Introduction to Global Health Data Science
glimpse(lifespan2023)Rows: 408
Columns: 5
$ location <chr> "Afghanistan", "Afghanistan", "Albania"…
$ sex <chr> "Female", "Male", "Female", "Male", "Fe…
$ lifeexp <dbl> 68.98985, 68.13812, 82.05155, 77.27016,…
$ worldbankregion <chr> "South Asia", "South Asia", "Europe and…
$ pop <dbl> 38041757, 38041757, 2854191, 2854191, 4…| Variable | Description |
|---|---|
location |
Country or area name |
worldbankregion |
World region, as classified by the World Bank |
pop |
Estimated 2023 population of the location |
sex |
Binary sex as reported by the country |
lifeexp |
Life expectancy from infancy |
| Variable | Type |
|---|---|
location |
Categorical, not ordinal |
worldbankregion |
Categorical, not ordinal |
pop |
Numerical, discrete |
sex |
Categorical, not ordinal |
lifeexp |
Numerical, continuous |
In the full data (not subset to 2023), year is an additional numerical, discrete variable.
mean), median (median), moderange), standard deviation (sd), variance (square of sd), interquartile range (IQR)Consider a random variable \(x_i\) that is the estimated life expectancy for country \(i\), \(i = 1, \ldots, n\), among \(n\) countries.
\[ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}\]
variance: average squared distance from mean
standard deviation (sd): square root of variance (on same scale as data). The sample variance \(s^2\) is estimated in a single sample as \[\frac{\sum_{i=1}^n (x_i-\overline{x})^2}{n-1}\]
range: difference between highest and lowest values, e.g. \(x_{(n)}-x_{(1)}\)
interquartile range (IQR): difference between 75th and 25th %iles
Previously we viewed a scatterplot showing the relationship between life expectancy of females and males in each location.
ggplot(
lifeexpwide2023,
aes(
x = Female,
y = Male
)
) +
geom_point() +
labs(
title = "Life expectancy",
subtitle = "2023",
x = "Female life expectancy",
y = "Male life expectancy"
)
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_histogram()
binwidth = 0.5
The bin width is the width of the interval used for grouping the data. It is selected automatically by R, but we can alter it. For example, a bin width of \(\frac{1}{2}\) plots a bar for each 6 month life expectancy group, while a bin width of 10 plots a bar for groups of 10 years.
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_histogram(binwidth = 0.5)
binwidth = 3
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_histogram(binwidth = 3)
binwidth = 10
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_histogram(binwidth = 10)
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_histogram(binwidth = 3) +
labs(
x = "Female life expectancy (years)",
y = "Frequency",
title = "2023 Life Expectancy of Women"
)
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(
x = lifeexp,
fill = worldbankregion
)
) +
geom_histogram(
binwidth = 3,
alpha = 0.5
) +
labs(
x = "Female life expectancy (years)",
y = "Frequency",
title = "2023 Life Expectancy of Women"
)
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(
x = lifeexp,
fill = worldbankregion
)
) +
geom_histogram(
binwidth = 3,
alpha = 0.5
) +
labs(
x = "Female life expectancy (years)",
y = "Frequency",
title = "2023 Life Expectancy of Women"
) +
facet_wrap(~worldbankregion, nrow = 3)
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(
x = lifeexp,
fill = worldbankregion
)
) +
geom_histogram(
binwidth = 3,
alpha = 0.5
) +
labs(
x = "Female life expectancy (years)",
y = "Frequency",
fill = "World Bank Region",
title = "2023 Life Expectancy of Women"
) +
facet_wrap(~worldbankregion, nrow = 3) +
theme(
strip.background = element_blank(),
strip.text.x = element_blank()
)
Which version of all these plots seems most useful, and why?
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_density()A density function is a function whose value at any given point can be interpreted as providing a relative likelihood of values. That is, higher values of the density function indicate values of the random variable that are more likely to be observed.
adjust = 0.5
The bandwidth is a parameter that specifies the degree of smoothing. A small bandwidth shows many bumps (like a histogram with a small bin width), while a large bandwidth smooths over many bumps. It is specified using the adjust argument.
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_density(adjust = 0.5)
adjust = 1
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_density(adjust = 1)
adjust = 2
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_density(adjust = 2)
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_density(adjust = 1) +
labs(
x = "Female life expectancy (years)",
y = "Density",
title = "2023 Life Expectancy of Women"
)
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(
x = lifeexp,
fill = worldbankregion
)
) +
geom_density(adjust = 1) +
labs(
x = "Female life expectancy (years)",
y = "Density",
title = "2023 Life Expectancy of Women",
fill = "Region"
)
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(x = lifeexp)
) +
geom_boxplot() + theme(
axis.title.y = element_blank(),
axis.text.y = element_blank(),
axis.ticks.y = element_blank()
)
The distribution of population is highly skewed.
Here we plot the natural logarithm of the population because the original population values are highly skewed (primarily due to China and India). On the log scale, the largest countries are no longer extreme outliers, and the smallest populations become the outliers.
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(aes(x = lifeexp)) +
geom_boxplot() +
scale_x_continuous(breaks = scales::breaks_width(5)) +
labs(
x = "Female life expectancy (years)",
y = NULL,
title = "2023 Life Expectancy of Women"
) +
theme(
axis.ticks.y = element_blank(),
axis.text.y = element_blank()
)
lifespan2023 %>%
filter(sex == "Female") %>%
ggplot(
aes(
x = lifeexp,
y = worldbankregion
)
) +
geom_boxplot() +
labs(
x = "Female life expectancy (years)",
y = NULL,
title = "2023 Life Expectancy of Women",
subtitle = "By region"
)