, and maximum. For weight this is
summary(cdc$weight)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 68.0 140.0 165.0 169.7 190.0 500.0Notice here that there are no missing observations for any of the variables. This means that we don’t have to think about how to deal with missing data. In other (applied) cases, this will be different, and you need to give some thought to missing data in your R commands and your data analysis.
R also functions like a very fancy calculator. If you wanted to compute the interquartile range for the respondents’ weight, you would look at the output from the summary command above and then enter
190 - 140## [1] 50R also has built-in functions to compute summary statistics one by one. For instance, to calculate the mean, median, and variance of weight, type
mean(cdc$weight) ## [1] 169.683var(cdc$weight)## [1] 1606.484median(cdc$weight)## [1] 165While it makes sense to describe a continuous variable like weight in terms of these statistics, what about categorical data? We would instead consider the sample frequency or relative frequency distribution. The function table does this for you by counting the number of times each kind of response was given. For example, to see the number of people who have smoked 100 cigarettes in their lifetime, type
table(cdc$smoke100)##
## 0 1
## 10559 9441or instead look at the relative frequency distribution by dividing the table by the total number of observations in the dataset. You can obtain the number of observations (remember: observations are rows) by using the command nrow(), which extracts the number of rows of the object you give to it:
table(cdc$smoke100) / nrow(cdc)##
## 0 1
## 0.52795 0.47205Notice how R automatically divides all entries in the table by 20,000 in the command above. This is similar to something we observed in the last tutorial; when we multiplied or divided a vector with a number, R applied that action across entries in the vectors. As we see above, this also works for tables. Next, we make a bar plot of the entries in the table by putting the table inside the barplot command.
barplot(table(cdc$smoke100))
Notice what we’ve done here! We’ve computed the table of cdc$smoke100 and then immediately applied the graphical function, barplot. This is an important idea: R commands can be nested. You could also break this into two steps by typing the following:
smoke <- table(cdc$smoke100)
barplot(smoke)
Here, we’ve made a new object, a table, called smoke (the contents of which we can see by typing smoke into the console) and then used it in as the input for barplot. The special symbol <- performs an assignment, taking the output of one line of code and saving it into an object in your workspace. This is another important idea that we’ll return to later.
The table command can be used to tabulate any number of variables that you provide. For example, to examine which participants have smoked across each gender, we could use the following.
table(cdc$gender, cdc$smoke100)##
## 0 1
## f 6012 4419
## m 4547 5022Here, we see column totals of 0 and 1. Recall that 1 indicates a respondent has smoked at least 100 cigarettes. The rows refer to gender. To create a mosaic plot of this table, we would enter the following command.
mosaicplot(table(cdc$gender, cdc$smoke100))
We could have accomplished this in two steps by saving the table in one line and applying mosaicplot in the next (see the table/barplot example above).
What does the mosaic plot reveal about smoking habits and gender?
We could also create a table with percentages if we need more precise numbers. Here, we continue using the table() command, but wrap it in another command: prop.table. This command allows us to express the cells of the table as percentages. We can display each cell as a percentage of all observations, or as the row percentage (using the option margin = 1) or as the column percentage (using the option margin = 2). Note that R usually thinks in the order “rows, then columns” - hence rows are coded as 1 in this function and columns as 2. Here, we may be interested in the percentage of males and females that are smokers or non-smokers:
prop.table(table(cdc$gender, cdc$smoke100), margin = 1)##
## 0 1
## f 0.5763589 0.4236411
## m 0.4751803 0.5248197Interlude: How R thinks about data
We mentioned that R stores data in data frames, which you might think of as a type of spreadsheet. Each row is a different observation (a different respondent) and each column is a different variable (the first is genhlth, the second exerany and so on). We can see the size of the data frame next to the object name in the workspace or we can type
dim(cdc)## [1] 20000 9which will return the number of rows and columns. Now, if we want to access a subset of the full data frame, we can use row-and-column notation. For example, to see the sixth variable of the 567th respondent, use the format
cdc[567, 6]## [1] 160which means we want the element of our data set that is in the 567th row (meaning the 567th person or observation) and the 6th column (in this case, weight). We know that weight is the 6th variable because it is the 6th entry in the list of variable names
names(cdc)## [1] "genhlth" "exerany" "hlthplan" "smoke100" "height" "weight"
## [7] "wtdesire" "age" "gender"To see the weights for the first 10 respondents we can type
cdc[1:10, 6]## [1] 175 125 105 132 150 114 194 170 150 180In this expression, we have asked just for rows in the range 1 through 10. R uses the : to create a range of values, so 1:10 expands to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. You can see this by entering
1:10## [1] 1 2 3 4 5 6 7 8 9 10Finally, if we want all of the data for the first 10 respondents, type
cdc[1:10, ]## genhlth exerany hlthplan smoke100 height weight wtdesire age gender
## 1 good 0 1 0 70 175 175 77 m
## 2 good 0 1 1 64 125 115 33 f
## 3 good 1 1 1 60 105 105 49 f
## 4 good 1 1 0 66 132 124 42 f
## 5 very good 0 1 0 61 150 130 55 f
## 6 very good 1 1 0 64 114 114 55 f
## 7 very good 1 1 0 71 194 185 31 m
## 8 very good 0 1 0 67 170 160 45 m
## 9 good 0 1 1 65 150 130 27 f
## 10 good 1 1 0 70 180 170 44 mBy leaving out an index or a range (we didn’t type anything between the comma and the square bracket), we get all the columns. When starting out in R, this is a bit counterintuitive. As a rule, we omit the column number to see all columns in a data frame. Similarly, if we leave out an index or range for the rows, we would access all the observations, not just the 567th, or rows 1 through 10. Try the following to see the weights for all 20,000 respondents fly by on your screen
cdc[ ,6]Recall that column 6 represents respondents’ weight, so the command above reported all of the weights in the data set. An alternative method to access the weight data is by referring to the name. Previously, we typed names(cdc) to see all the variables contained in the cdc data set. We can use any of the variable names to select items in our data set.
cdc$weightThe dollar-sign tells R to look in data frame cdc for the column called weight. Since that’s a single vector, we can subset it with just a single index inside square brackets. We see the weight for the 567th respondent by typing
cdc$weight[567]## [1] 160Similarly, for just the first 10 respondents
cdc$weight[1:10]## [1] 175 125 105 132 150 114 194 170 150 180The command above returns the same result as the cdc[1:10,6] command. Both row-and-column notation and dollar-sign notation are widely used, which one you choose to use depends on your personal preference.
A little more on subsetting
It’s often useful to extract all individuals (cases) in a data set that have specific characteristics. We accomplish this through conditioning commands. First, consider expressions like
cdc$gender == "m"or
cdc$age > 30These commands produce a series of TRUE and FALSE values. There is one value for each respondent, where TRUE indicates that the person was male (via the first command) or older than 30 (second command).
Suppose we want to extract just the data for the men in the sample, or just for those over 30. We can use the R function subset to do that for us. For example, the command
mdata <- subset(cdc, cdc$gender == "m")will create a new data set called mdata that contains only the men from the cdc data set. In addition to finding it in your workspace alongside its dimensions, you can take a peek at the first several rows as usual
head(mdata)## genhlth exerany hlthplan smoke100 height weight wtdesire age gender
## 1 good 0 1 0 70 175 175 77 m
## 7 very good 1 1 0 71 194 185 31 m
## 8 very good 0 1 0 67 170 160 45 m
## 10 good 1 1 0 70 180 170 44 m
## 11 excellent 1 1 1 69 186 175 46 m
## 12 fair 1 1 1 69 168 148 62 mThis new data set contains all the same variables but just under half the rows. It is also possible to tell R to keep only specific variables, which is a topic we’ll discuss in a future tutorial. For now, the important thing is that we can carve up the data based on values of one or more variables.
As an aside, you can use several of these conditions together with & and |. The & is read “and” so that
m_and_over30 <- subset(cdc, gender == "m" & age > 30)will give you the data for men over the age of 30. The | character is read “or” so that
m_or_over30 <- subset(cdc, gender == "m" | age > 30)will take people who are men or over the age of 30 (why that’s an interesting group is hard to say, but right now the mechanics of this are the important thing). In principle, you may use as many “and” and “or” clauses as you like when forming a subset.
As an alternative to the subset command, and as a more flexible option, you can subset using hard brackets and by placing conditions on rows (before the comma). The equivalents to the commands above read like this:
mdata <- cdc[cdc$gender == "m", ]
m_and_over30 <- cdc[cdc$gender == "m" & cdc$age > 30, ]
m_or_over30 <- cdc[cdc$gender == "m" | cdc$age > 30, ]Continuous data
With our subsetting tools in hand, we’ll now return to the task of the day: making basic summaries of the BRFSS questionnaire. We’ve already looked at categorical data such as smoke and gender so now let’s turn our attention to continuous data. Two common ways to visualize continuous data are with box plots and histograms. We can construct a box plot for a single variable with the following command.
boxplot(cdc$height)
You can compare the locations of the components of the box by examining the summary statistics.
summary(cdc$height)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 48.00 64.00 67.00 67.18 70.00 93.00Confirm that the median and upper and lower quartiles reported in the numerical summary match those in the graph. The purpose of a boxplot is to provide a thumbnail sketch of a variable for the purpose of comparing across several categories. So we can, for example, compare the heights of men and women with
boxplot(cdc$height ~ cdc$gender)
The notation here is new. The ~ character can be read versus or as a function of. So we’re asking R to give us a box plots of heights where the groups are defined by gender.
Next let’s consider a new variable that doesn’t show up directly in this data set: Body Mass Index (BMI) (http://en.wikipedia.org/wiki/Body_mass_index). BMI is a weight to height ratio and can be calculated as:
\[ BMI = \frac{weight~(lb)}{height~(in)^2} * 703 \]
703 is the approximate conversion factor to change units from metric (meters and kilograms) to imperial (inches and pounds).
The following two lines first make a new object called bmi and then creates box plots of these values, defining groups by the variable cdc$genhlth. Note that we add the bmi object to the cdc data frame by preceding bmi with cdc$. This command simply adds a new column (variable) ot the cdc data frame.
cdc$bmi <- (cdc$weight / cdc$height^2) * 703
boxplot(cdc$bmi ~ cdc$genhlth)
Notice that the first line above is just some arithmetic, but it’s applied to all 20,000 numbers in the cdc data set. That is, for each of the 20,000 participants, we take their weight, divide by their height-squared and then multiply by 703. The result is 20,000 BMI values, one for each respondent. This is one reason why we like R: it lets us perform computations like this using very simple expressions.
Now, let’s make some histograms. We can look at the histogram for the age of our respondents with the command
hist(cdc$age)
Histograms are generally a very good way to see the shape of a single distribution, but that shape can change depending on how the data is split between the different bins. You can control the number of bins by adding an argument to the command. In the next two lines, we first make a default histogram of bmi and then one with 50 breaks.
hist(cdc$bmi)
hist(cdc$bmi, breaks = 50)
Note that you can flip between plots that you’ve created by clicking the forward and backward arrows in the lower right region of RStudio, just above the plots. How do these two histograms compare?
Finally, we will make a scatterplot of two variables to check visually if they might be related. For this exercise, let’s look at height and weight. We make use of the with() command; this command saves us some typing. The idea: with(dataset, function(x)) is equivalent to function(dataset\$x). In addition, we use different colors for male and female subjects.
with(cdc[cdc$gender == "m", ],
plot(x = height,
y = weight,
col = "blue")
)
with(cdc[cdc$gender == "f", ],
points(x = height,
y = weight,
col = "red")
)
Again, you could make some modifications to the plot for better quality - look up the functions and arguments in R help or google them:
library(scales)
with(cdc,
plot(x = height,
y = weight,
type = "n",
las = 1,
xlab = "Height in Inches",
ylab = "Weight in Pounds"
)
)
grid()
with(cdc[cdc$gender == "m", ],
points(x = jitter(height),
y = weight,
col = alpha(colour = "blue", alpha = 0.5),
pch = 19,
cex = 0.5)
)
with(cdc[cdc$gender == "f", ],
points(x = jitter(height),
y = weight,
col = alpha(colour = "red", alpha = 0.1),
pch = 19,
cex = 0.5)
)
A second option to construct plots in R is to use the ggplot2 package. This package is very useful for a wide range of plotting commands and we will use it from time to time in this class. The above plot can be constructed in ggplot2 using the following command:
library(ggplot2)
p <- ggplot(data = cdc,
aes(x = height,
y = weight,
color = gender)
) +
geom_point()
p
At this point, we’ve done a good first pass at analyzing the information in the BRFSS questionnaire. We’ve found an interesting association between smoking and gender, and we can say something about the relationship between people’s assessment of their general health and their own BMI. We’ve also picked up essential computing tools – summary statistics, subsetting, and plots – that will serve us well throughout this course.
Addendum: Sharing and importing data from a Dropbox folder
Current procedure using the curl package
Note: I updated this section on 2/16/2016 because of a change in the Dropbox API that led to a change in this routine.
From today on, I will ask you to store any data set you create in this course on a folder on your computer that is linked to Dropbox. You can then share a URL of this data set with me and others. This facilitates sharing data and reproducing any issues you may run into during your data analysis.
To do this, go to http://www.dropbox.com, create an account, download the Dropbox software, and designate a Dropbox folder on your computer. Move all your RPOS/RPAD 517 folders into the Dropbox folder.
Once you are ready to share your data, right-click the data set you’d like to share and send the resulting link to me (or whomever you want to share your data with).
To access a data set from someone else’s Dropbox folder, use the curl package. First, install the package:
install.packages("curl")For this example, I will share a data set containing U.S. population information for diferent age groups. This data set is stored in a folder within my personal Dropbox folder. Right-clicking the file yields the following link: https://www.dropbox.com/s/miigloo2k90xm1y/US-EST00INT-ALLDATA.csv?dl=0.
You can now use the curl_download function and its arguments url and destfile to download the data set to a folder on your computer. However, you need to change the last part of the URL to ?dl=1.
library(curl)
curl_download(url = "https://www.dropbox.com/s/miigloo2k90xm1y/US-EST00INT-ALLDATA.csv?dl=1",
destfile = "~/Desktop/census.csv")Now, you can read the data into R as usual:
census <- read.csv(file = "~/Desktop/census.csv")
head(census)## MONTH YEAR AGE TOT_POP TOT_MALE TOT_FEMALE WA_MALE WA_FEMALE
## 1 4 2000 999 281424600 138056128 143368472 112478128 115628370
## 2 4 2000 0 3805718 1949050 1856668 1492186 1415163
## 3 4 2000 1 3820647 1953136 1867511 1496086 1422284
## 4 4 2000 2 3790534 1939037 1851497 1482944 1409010
## 5 4 2000 3 3832855 1958991 1873864 1503352 1429256
## 6 4 2000 4 3926400 2010693 1915707 1543765 1462539
## BA_MALE BA_FEMALE IA_MALE IA_FEMALE AA_MALE AA_FEMALE NA_MALE NA_FEMALE
## 1 16971838 18733033 1332962 1330889 5127697 5461425 235205 227331
## 2 291477 282702 23723 22582 70510 67182 4151 3936
## 3 294701 286083 23998 22934 69060 69154 4239 4055
## 4 295966 285507 23357 22631 71200 70472 4155 3892
## 5 296488 287904 23647 22904 72170 72214 4176 3890
## 6 306742 297260 23984 23013 73383 72582 4275 4111
## TOM_MALE TOM_FEMALE NH_MALE NH_FEMALE NHWA_MALE NHWA_FEMALE NHBA_MALE
## 1 1910298 1987424 119894001 126224223 95697274 99879722 16293733
## 2 67003 65103 1554434 1480223 1135191 1074964 274068
## 3 65052 63001 1572816 1502140 1151875 1092310 277760
## 4 61415 59985 1565050 1493975 1143842 1085289 279534
## 5 59158 57696 1585022 1516389 1163794 1104992 280217
## 6 58544 56202 1633125 1554957 1200617 1134663 290353
## NHBA_FEMALE NHIA_MALE NHIA_FEMALE NHAA_MALE NHAA_FEMALE NHNA_MALE
## 1 18019983 1036267 1061197 5012924 5343737 185619
## 2 266105 17228 16438 67356 64138 2910
## 3 269485 17675 17017 66012 66174 3078
## 4 269737 17290 16723 68278 67615 3029
## 5 272192 17473 17007 69290 69411 2990
## 6 281567 17853 17179 70497 69873 3085
## NHNA_FEMALE NHTOM_MALE NHTOM_FEMALE H_MALE H_FEMALE HWA_MALE
## 1 181484 1668184 1738100 18162127 17144249 16780854
## 2 2752 57681 55826 394616 376445 356995
## 3 2882 56416 54272 380320 365371 344211
## 4 2800 53077 51811 373987 357522 339102
## 5 2796 51258 49991 373969 357475 339558
## 6 3007 50720 48668 377568 360750 343148
## HWA_FEMALE HBA_MALE HBA_FEMALE HIA_MALE HIA_FEMALE HAA_MALE HAA_FEMALE
## 1 15748648 678105 713050 296695 269692 114773 117688
## 2 340199 17409 16597 6495 6144 3154 3044
## 3 329974 16941 16598 6323 5917 3048 2980
## 4 323721 16432 15770 6067 5908 2922 2857
## 5 324264 16271 15712 6174 5897 2880 2803
## 6 327876 16389 15693 6131 5834 2886 2709
## HNA_MALE HNA_FEMALE HTOM_MALE HTOM_FEMALE
## 1 49586 45847 242114 249324
## 2 1241 1184 9322 9277
## 3 1161 1173 8636 8729
## 4 1126 1092 8338 8174
## 5 1186 1094 7900 7705
## 6 1190 1104 7824 7534ARCHIVED: Using version 0.4.4 of the repmis package
If you have the old version 0.4.4. of the repmis package installed, you can still use this routine:
For this example, I will share a data set containing U.S. population information for diferent age groups. This data set is stored in a folder within my personal Dropbox folder. Right-clicking the file yields the following link: https://www.dropbox.com/s/miigloo2k90xm1y/US-EST00INT-ALLDATA.csv?dl=0. This link contains two pieces of information:
- a “key”:
miigloo2k90xm1y - a file name:
US-EST00INT-ALLDATA.csv
You can now use the source_DropboxData function and its arguments file and key to directly access the data set on your computer:
library(repmis)
us_pop <- source_DropboxData(file = "US-EST00INT-ALLDATA.csv",
key = "miigloo2k90xm1y")## Downloading data from: https://dl.dropboxusercontent.com/s/miigloo2k90xm1y/US-EST00INT-ALLDATA.csv## SHA-1 hash of the downloaded data file is:
## ee0037e31e23efac0e59059c2b527b12107ba28ehead(us_pop)## MONTH YEAR AGE TOT_POP TOT_MALE TOT_FEMALE WA_MALE WA_FEMALE
## 1 4 2000 999 281424600 138056128 143368472 112478128 115628370
## 2 4 2000 0 3805718 1949050 1856668 1492186 1415163
## 3 4 2000 1 3820647 1953136 1867511 1496086 1422284
## 4 4 2000 2 3790534 1939037 1851497 1482944 1409010
## 5 4 2000 3 3832855 1958991 1873864 1503352 1429256
## 6 4 2000 4 3926400 2010693 1915707 1543765 1462539
## BA_MALE BA_FEMALE IA_MALE IA_FEMALE AA_MALE AA_FEMALE NA_MALE NA_FEMALE
## 1 16971838 18733033 1332962 1330889 5127697 5461425 235205 227331
## 2 291477 282702 23723 22582 70510 67182 4151 3936
## 3 294701 286083 23998 22934 69060 69154 4239 4055
## 4 295966 285507 23357 22631 71200 70472 4155 3892
## 5 296488 287904 23647 22904 72170 72214 4176 3890
## 6 306742 297260 23984 23013 73383 72582 4275 4111
## TOM_MALE TOM_FEMALE NH_MALE NH_FEMALE NHWA_MALE NHWA_FEMALE NHBA_MALE
## 1 1910298 1987424 119894001 126224223 95697274 99879722 16293733
## 2 67003 65103 1554434 1480223 1135191 1074964 274068
## 3 65052 63001 1572816 1502140 1151875 1092310 277760
## 4 61415 59985 1565050 1493975 1143842 1085289 279534
## 5 59158 57696 1585022 1516389 1163794 1104992 280217
## 6 58544 56202 1633125 1554957 1200617 1134663 290353
## NHBA_FEMALE NHIA_MALE NHIA_FEMALE NHAA_MALE NHAA_FEMALE NHNA_MALE
## 1 18019983 1036267 1061197 5012924 5343737 185619
## 2 266105 17228 16438 67356 64138 2910
## 3 269485 17675 17017 66012 66174 3078
## 4 269737 17290 16723 68278 67615 3029
## 5 272192 17473 17007 69290 69411 2990
## 6 281567 17853 17179 70497 69873 3085
## NHNA_FEMALE NHTOM_MALE NHTOM_FEMALE H_MALE H_FEMALE HWA_MALE
## 1 181484 1668184 1738100 18162127 17144249 16780854
## 2 2752 57681 55826 394616 376445 356995
## 3 2882 56416 54272 380320 365371 344211
## 4 2800 53077 51811 373987 357522 339102
## 5 2796 51258 49991 373969 357475 339558
## 6 3007 50720 48668 377568 360750 343148
## HWA_FEMALE HBA_MALE HBA_FEMALE HIA_MALE HIA_FEMALE HAA_MALE HAA_FEMALE
## 1 15748648 678105 713050 296695 269692 114773 117688
## 2 340199 17409 16597 6495 6144 3154 3044
## 3 329974 16941 16598 6323 5917 3048 2980
## 4 323721 16432 15770 6067 5908 2922 2857
## 5 324264 16271 15712 6174 5897 2880 2803
## 6 327876 16389 15693 6131 5834 2886 2709
## HNA_MALE HNA_FEMALE HTOM_MALE HTOM_FEMALE
## 1 49586 45847 242114 249324
## 2 1241 1184 9322 9277
## 3 1161 1173 8636 8729
## 4 1126 1092 8338 8174
## 5 1186 1094 7900 7705
## 6 1190 1104 7824 7534This is a product of OpenIntro that is released under a Creative Commons Attribution-ShareAlike 3.0 Unported license. This tutorial was adapted for OpenIntro by Andrew Bray and Mine Cetinkaya-Rundel from a tutorial written by Mark Hansen of UCLA Statistics. It was modified by Johannes Karreth for use in RPOS/RPAD 517 at the University at Albany, State University of New York.