Visualizing Uncertainty

Every estimate you plot has uncertainty attached. Hiding it makes graphs look more precise than the analysis warrants; showing it badly makes graphs unreadable. Since much of social science communication consists of plotting model estimates, this deserves its own section.

Code

library(ggplot2)
library(dplyr)
library(gapminder)

gap2007 <- gapminder %>% filter(year == 2007)

Error bars: the workhorse

You have seen coefficient plots with geom_errorbar() in the Applied Examples. Two rules:

1. Say what the interval is. A bar could be a standard error, a 90% CI, or a 95% CI. The reader cannot tell. Put it in the caption.
2. Beware the “cliff edge” effect. Readers treat values inside the interval as certain and values outside as impossible. Neither is true.

Code

cont_summary <- gap2007 %>%
  group_by(continent) %>%
  summarise(mean_le = mean(lifeExp),
            se = sd(lifeExp) / sqrt(n()))

ggplot(cont_summary, aes(x = reorder(continent, mean_le), y = mean_le)) +
  geom_point(size = 3) +
  geom_errorbar(aes(ymin = mean_le - 1.96 * se, ymax = mean_le + 1.96 * se),
                width = 0.15) +
  coord_flip() +
  labs(x = NULL, y = "Mean Life Expectancy",
       caption = "Error bars show 95% confidence intervals.") +
  theme_minimal() +
  theme(axis.text = element_text(size = 14),
        axis.title = element_text(size = 15))

Do not put error bars on top of bar charts (“dynamite plots”). The bar’s length encodes the mean, but the filled area below carries no information and the interval below the mean is hidden. Use a point range instead, as above.

Ribbons for continuous predictions

For predicted values across a continuous variable, use geom_ribbon(), you have seen this pattern with ggeffects:

Code

ggplot(gap2007, aes(x = gdpPercap, y = lifeExp)) +
  geom_point(alpha = 0.25) +
  geom_smooth(method = "loess", se = TRUE, alpha = 0.3) +
  scale_x_log10() +
  labs(x = "GDP per Capita (log scale)", y = "Life Expectancy",
       caption = "Shaded band: 95% confidence interval of the LOESS fit.") +
  theme_minimal() +
  theme(axis.text = element_text(size = 14),
        axis.title = element_text(size = 15))

Beyond intervals: ggdist

The ggdist package provides geoms that show whole distributions of uncertainty instead of a single interval, half-eyes, gradient intervals, and quantile dotplots.

Code

library(ggdist)

ggplot(gap2007, aes(x = lifeExp, y = continent)) +
  stat_halfeye(aes(fill = continent), alpha = 0.7,
               .width = c(0.66, 0.95)) +
  scale_fill_viridis_d(end = 0.95, guide = "none") +
  labs(x = "Life Expectancy", y = NULL,
       caption = "Points: medians. Bars: 66% and 95% intervals. Curves: distributions.") +
  theme_minimal() +
  theme(axis.text = element_text(size = 14),
        axis.title = element_text(size = 15))

The gradient interval avoids the cliff-edge problem entirely, certainty fades out gradually:

Code

ggplot(gap2007, aes(x = lifeExp, y = continent)) +
  stat_gradientinterval(aes(fill = continent)) +
  scale_fill_viridis_d(end = 0.95, guide = "none") +
  labs(x = "Life Expectancy", y = NULL) +
  theme_minimal() +
  theme(axis.text = element_text(size = 14),
        axis.title = element_text(size = 15))

Quantile dotplots show uncertainty as a countable number of dots, lay audiences read frequencies (“18 of 20 dots are above 60”) far better than probability densities:

Code

ggplot(gap2007, aes(x = lifeExp)) +
  stat_dots(quantiles = 50, fill = "darkred", color = NA) +
  labs(x = "Life Expectancy",
       caption = "Each dot represents 2% of countries.") +
  theme_minimal() +
  theme(axis.text = element_text(size = 14),
        axis.title = element_text(size = 15))

Guidelines

• Always show uncertainty when plotting estimates; always say what the interval is.
• Prefer point ranges over bars + error bars.
• Two interval widths (66% + 95%) communicate more than one.
• For general audiences, frequency framings (dotplots, “1 in 5”) beat densities and CIs.
• Uncertainty visualization is an active research area, see Padilla, Kay & Hullman (2021), Uncertainty Visualization, for an overview.