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 sub-setting.

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)

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, 10…
## $ 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, 940…
## $ 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", "LGA…
## $ dest      <chr> "LAX", "SJU", "LAX", "TPA", "ORF", "ORD", "HOU", "IAD", "MIA…
## $ 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, 6…
## $ minute    <dbl> 40, 57, 59, 41, 2, 17, 59, 20, 25, 23, 40, 20, 9, 54, 17, 24…

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

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()

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?

Insert your answer here

# Actually yes- in the original histogram, notice how there's a slight overlap from the dep_delay = 0 and a negative dep_delay, because they are grouped together due to the default bin width. This tells us that the majority of the data occurs in situations where there is either no delay, or a negative delay (meaning the plane departs a bit early) , but not which one. 

# In the second histogram, which has a smaller bin width, we get to see the data with finer nuance- that the majority of the plane departures have no delay, and an almost equivalent amount of minor positive and minor negative delays, with significantly less amounts of more positive delay. There are however, a bit more cases of minor positive than minor negative delay from a basic glance.

# In the third histogram, there is very little value as the bin width is far too wide to actually extrapolate any real meaning. The more bins a histogrm has, the more detailed it is.

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() +labs(title="Los Angeles Flight Delays")

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 × 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?

Insert your answer here

sfo_feb_flights <- nycflights %>%
  filter(dest == "SFO", month == 2)
# The same as the query provided in the lab. Thanks for the freebie professor. 


sfo_feb_flights %>%
  summarise(number= n())
## # A tibble: 1 × 1
##   number
##    <int>
## 1     68
# There are 68 flights headed to San Francisco in February
  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.

Insert your answer here

ggplot(data = sfo_feb_flights, aes(x = arr_delay)) +
  geom_histogram(binwidth = 2)

# For full accuracy, I wanted to see the detailed view of the histogram for these 68 flights and their arrival delays. I see that when the bin width is larger, it almost looks like a regular normal distribution with a few outliers. However, by making the bin width small, I can see that the distribution of arrival delays is a bit more scattered. By looking at the dataframe itself, I can see that 49 flights out of the 68 have a negative arrival delay, but not by too much, which is backed up by the visual. There is, of course, a few outliers that have a positive arrival delay with a large value (196)

sfo_feb_flights %>%
  summarise(mean_ad   = mean(arr_delay), 
            median_ad = median(arr_delay), 
            number    = n(),
            min_ad = min(arr_delay),
            max_ad = max(arr_delay)
            )
## # A tibble: 1 × 5
##   mean_ad median_ad number min_ad max_ad
##     <dbl>     <dbl>  <int>  <dbl>  <dbl>
## 1    -4.5       -11     68    -66    196
# Looking at the statistics, I see that both the mean and median of the arrival delays are negative values, which is in accordance with the histogram skewing left, toward negative arrival delays.

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())
## # A tibble: 2 × 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.

  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?

Insert your answer here

sfo_feb_flights %>%
  group_by(carrier) %>%
  summarise(median_ad = median(arr_delay), 
            iqr_ad = IQR(arr_delay), 
            n_flights = n())
## # A tibble: 5 × 4
##   carrier median_ad iqr_ad n_flights
##   <chr>       <dbl>  <dbl>     <int>
## 1 AA            5     17.5        10
## 2 B6          -10.5   12.2         6
## 3 DL          -15     22          19
## 4 UA          -10     22          21
## 5 VX          -22.5   21.2        12
# The most delays is 21 delays, with UA (United Airlines)

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))
## # A tibble: 12 × 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?

Insert your answer here

nycflights %>%
  group_by(month) %>%
  summarise(mean_dd = mean(dep_delay)) %>%
  arrange(mean_dd)
## # A tibble: 12 × 2
##    month mean_dd
##    <int>   <dbl>
##  1    10    5.88
##  2    11    6.10
##  3     9    6.87
##  4     1   10.2 
##  5     2   10.7 
##  6     8   12.6 
##  7     5   13.3 
##  8     3   13.5 
##  9     4   14.6 
## 10    12   17.4 
## 11     6   20.4 
## 12     7   20.8
# Mean departure delay from lowest to highest; This shows that the last 3 months (Sept., Oct., Nov.) of the year, with the exception of December, are the months with the lowest mean departure delay, and are thus the best to travel.

nycflights %>%
  group_by(month) %>%
  summarise(median_dd = median(dep_delay)) %>%
  arrange(median_dd)
## # A tibble: 12 × 2
##    month median_dd
##    <int>     <dbl>
##  1     9        -3
##  2    10        -3
##  3     1        -2
##  4     2        -2
##  5     4        -2
##  6    11        -2
##  7     3        -1
##  8     5        -1
##  9     8        -1
## 10     6         0
## 11     7         0
## 12    12         1
# Median departure delay from lowest to highest; This shows that the best months are the Sept. and Oct. are the best months to travel, as they have the largest negative departure delay, hence the plane leaves earlier.

# The pros and cons of the mean method is that it allows you to see the average expected delay, which allows a traveler to anticipate and know what to expect when it comes to their flight being delayed. However, this could become skewed if there is an outlier which pushes the average to a positive or negative value that is far removed from what happens the most. Specifically speaking, 44 out of the 68 flights have either 0 departure delay, or a negative delay (hence they depart early,), but because of 3 flights (N335AA, N842VA, and N508UA), which have delays ranging from 91- 209, this skews the mean to a positive value. This could become a con if the passenger is expecting the flight to leave a little later than the reported departure time, whereas it is more likely to leave on time, or even a bit early.

# For the median method, I believe this approach allows a traveler to see what is the most likely departure delay for their flight, and for each month. However, this does not account for any extreme outliers, and large positive/negative delays. This could lead to a circumstance in which the flights leaves early, or be delayed a large amount, and the traveler would have no way of anticipating this.

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 suppose 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))
## # A tibble: 3 × 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.

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

Insert your answer here

# I'd choose the airport with the smallest amount of delayed flights, and the most on-time flights. However, looking at the ggplot, it seems all 3 airports have essentially the same amount of non-delayed flights, but LGA has the least delayed flights, hence I'd choose it.

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.

Insert your answer here

nycflights <- nycflights %>%
  mutate(avg_speed = distance * 60/ (air_time))
# This gives us the average speed of each flight in mph
  1. Make a scatterplot of avg_speed vs. distance. Describe the relationship between average speed and distance. Hint: Use geom_point().

Insert your answer here

library(ggplot2)

ggplot(data = nycflights, aes(x=avg_speed, y=distance)) + geom_point(aes(color = dep_type))

# The relationship between avg_speed and distance, is that as the distance of the flight increases, the plane will generally fly faster. There are of course a few outliers, and I could only posit a guess as to why that is- perhaps the plane model was faster, or the pilots were in a rush. There does seem to be an interesting trend however- the majority of the flights stop when distance reaches 2586 (which is confirmed by looking at the dataframe as San Francisco is the destination), but there are 66 flights heading to HNL airport (Honolulu, Hawaii), all of which travel about 500 mph and take about 10-11 hours.
  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.

Insert your answer here

replicated_frame <- nycflights %>%
  filter(carrier == "AA" | carrier == "DL" | carrier == "UA")

ggplot(data = replicated_frame, aes(x=dep_delay, y=arr_delay)) + 
  geom_point(aes(color = carrier)) +
  geom_smooth(method = "lm", se = FALSE) +
  xlab('Departure Delay (Mins)') + ylab('Arrival Delay (Mins)') + labs(title = "Delays in American Airlines, Delta, & United Airlines") +
  geom_hline(yintercept = 0, linetype="dotted", color = "red", size = 1) +
  scale_x_continuous(breaks = seq(0, 1000, by = 50)) +
  scale_y_continuous(breaks = seq(0, 1000, by = 50))

# Arrival delay should be 0, so we need to set y-axis line to 0, and find average cutoff point. This is where the best-fit line intercepts the y=0 axis as the question asks for arrival delay to be 0, with some degree of departure delay allowed. 



ggplot(data = replicated_frame, aes(x=dep_delay, y=arr_delay)) + 
  geom_point(aes(color = carrier)) +
  geom_smooth(method = "lm", se = FALSE) +
  xlab('Departure Delay (Mins)') + ylab('Arrival Delay (Mins)') + labs(title = "Delays in American Airlines, Delta, & United Airlines") +
  geom_hline(yintercept = 0, linetype="dotted", color = "red", size = 1) +
  coord_cartesian(xlim=c(5,15), ylim =c(-1,1)) 

# By limiting this ggplot to only look at where the prior ggplot has the best-line intersect the y-axis, we can see that flights have a cutoff point for departure delays at what appears to be 8 minutes