# Load libraries
library(tidyverse)
Airline_Delay_Post_COVID_2021_2023 <- read.csv("Airline_Delay_Post_COVID_2021_2023.csv")
df <- Airline_Delay_Post_COVID_2021_2023sample_frac <- 0.25
n_samples <- 3
df_samples <- tibble()
for (sample_i in 1:n_samples) {
df_i <- df |>
sample_n(size = sample_frac * nrow(df), replace = TRUE) |>
mutate(sample_num = sample_i)
df_samples <- bind_rows(df_samples, df_i)
}Using a 25% subsample, I observed moderate variation across the three simulated samples. While overall arrival delay averages were similar, the maximum delay values differed noticeably. This suggests that conclusions drawn from a single moderate-sized sample may be influenced by whether rare but extreme delay events are included.
df_samples |>
group_by(sample_num) |>
summarize(
mean_arr_delay = mean(arr_delay, na.rm = TRUE),
median_arr_delay = median(arr_delay, na.rm = TRUE),
max_arr_delay = max(arr_delay, na.rm = TRUE),
total_flights = sum(arr_flights, na.rm = TRUE)
)## # A tibble: 3 × 5
## sample_num mean_arr_delay median_arr_delay max_arr_delay total_flights
## <int> <dbl> <dbl> <dbl> <dbl>
## 1 1 3947. 934. 305694 3464544
## 2 2 3880. 939 305694 3478460
## 3 3 4118. 936. 337375 3628608df_samples |>
group_by(sample_num) |>
summarize(
max_weather_delay = max(weather_delay, na.rm = TRUE),
max_carrier_delay = max(carrier_delay, na.rm = TRUE),
max_late_aircraft_delay = max(late_aircraft_delay, na.rm = TRUE)
)## # A tibble: 3 × 4
## sample_num max_weather_delay max_carrier_delay max_late_aircraft_delay
## <int> <dbl> <dbl> <dbl>
## 1 1 21063 109056 130753
## 2 2 26428 105806 130753
## 3 3 21362 118554 155262Extreme delay values, particularly those related to weather and late aircraft delays, appeared inconsistently across subsamples. A delay that would appear anomalous in one subsample was absent or less severe in another. This highlights how small numbers of extreme events can disproportionately affect interpretations when sample sizes are limited.
df_samples |>
group_by(sample_num) |>
summarize(
avg_carrier_delay = mean(carrier_delay, na.rm = TRUE),
avg_weather_delay = mean(weather_delay, na.rm = TRUE),
avg_nas_delay = mean(nas_delay, na.rm = TRUE),
avg_late_aircraft_delay = mean(late_aircraft_delay, na.rm = TRUE)
)## # A tibble: 3 × 5
## sample_num avg_carrier_delay avg_weather_delay avg_nas_delay
## <int> <dbl> <dbl> <dbl>
## 1 1 1557. 236. 687.
## 2 2 1552. 236. 668.
## 3 3 1614. 254. 728.
## # ℹ 1 more variable: avg_late_aircraft_delay <dbl>Despite variability in extreme values, the relative contribution of different delay causes remained consistent across subsamples. Carrier-related and late-aircraft delays were consistently larger than weather or security delays, suggesting that these operational factors were persistent contributors to airline delays during the post-COVID period.
df_samples |>
group_by(sample_num, carrier_name) |>
summarize(
avg_arr_delay = mean(arr_delay, na.rm = TRUE),
.groups = "drop"
) |>
arrange(sample_num, desc(avg_arr_delay))## # A tibble: 51 × 3
## sample_num carrier_name avg_arr_delay
## <int> <chr> <dbl>
## 1 1 Southwest Airlines Co. 10972.
## 2 1 American Airlines Inc. 8903.
## 3 1 JetBlue Airways 7334.
## 4 1 United Air Lines Inc. 5464.
## 5 1 Spirit Air Lines 5322.
## 6 1 Delta Air Lines Inc. 5032.
## 7 1 SkyWest Airlines Inc. 3375.
## 8 1 Republic Airline 3230.
## 9 1 Frontier Airlines Inc. 3099.
## 10 1 PSA Airlines Inc. 1999.
## # ℹ 41 more rowssample_frac <- 0.10
df_samples <- tibble()
for (sample_i in 1:n_samples) {
df_i <- df |>
sample_n(size = sample_frac * nrow(df), replace = TRUE) |>
mutate(sample_num = sample_i)
df_samples <- bind_rows(df_samples, df_i)
}df_samples |>
group_by(sample_num) |>
summarize(
mean_arr_delay = mean(arr_delay, na.rm = TRUE),
max_arr_delay = max(arr_delay, na.rm = TRUE)
)## # A tibble: 3 × 3
## sample_num mean_arr_delay max_arr_delay
## <int> <dbl> <dbl>
## 1 1 3800. 215233
## 2 2 4376. 337375
## 3 3 3880. 281392When the subsample size was reduced to 10%, variability increased substantially. Mean arrival delays and maximum delay values differed more dramatically between samples, indicating that small samples are highly sensitive to random variation and rare events. Conclusions based on such small samples would therefore be less reliable.
sample_frac <- 0.75
df_samples <- tibble()
for (sample_i in 1:n_samples) {
df_i <- df |>
sample_n(size = sample_frac * nrow(df), replace = TRUE) |>
mutate(sample_num = sample_i)
df_samples <- bind_rows(df_samples, df_i)
}df_samples |>
group_by(sample_num, year) |>
summarize(
avg_arr_delay = mean(arr_delay, na.rm = TRUE),
.groups = "drop"
)## # A tibble: 9 × 3
## sample_num year avg_arr_delay
## <int> <int> <dbl>
## 1 1 2021 3393.
## 2 1 2022 4674.
## 3 1 2023 4585.
## 4 2 2021 3346.
## 5 2 2022 4594.
## 6 2 2023 5001.
## 7 3 2021 3289.
## 8 3 2022 4473.
## 9 3 2023 4725.With a 75% subsample, results became much more stable across samples. Average arrival delays by year were consistent, and differences between subsamples were minimal. This demonstrates how larger samples reduce uncertainty and provide more reliable insights into underlying delay patterns.
This investigation demonstrates how sampling variability can affect conclusions drawn from airline delay data. Smaller subsamples exaggerated anomalies and produced less stable results, while larger subsamples yielded consistent and reliable patterns. In future analyses, I would be cautious about drawing strong conclusions from limited samples and would prioritize larger datasets or repeated sampling. This raises further questions about whether extreme delay events are driven disproportionately by specific airports, seasons, or carriers, and whether these factors should be modeled separately rather than treated as random noise.