Table of Contents
This analysis is based on the members data set, which contains
information about climbing expeditions in the Himalayas from 1905 up to
Spring 2019. Each row in the data set represents a person that climbed a
unique expedition. Information about the five relevant variables
(columns) used in this analysis is provided as follows:
expedition_idis a unique identifier for a particular expedition.seasondescribes whether the expedition took place in Autumn, Spring, Summer, or Winter.successdescribes whether a person accomplished the goal of their particular expedition.agedescribes a person’s age (could be at the age of summit, death, or base camp arrival depending on data availability).highpoint_metresdescribes a person’s highpoint elevation in meters.
- How do the likelihoods of successfully completing an expedition change throughout the year?
- How does age affect a person’s ability to reach high elevations?
members = readr::read_csv('https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2020/2020-09-22/members.csv')More information about the dataset can be found on this Himalayan database and on the Tidy Tuesday repository.
To determine the likelihood of successfully completing an expedition at
various points throughout the year, I calculate the proportion of
expeditions that are successful across each season of the year. This is
accomplished by finding all distinct expedition_id’s and calculating
the proportion of successful expeditions grouped by season. A limitation
of this method is that some individuals in an expedition may not have
been successful, whereas the rest of their group may have been. For
simplicity, this analysis assumes that most individuals in an expedition
have the same success outcome.
Although proportions can be displayed numerically, frequency framing can allow readers to understand frequencies visually through discrete probability outcomes. As such, this method was chosen to display how the likelihoods of successfully completing an expedition change across seasons.
A 2-D density plot was chosen to visualize the relationship between a
person’s age and their highpoint elevation. This visualization was
chosen to avoid an overcrowded scatterplot, due to the high density of
records present in the members data set.
# Determine proportion of successful expeditions based on season
pr_success_df = members %>%
filter(season != 'Unknown') %>%
distinct(expedition_id, .keep_all = T) %>%
group_by(season) %>%
summarise(pr_success = mean(success, na.rm = T), season) %>%
distinct(pr_success) %>%
arrange(pr_success)
# Save probabilities as vector
pr_success_ls = pr_success_df$pr_success
# This function is used to create a df representing a sampling grid with overall
# probabilities defined by `pr_success_ls`
# written by Kris Sankaran:
# https://krisrs1128.github.io/stat679_notes/2022/06/02/week13-1.html
sample_grid = function(p = 0.5) {
expand.grid(seq_len(25), seq_len(25)) %>%
mutate(response = sample(0:1, n(), replace = TRUE, prob = c(1 - p, p)))
}
# Lines 64-66 also written by Kris Sankaran :
# https://krisrs1128.github.io/stat679_notes/2022/06/02/week13-1.html
success_grid = map(pr_success_ls, ~ sample_grid(.)) %>%
bind_rows(.id = "p") %>%
mutate(pr_success_ls = pr_success_ls[as.integer(p)])
# Loop creates labels that will be used in frequency framing plot
for (i in 1:4) {
# Label: {season} (XX.X%)
pct_label = paste0(
pr_success_df$season[i],
' (',
round(pr_success_df$pr_success[i]*100, 1),
'%)'
)
success_grid$pr_success_ls = gsub(
pr_success_df$pr_success[i],
pct_label,
success_grid$pr_success_ls
)
}
# Plot frequency framing grid
success_grid %>%
ggplot() +
geom_tile(
aes(Var1, Var2, fill = as.factor(response)),
col = "white",
linewidth = 0.5
) +
facet_grid(~pr_success_ls) +
scale_y_continuous(expand = c(0, 0)) +
scale_x_continuous(expand = c(0, 0)) +
coord_fixed() +
labs(
fill = '',
col = '',
title = 'Proportion of Successful Expeditions Across Seasons'
) +
scale_fill_manual(
values = c("light grey", "black"),
labels = c('Unsuccessful', 'Successful')
) +
theme_minimal() +
theme(
axis.text = element_blank(),
axis.ticks = element_blank(),
axis.title = element_blank(),
plot.title = element_text(hjust = 0.5)
)
members %>%
select(age, highpoint_metres) %>%
ggplot(aes(age, highpoint_metres)) +
geom_density_2d_filled(alpha = 0.8) +
labs(
x = 'Age (years)',
y = 'Elevation highpoint (m)',
title = 'Effect of Age on a Climber\'s Elevation Highpoint'
) +
scale_fill_manual(
values = colorRampPalette(brewer.pal(9, 'Blues'))(14)
) +
scale_x_continuous(limits = c(15, 65)) +
scale_y_continuous(limits = c(5000, 9000)) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5),
legend.position = 'none'
)
How do the likelihoods of successfully completing an expedition change throughout the year?
Climbers with aspirations of visiting the Himalayas may be interested in the likelihood of their climbing expedition being successful in a particular season, especially considering the frigid conditions that ensue in winter. The first figure supports that there is slight variation in the proportion of expeditions that are successful throughout the year. Newcomers may be more inclined to attempt a climb in Spring or Autumn, given seasonal success rates of ~35%, as opposed to the lower success rates of Summer and Winter.
How does age affect a person’s ability to reach high elevations?
There does not appear to be a strong linear correlation between a person’s age and their elevation highpoint based on the second figure. However, it is clear that regardless of age, the most common elevation highpoints occur at ~7000 m, ~8000 m, and ~9000 m. Additionally, it appears that most climbers’ ages fall in the range 25-45, irrespective of how high they climbed.