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 we explore flights, specifically a random sample of domestic flights that departed from the three major New York City airports in 2013. We will generate simple graphical and numerical summaries of data on these flights and explore delay times. Since this is a large data set, along the way you’ll also learn the indispensable skills of data processing and subsetting.

Getting started

Load packages

In this lab, we will explore and visualize the data using the tidyverse suite of packages. The data can be found in the companion package for OpenIntro labs, openintro.

Let’s load the packages.

library(tidyverse)
library(openintro)

Creating a reproducible lab report

Remember that we will be using R Markdown to create reproducible lab reports. In RStudio, go to New File -> R Markdown… Then, choose From Template and then choose Lab Report for OpenIntro Statistics Labs from the list of templates.

See the following video describing how to get started with creating these reports for this lab, and all future labs:

Basic R Markdown with an OpenIntro Lab

The data

The Bureau of Transportation Statistics (BTS) is a statistical agency that is a part of the Research and Innovative Technology Administration (RITA). As its name implies, BTS collects and makes transportation data available, such as the flights data we will be working with in this lab.

First, we’ll view the nycflights data frame. Type the following in your console to load the data:

data(nycflights)

The data set nycflights that shows up in your workspace is a data matrix, with each row representing an observation 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. For this data set, each observation is a single flight.

To view the names of the variables, type the command

names(nycflights)
##  [1] "year"      "month"     "day"       "dep_time"  "dep_delay" "arr_time" 
##  [7] "arr_delay" "carrier"   "tailnum"   "flight"    "origin"    "dest"     
## [13] "air_time"  "distance"  "hour"      "minute"

This returns the names of the variables in this data frame. The codebook (description of the variables) can be accessed by pulling up the help file:

?nycflights

One of the variables refers to the carrier (i.e. airline) of the flight, which is coded according to the following system.

  • carrier: Two letter carrier abbreviation.
    • 9E: Endeavor Air Inc.
    • AA: American Airlines Inc.
    • AS: Alaska Airlines Inc.
    • B6: JetBlue Airways
    • DL: Delta Air Lines Inc.
    • EV: ExpressJet Airlines Inc.
    • F9: Frontier Airlines Inc.
    • FL: AirTran Airways Corporation
    • HA: Hawaiian Airlines Inc.
    • MQ: Envoy Air
    • OO: SkyWest Airlines Inc.
    • UA: United Air Lines Inc.
    • US: US Airways Inc.
    • VX: Virgin America
    • WN: Southwest Airlines Co.
    • YV: Mesa Airlines Inc.

Remember that you can use glimpse to take a quick peek at your data to understand its contents better.

glimpse(nycflights)
## Rows: 32,735
## Columns: 16
## $ year      <int> 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013,…
## $ month     <int> 6, 5, 12, 5, 7, 1, 12, 8, 9, 4, 6, 11, 4, 3, 10, 1, 2, 8, 1…
## $ day       <int> 30, 7, 8, 14, 21, 1, 9, 13, 26, 30, 17, 22, 26, 25, 21, 23,…
## $ dep_time  <int> 940, 1657, 859, 1841, 1102, 1817, 1259, 1920, 725, 1323, 94…
## $ dep_delay <dbl> 15, -3, -1, -4, -3, -3, 14, 85, -10, 62, 5, 5, -2, 115, -4,…
## $ arr_time  <int> 1216, 2104, 1238, 2122, 1230, 2008, 1617, 2032, 1027, 1549,…
## $ arr_delay <dbl> -4, 10, 11, -34, -8, 3, 22, 71, -8, 60, -4, -2, 22, 91, -6,…
## $ carrier   <chr> "VX", "DL", "DL", "DL", "9E", "AA", "WN", "B6", "AA", "EV",…
## $ tailnum   <chr> "N626VA", "N3760C", "N712TW", "N914DL", "N823AY", "N3AXAA",…
## $ flight    <int> 407, 329, 422, 2391, 3652, 353, 1428, 1407, 2279, 4162, 20,…
## $ origin    <chr> "JFK", "JFK", "JFK", "JFK", "LGA", "LGA", "EWR", "JFK", "LG…
## $ dest      <chr> "LAX", "SJU", "LAX", "TPA", "ORF", "ORD", "HOU", "IAD", "MI…
## $ air_time  <dbl> 313, 216, 376, 135, 50, 138, 240, 48, 148, 110, 50, 161, 87…
## $ distance  <dbl> 2475, 1598, 2475, 1005, 296, 733, 1411, 228, 1096, 820, 264…
## $ hour      <dbl> 9, 16, 8, 18, 11, 18, 12, 19, 7, 13, 9, 13, 8, 20, 12, 20, …
## $ minute    <dbl> 40, 57, 59, 41, 2, 17, 59, 20, 25, 23, 40, 20, 9, 54, 17, 2…

The nycflights data frame is a massive trove of information. Let’s think about some questions we might want to answer with these data:

  • How delayed were flights that were headed to Los Angeles?
  • How do departure delays vary by month?
  • Which of the three major NYC airports has the best on time percentage for departing flights?

Analysis

Lab report

To record your analysis in a reproducible format, you can adapt the general Lab Report template from the openintro package. Watch the video above to learn how.

Departure delays

Let’s start by examing the distribution of departure delays of all flights with a histogram.

ggplot(data = nycflights, aes(x = dep_delay)) +
  geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

This function says to plot the dep_delay variable from the nycflights data frame on the x-axis. It also defines a geom (short for geometric object), which describes the type of plot you will produce.

Histograms are generally a very good way to see the shape of a single distribution of numerical data, but that shape can change depending on how the data is split between the different bins. You can easily define the binwidth you want to use:

ggplot(data = nycflights, aes(x = dep_delay)) +
  geom_histogram(binwidth = 15)

ggplot(data = nycflights, aes(x = dep_delay)) +
  geom_histogram(binwidth = 150)

  1. Look carefully at these three histograms. How do they compare? Are features revealed in one that are obscured in another?

The Answer: the three histograms show there are many flights are leaving earlier than schedule. and majority of of flights leaves on time. and then the higher the delays the less flights are leaving.

If you want to visualize only on delays of flights headed to Los Angeles, you need to first filter the data for flights with that destination (dest == "LAX") and then make a histogram of the departure delays of only those flights.

lax_flights <- nycflights %>%
  filter(dest == "LAX")
ggplot(data = lax_flights, aes(x = dep_delay)) +
  geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Let’s decipher these two commands (OK, so it might look like four lines, but the first two physical lines of code are actually part of the same command. It’s common to add a break to a new line after %>% to help readability).

  • Command 1: Take the nycflights data frame, filter for flights headed to LAX, and save the result as a new data frame called lax_flights.
    • == means “if it’s equal to”.
    • LAX is in quotation marks since it is a character string.
  • Command 2: Basically the same ggplot call from earlier for making a histogram, except that it uses the smaller data frame for flights headed to LAX instead of all flights.

Logical operators: Filtering for certain observations (e.g. flights from a particular airport) is often of interest in data frames where we might want to examine observations with certain characteristics separately from the rest of the data. To do so, you can use the filter function and a series of logical operators. The most commonly used logical operators for data analysis are as follows:

  • == means “equal to”
  • != means “not equal to”
  • > or < means “greater than” or “less than”
  • >= or <= means “greater than or equal to” or “less than or equal to”

You can also obtain numerical summaries for these flights:

lax_flights %>%
  summarise(mean_dd   = mean(dep_delay), 
            median_dd = median(dep_delay), 
            n         = n())
## # A tibble: 1 x 3
##   mean_dd median_dd     n
##     <dbl>     <dbl> <int>
## 1    9.78        -1  1583

Note that in the summarise function you created a list of three different numerical summaries that you were interested in. The names of these elements are user defined, like mean_dd, median_dd, n, and you can customize these names as you like (just don’t use spaces in your names). Calculating these summary statistics also requires that you know the function calls. Note that n() reports the sample size.

Summary statistics: Some useful function calls for summary statistics for a single numerical variable are as follows:

  • mean
  • median
  • sd
  • var
  • IQR
  • min
  • max

Note that each of these functions takes a single vector as an argument and returns a single value.

You can also filter based on multiple criteria. Suppose you are interested in flights headed to San Francisco (SFO) in February:

sfo_feb_flights <- nycflights %>%
  filter(dest == "SFO", month == 2)

Note that you can separate the conditions using commas if you want flights that are both headed to SFO and in February. If you are interested in either flights headed to SFO or in February, you can use the | instead of the comma.

  1. Create a new data frame that includes flights headed to SFO in February, and save this data frame as sfo_feb_flights. How many flights meet these criteria?

The answer: 68 flights.

summary(sfo_feb_flights)
##       year          month        day           dep_time      dep_delay    
##  Min.   :2013   Min.   :2   Min.   : 1.00   Min.   : 613   Min.   :-10.0  
##  1st Qu.:2013   1st Qu.:2   1st Qu.: 7.00   1st Qu.: 943   1st Qu.: -5.0  
##  Median :2013   Median :2   Median :16.00   Median :1268   Median : -2.0  
##  Mean   :2013   Mean   :2   Mean   :15.26   Mean   :1298   Mean   : 10.5  
##  3rd Qu.:2013   3rd Qu.:2   3rd Qu.:22.50   3rd Qu.:1742   3rd Qu.:  9.0  
##  Max.   :2013   Max.   :2   Max.   :28.00   Max.   :2159   Max.   :209.0  
##     arr_time      arr_delay        carrier            tailnum         
##  Min.   : 118   Min.   :-66.00   Length:68          Length:68         
##  1st Qu.:1233   1st Qu.:-21.25   Class :character   Class :character  
##  Median :1497   Median :-11.00   Mode  :character   Mode  :character  
##  Mean   :1607   Mean   : -4.50                                        
##  3rd Qu.:2062   3rd Qu.:  2.00                                        
##  Max.   :2256   Max.   :196.00                                        
##      flight          origin              dest              air_time    
##  Min.   :  11.0   Length:68          Length:68          Min.   :317.0  
##  1st Qu.:  85.0   Class :character   Class :character   1st Qu.:345.0  
##  Median : 641.0   Mode  :character   Mode  :character   Median :354.0  
##  Mean   : 795.1                                         Mean   :351.9  
##  3rd Qu.:1487.2                                         3rd Qu.:360.0  
##  Max.   :2126.0                                         Max.   :376.0  
##     distance         hour           minute     
##  Min.   :2565   Min.   : 6.00   Min.   : 1.00  
##  1st Qu.:2586   1st Qu.: 9.00   1st Qu.:25.00  
##  Median :2586   Median :12.50   Median :33.50  
##  Mean   :2584   Mean   :12.62   Mean   :36.35  
##  3rd Qu.:2586   3rd Qu.:17.00   3rd Qu.:54.00  
##  Max.   :2586   Max.   :21.00   Max.   :59.00
var(sfo_feb_flights)
## Warning in var(sfo_feb_flights): NAs introduced by coercion
##           year month          day    dep_time   dep_delay    arr_time
## year         0     0     0.000000      0.0000     0.00000      0.0000
## month        0     0     0.000000      0.0000     0.00000      0.0000
## day          0     0    71.719930   1480.2221    37.95522   1489.5777
## dep_time     0     0  1480.222125 214100.0158  5191.25373 178443.3679
## dep_delay    0     0    37.955224   5191.2537  1107.53731  -2079.9701
## arr_time     0     0  1489.577700 178443.3679 -2079.97015 227437.5838
## arr_delay    0     0   -35.298507   1749.9403  1077.71642  -5254.2388
## carrier     NA    NA           NA          NA          NA          NA
## tailnum     NA    NA           NA          NA          NA          NA
## flight       0     0 -1107.776997 -47789.5443 -6138.62687 -21006.1071
## origin      NA    NA           NA          NA          NA          NA
## dest        NA    NA           NA          NA          NA          NA
## air_time     0     0   -51.266901  -2830.4934   -87.26866  -2341.2485
## distance     0     0    -6.545215   -240.4214    20.05970   -296.7103
## hour         0     0    14.953468   2151.2397    52.74627   1800.0246
## minute       0     0   -15.124671  -1023.9526   -83.37313  -1559.0904
##             arr_delay carrier tailnum      flight origin dest     air_time
## year          0.00000      NA      NA      0.0000     NA   NA     0.000000
## month         0.00000      NA      NA      0.0000     NA   NA     0.000000
## day         -35.29851      NA      NA  -1107.7770     NA   NA   -51.266901
## dep_time   1749.94030      NA      NA -47789.5443     NA   NA -2830.493415
## dep_delay  1077.71642      NA      NA  -6138.6269     NA   NA   -87.268657
## arr_time  -5254.23881      NA      NA -21006.1071     NA   NA -2341.248464
## arr_delay  1316.28358      NA      NA  -5497.5224     NA   NA    53.014925
## carrier            NA      NA      NA          NA     NA   NA           NA
## tailnum            NA      NA      NA          NA     NA   NA           NA
## flight    -5497.52239      NA      NA 551286.8622     NA   NA   764.424934
## origin             NA      NA      NA          NA     NA   NA           NA
## dest               NA      NA      NA          NA     NA   NA           NA
## air_time     53.01493      NA      NA    764.4249     NA   NA   167.926251
## distance     26.64179      NA      NA  -1321.9122     NA   NA    14.122915
## hour         18.40299      NA      NA   -519.7085     NA   NA   -28.388938
## minute      -90.35821      NA      NA   4181.3073     NA   NA     8.400351
##               distance       hour       minute
## year          0.000000    0.00000     0.000000
## month         0.000000    0.00000     0.000000
## day          -6.545215   14.95347   -15.124671
## dep_time   -240.421422 2151.23968 -1023.952590
## dep_delay    20.059701   52.74627   -83.373134
## arr_time   -296.710272 1800.02458 -1559.090430
## arr_delay    26.641791   18.40299   -90.358209
## carrier             NA         NA           NA
## tailnum             NA         NA           NA
## flight    -1321.912204 -519.70852  4181.307287
## origin              NA         NA           NA
## dest                NA         NA           NA
## air_time     14.122915  -28.38894     8.400351
## distance     46.461809   -2.52590    12.168569
## hour         -2.525900   21.64267   -13.027217
## minute       12.168569  -13.02722   278.769096
  1. Describe the distribution of the arrival delays of these flights using a histogram and appropriate summary statistics. Hint: The summary statistics you use should depend on the shape of the distribution.

using histogram

ggplot(data = sfo_feb_flights, mapping = aes(x = arr_delay)) +
        geom_histogram(bins = 50)

using boxplot

ggplot(data = sfo_feb_flights, mapping = aes(x = carrier, y = arr_delay)) +
        geom_boxplot()

using point

ggplot(data = sfo_feb_flights, mapping = aes(y = arr_delay, x = carrier)) +
        geom_point()

summary of over one hour delays

arrival_delayed <- filter(sfo_feb_flights, arr_delay > 60)
summary(sfo_feb_flights$arr_delay)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  -66.00  -21.25  -11.00   -4.50    2.00  196.00

The answer: almost half of February arrived more than 11 minutes early, this vary between different carriers. American Airlines has the most delays and Virgin American has the best arrival time.

Another useful technique is quickly calculating summary statistics for various groups in your data frame. For example, we can modify the above command using the group_by function to get the same summary stats for each origin airport:

sfo_feb_flights %>%
  group_by(origin) %>%
  summarise(median_dd = median(dep_delay), iqr_dd = IQR(dep_delay), n_flights = n())
## `summarise()` ungrouping output (override with `.groups` argument)
## # A tibble: 2 x 4
##   origin median_dd iqr_dd n_flights
##   <chr>      <dbl>  <dbl>     <int>
## 1 EWR          0.5   5.75         8
## 2 JFK         -2.5  15.2         60

Here, we first grouped the data by origin and then calculated the summary statistics.

nycflights %>% 
  group_by(carrier) %>%
  summarise(median_dd = median(dep_delay), iqr_dd = IQR(dep_delay), n_flights = n())
## `summarise()` ungrouping output (override with `.groups` argument)
## # A tibble: 16 x 4
##    carrier median_dd iqr_dd n_flights
##    <chr>       <dbl>  <dbl>     <int>
##  1 9E           -1    23.2       1696
##  2 AA           -2     9         3188
##  3 AS           -4.5   8.75        66
##  4 B6           -1    18         5376
##  5 DL           -2     9         4751
##  6 EV           -1    31         5142
##  7 F9            1    18           69
##  8 FL            1    22          307
##  9 HA           -3.5   6.75        34
## 10 MQ           -3    16         2507
## 11 OO           -6    49            3
## 12 UA            0    14         5770
## 13 US           -4     7         2015
## 14 VX           -1    12          497
## 15 WN            1    19         1261
## 16 YV           -4    26           53
  1. Calculate the median and interquartile range for arr_delays of flights in in the sfo_feb_flights data frame, grouped by carrier. Which carrier has the most variable arrival delays?

The Answer: UA united airlines and DL delta both have teh highest interquartile range of the delays of flights in this new data frame.

sfo_feb_flights1 <- group_by(sfo_feb_flights, carrier)
summarise(sfo_feb_flights1, Median = median(arr_delay), IQR = IQR(arr_delay))
## `summarise()` ungrouping output (override with `.groups` argument)
## # A tibble: 5 x 3
##   carrier Median   IQR
##   <chr>    <dbl> <dbl>
## 1 AA         5    17.5
## 2 B6       -10.5  12.2
## 3 DL       -15    22  
## 4 UA       -10    22  
## 5 VX       -22.5  21.2

Departure delays by month

Which month would you expect to have the highest average delay departing from an NYC airport?

Let’s think about how you could answer this question:

  • First, calculate monthly averages for departure delays. With the new language you are learning, you could
    • group_by months, then
    • summarise mean departure delays.
  • Then, you could to arrange these average delays in descending order
nycflights %>%
  group_by(month) %>%
  summarise(mean_dd = mean(dep_delay)) %>%
  arrange(desc(mean_dd))
## `summarise()` ungrouping output (override with `.groups` argument)
## # A tibble: 12 x 2
##    month mean_dd
##    <int>   <dbl>
##  1     7   20.8 
##  2     6   20.4 
##  3    12   17.4 
##  4     4   14.6 
##  5     3   13.5 
##  6     5   13.3 
##  7     8   12.6 
##  8     2   10.7 
##  9     1   10.2 
## 10     9    6.87
## 11    11    6.10
## 12    10    5.88
  1. Suppose you really dislike departure delays and you want to schedule your travel in a month that minimizes your potential departure delay leaving NYC. One option is to choose the month with the lowest mean departure delay. Another option is to choose the month with the lowest median departure delay. What are the pros and cons of these two choices?

The Answer: the mean has a tendency to be pulled toward the extreme values, while the median is more robust measure than the arithmetic mean, but the outliers here could cause an issue and It could happen that one experiences one of these extra delayed flights, I think in this example its better to use the mean.

nycflights %>%
  group_by(month) %>%
  summarise(mean_dd = mean(dep_delay)) %>%
  arrange(desc(mean_dd))
## `summarise()` ungrouping output (override with `.groups` argument)
## # A tibble: 12 x 2
##    month mean_dd
##    <int>   <dbl>
##  1     7   20.8 
##  2     6   20.4 
##  3    12   17.4 
##  4     4   14.6 
##  5     3   13.5 
##  6     5   13.3 
##  7     8   12.6 
##  8     2   10.7 
##  9     1   10.2 
## 10     9    6.87
## 11    11    6.10
## 12    10    5.88

On time departure rate for NYC airports

Suppose you will be flying out of NYC and want to know which of the three major NYC airports has the best on time departure rate of departing flights. Also supposed that for you, a flight that is delayed for less than 5 minutes is basically “on time.”" You consider any flight delayed for 5 minutes of more to be “delayed”.

In order to determine which airport has the best on time departure rate, you can

  • first classify each flight as “on time” or “delayed”,
  • then group flights by origin airport,
  • then calculate on time departure rates for each origin airport,
  • and finally arrange the airports in descending order for on time departure percentage.

Let’s start with classifying each flight as “on time” or “delayed” by creating a new variable with the mutate function.

nycflights <- nycflights %>%
  mutate(dep_type = ifelse(dep_delay < 5, "on time", "delayed"))

The first argument in the mutate function is the name of the new variable we want to create, in this case dep_type. Then if dep_delay < 5, we classify the flight as "on time" and "delayed" if not, i.e. if the flight is delayed for 5 or more minutes.

Note that we are also overwriting the nycflights data frame with the new version of this data frame that includes the new dep_type variable.

We can handle all of the remaining steps in one code chunk:

nycflights %>%
  group_by(origin) %>%
  summarise(ot_dep_rate = sum(dep_type == "on time") / n()) %>%
  arrange(desc(ot_dep_rate))
## `summarise()` ungrouping output (override with `.groups` argument)
## # A tibble: 3 x 2
##   origin ot_dep_rate
##   <chr>        <dbl>
## 1 LGA          0.728
## 2 JFK          0.694
## 3 EWR          0.637
  1. If you were selecting an airport simply based on on time departure percentage, which NYC airport would you choose to fly out of? You can also visualize the distribution of on on time departure rate across the three airports using a segmented bar plot.

The Answer: I would choose LGA LaGuardia since it has the least delays.

ggplot(data = nycflights, aes(x = origin, fill = dep_type)) +
  geom_bar()

qplot(x = origin, fill = dep_type, data = nycflights, geom = "bar")

More Practice

  1. Mutate the data frame so that it includes a new variable that contains the average speed, avg_speed traveled by the plane for each flight (in mph). Hint: Average speed can be calculated as distance divided by number of hours of travel, and note that air_time is given in minutes.
nycflights <- nycflights %>%
        mutate(avg_speed = distance / (air_time / 60))
  1. Make a scatterplot of avg_speed vs. distance. Describe the relationship between average speed and distance. Hint: Use geom_point().

The answer: There is a relation between the speed range and the distance, the speed is more when the distance is longer, like the flights from NYC to Honolulu HNL.

ggplot(nycflights, aes(distance, avg_speed )) + geom_point()

  1. Replicate the following plot. Hint: The data frame plotted only contains flights from American Airlines, Delta Airlines, and United Airlines, and the points are colored by carrier. Once you replicate the plot, determine (roughly) what the cutoff point is for departure delays where you can still expect to get to your destination on time.

The asnswer: the cutoff point of when you can still expect to get to your distincation on time is around 20 minutes.

ggplot(dl_aa_ua, aes(x = dep_delay, y = arr_delay, color = carrier)) +
        xlim(-25, 150) +
        geom_point()
## Warning: Removed 219 rows containing missing values (geom_point).

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.