## This first command can install the pacakge. I've commented it out here because it only needs to run once.
## You can also install packages from the 'Packages' tab of the Rstudio interface.
##
## install.packages("openintro")
library(openintro)
## Loading required package: airports
## Loading required package: cherryblossom
## Loading required package: usdata
data("county")
class(county)
## [1] "tbl_df" "tbl" "data.frame"
Notice that the results of that last call to class()
produced something you might not have expected: three different values! This is because the OpenIntro authors have provided this dataset as something called a “tibble” (that’s the tbl_df
and tbl
bits) which is basically a souped-up Tidyverse analogue to a Base-R dataframe. You can do some nice things with Tidyverse tibbles. For example, you can invoke them directly and not worry that R is going to print out a massive amonut of data at your console. The output also includes information about the dimensions and the types/classes of the columns/variables in the Tibble. Here’s what it looks like:
county
## # A tibble: 3,142 x 15
## name state pop2000 pop2010 pop2017 pop_change poverty homeownership
## <chr> <fct> <dbl> <dbl> <int> <dbl> <dbl> <dbl>
## 1 Auta… Alab… 43671 54571 55504 1.48 13.7 77.5
## 2 Bald… Alab… 140415 182265 212628 9.19 11.8 76.7
## 3 Barb… Alab… 29038 27457 25270 -6.22 27.2 68
## 4 Bibb… Alab… 20826 22915 22668 0.73 15.2 82.9
## 5 Blou… Alab… 51024 57322 58013 0.68 15.6 82
## 6 Bull… Alab… 11714 10914 10309 -2.28 28.5 76.9
## 7 Butl… Alab… 21399 20947 19825 -2.69 24.4 69
## 8 Calh… Alab… 112249 118572 114728 -1.51 18.6 70.7
## 9 Cham… Alab… 36583 34215 33713 -1.2 18.8 71.4
## 10 Cher… Alab… 23988 25989 25857 -0.6 16.1 77.5
## # … with 3,132 more rows, and 7 more variables: multi_unit <dbl>,
## # unemployment_rate <dbl>, metro <fct>, median_edu <fct>,
## # per_capita_income <dbl>, median_hh_income <int>, smoking_ban <fct>
Notice that the Tibble refers to some numeric variables as “
The results of this call are actually sufficient to answer PC1.3 and PC1.4 below.
If you didn’t know or didn’t realize that calling a Tibble directly answered this, here are some other ways to find the dimensions of a dataset:
dim(county)
## [1] 3142 15
nrow(county)
## [1] 3142
ncol(county)
## [1] 15
Again, some additional tools/approaches you might use to answer this if the Tibble method isn’t available/known to you. Note that you can find out the class for any one variable easily with the class()
command. Iterating this over the names of all the variables in a dataframe is feasible, but tedious and inefficient, so I provide a more concise method with lapply()
below:
names(county)
## [1] "name" "state" "pop2000"
## [4] "pop2010" "pop2017" "pop_change"
## [7] "poverty" "homeownership" "multi_unit"
## [10] "unemployment_rate" "metro" "median_edu"
## [13] "per_capita_income" "median_hh_income" "smoking_ban"
## just an example here:
class(county$poverty)
## [1] "numeric"
## lapply() is useful for doing this over all variables in a dataframe/tibble
lapply(county, class)
## $name
## [1] "character"
##
## $state
## [1] "factor"
##
## $pop2000
## [1] "numeric"
##
## $pop2010
## [1] "numeric"
##
## $pop2017
## [1] "integer"
##
## $pop_change
## [1] "numeric"
##
## $poverty
## [1] "numeric"
##
## $homeownership
## [1] "numeric"
##
## $multi_unit
## [1] "numeric"
##
## $unemployment_rate
## [1] "numeric"
##
## $metro
## [1] "factor"
##
## $median_edu
## [1] "factor"
##
## $per_capita_income
## [1] "numeric"
##
## $median_hh_income
## [1] "integer"
##
## $smoking_ban
## [1] "factor"
For my example, I’ll work with the poverty
variable:
length(county$poverty)
## [1] 3142
min(county$poverty, na.rm=TRUE) ## That na.rm=TRUE part is crucial!
## [1] 2.4
max(county$poverty, na.rm=TRUE)
## [1] 52
mean(county$poverty, na.rm=TRUE) ## So many significant digits...
## [1] 15.96885
sd(county$poverty, na.rm=TRUE)
## [1] 6.515682
## And here's a built-in command that covers many of these:
summary(county$poverty)
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 2.40 11.30 15.20 15.97 19.40 52.00 2
hist(county$poverty)
boxplot(county$poverty)
Because each row in the dataset corresponds to a county, the following will summarize the number of counties per state in the data
table(county$state)
##
## Alabama Alaska Arizona
## 67 29 15
## Arkansas California Colorado
## 75 58 64
## Connecticut Delaware District of Columbia
## 8 3 1
## Florida Georgia Hawaii
## 67 159 5
## Idaho Illinois Indiana
## 44 102 92
## Iowa Kansas Kentucky
## 99 105 120
## Louisiana Maine Maryland
## 64 16 24
## Massachusetts Michigan Minnesota
## 14 83 87
## Mississippi Missouri Montana
## 82 115 56
## Nebraska Nevada New Hampshire
## 93 17 10
## New Jersey New Mexico New York
## 21 33 62
## North Carolina North Dakota Ohio
## 100 53 88
## Oklahoma Oregon Pennsylvania
## 77 36 67
## Rhode Island South Carolina South Dakota
## 5 46 66
## Tennessee Texas Utah
## 95 254 29
## Vermont Virginia Washington
## 14 133 39
## West Virginia Wisconsin Wyoming
## 55 72 23
set.seed(220920) ## A recent date.
sample(x=c(1:20), size=1)
## [1] 3
My dataset number for the rest of this worked solution to the programming challenge is 3. That said, the code should work if you substitute an appropriate group number into the url below.
I’ll do this by pointing RStudio directly to the URL for the data using the url()
and load()
commands.
load(url("https://communitydata.science/~ads/teaching/2020/stats/data/week_03/group_03.RData"))
ls() # shows me what's available. The counties dataset is still hanging around.
## [1] "county" "d"
head(d)
## [1] 5.0165660 0.7734509 24.9639274 1.7455026 1.1062885 454.2820677
Note: If you downloaded the file, you’ll need to point R’s load()
command at the correct file location on your machine. RStudio can be…picky about this sort of thing.
Also, a clarifying point: if you’re compiling your own RMarkdown scripts, you will need to load the dataset explicitly (not just open the file with RStudio). When RMarkdown tries to “knit” the .Rmd file into HTML or whatever, it is as if you are running the entire contents of the .Rmd script in an entirely new RStudio environment. This means if you don’t load something explicitly within the .Rmd script RStudio will not know where to find it.
I’ll do all the ones I asked for as well as some I didn’t (just so you have an example what the commands look like)
min(d)
## [1] -42.34089
max(d)
## [1] 33720.15
mean(d)
## [1] 831.6718
sd(d)
## [1] 3775.512
## extras
median(d)
## [1] 5.183996
var(d) ## variance. compare to the standard deviation
## [1] 14254490
IQR(d) ## interquartile range
## [1] 76.51708
## A handy Base-R command that does a bunch of these at once:
summary(d)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -42.34 0.71 5.18 831.67 77.22 33720.15
Graphing using R’s built-in functions:
hist(d)
boxplot(d)
d[d < 0] <- NA
Fwiw, I want to point out that this last line of code is a little “fast and loose.” I have reused my original variable name when I recode the negative values to NA
. This means that my copy of d
has been changed and the only way I can restore it is by reading in the raw data again (which would, in turn, overwrite my recoded copy). It is often a good idea to check your work after recoding. You could do that here by “stashing” the original variable in a new object/name (e.g., run something like d.orig <- d
before running the line above). Then after you’ve recoded the negative values, you could run whatever tests/comparisons you like to make sure the recoding is correct before deleting the original data (which can be done with rm(d.orig)
).
Onwards to the new mean and standard deviation:
mean(d, na.rm=T) # R can understand "T" in place of TRUE
## [1] 876.5269
sd(d, na.rm=T)
## [1] 3869.37
Both values here are larger than before I removed my negative values. This is pretty intuitive in the case of the mean, but maybe less so with the standard deviation since the range of the values in the recoded variable is smaller. Can you explain how the standard deviation would increase?
d.log <- log1p(d) # Note: I use log1p() because some values are very close to zero
mean(d.log, na.rm=T)
## [1] 2.845581
median(d.log, na.rm=T)
## [1] 2.098321
sd(d.log, na.rm=T)
## [1] 2.667537
hist(d.log)
boxplot(d.log)
Next week, I will introduce the ggplot2
package in the R tutorial. For now, I’ll reproduce the historgram and boxplot I made above in ggplot2 and leave these examples here for future reference. Graphing a single vector in ggplot2 is a bit weird, so this looks a little different than the examples from the R lecture:
## if you haven't already you'll need to make sure ggplot2 is installed
## install.packages("ggplot2")
library(ggplot2)
p <- ggplot() + aes(d.log)
p + geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 5 rows containing non-finite values (stat_bin).
p + geom_boxplot(aes(x="", y=d.log))
## Warning: Removed 5 rows containing non-finite values (stat_boxplot).
Note that ggplot2 generates a warning about 5 “non-fininte values.” In this case, that is due to the 5 NA
values I created when I recoded the negatives, so I don’t need to worry about the warning.
A compelling answer to this depends on the variable you chose. For the one I looked at in my example code (poverty
) the data is somewhat right skewed, but not much. In this case, the mean and standard deviation should represent the central tendency and spread of the variable pretty well. If your variable was different (e.g., one of the population or income measures, it would probably be good to also examine and report the median and interquartile range. See OpenIntro
chapter 2 for more on distinctions/reasons behind this.
Definitely not. The data is very skewed with a long (positive) tail, suggesting that median and interquartile range would be better measures to report.
The cleaned and log-transformed version of the variable has no negative values and is far less right-skewed than the original. You should absolutely prefer the cleaned variable with no negative values since they resulted from a coding error (see the text of PC2.5). However, a preference for the log-transformed or untransformed variable likely depends on the situation. It’s almost always good to report descriptive statistics for “raw,” untransformed versions of your variables. However, you might prefer the log-transformed version for developing a stronger set of intuitions about your data, comparing with prior work that uses log-transformed versions of a similar measure, or conducting certain statistical tests (we’ll talk more about this later in the course).