What is the right way to present error bars when plotting points on a log scale? Because error bars are symetric on the absolute scale, I thought they would be asymmetric on the log scale. However, with the below code, they show up as symmetric on the log scale. My initial question was 'Is the code displaying the error bars properly?' After a little bit of looking I am left a little uncertain.
library(ggplot2
pde=1.1 #position dodge for error bars
pdp=0.35 #position dodge for points
p<-ggplot(data=mtcars, aes(x=vs, y=mpg, colour=factor(am)))+
geom_point(position=position_dodge(width=pdp), size=3)+
stat_summary( fun = "mean", geom="point", size=2,stroke=1.1, position=position_dodge(width=pde))+
stat_summary( fun.data = "mean_se", geom = "errorbar", width=0.15, position=position_dodge(width=pde))+
scale_y_log10(limits = c(1,150))
The help for coord_trans() explains that scale transformations (e.g., scale_y_log10()) are performed before statistics are calculated, while coordinate transformations (e.g., coord_trans(y="log10")) are performed after statistics are calculated.
In your case, this means that with scale_y_log10 the mean and se are being calculated on the log-transformed data, rather than on the original untransformed data. To calculate the statistics on the untransformed data, remove scale_y_log10() and use coord_trans(y="log10").
The example below shows the values that ggplot is calculating internally and then reproduces those values by direct calculation:
library(tidyverse)
pde=1.1 #position dodge for error bars
pdp=0.35 #position dodge for points
p1 = ggplot(data=mtcars, aes(x=vs, y=mpg, colour=factor(am))) +
geom_point(position=position_dodge(width=pdp), size=3) +
stat_summary(fun = "mean", geom="point", size=2, stroke=1.1,
position=position_dodge(width=pde)) +
stat_summary( fun.data = "mean_se", geom = "errorbar",
width=0.15, position=position_dodge(width=pde)) +
theme_bw()
p2 = p1 + scale_y_log10()
# Get data frames for each set of mean/errorbar layers
# that ggplot calculates internally
p1dat = ggplot_build(p1)$data[[3]]
p2dat = ggplot_build(p2)$data[[3]]
p1dat %>% select(y, ymin, ymax)
#> y ymin ymax
#> 1 15.05000 14.24910 15.85090
#> 2 20.74286 19.80888 21.67683
#> 3 19.75000 18.11339 21.38661
#> 4 28.37143 26.57319 30.16967
p2dat %>% select(y, ymin, ymax) %>%
mutate(y.trans = 10^y,
ymax.trans = 10^ymax)
#> y ymin ymax y.trans ymax.trans
#> 1 1.170219 1.145648 1.194790 14.79853 15.65992
#> 2 1.314225 1.294657 1.333793 20.61699 21.56718
#> 3 1.288104 1.252044 1.324165 19.41353 21.09431
#> 4 1.447286 1.418346 1.476226 28.00826 29.93823
Now reproduce those same values by direct calculation:
mtcars %>%
group_by(am, vs) %>%
summarise(mean = mean(mpg),
mean.log = mean(log10(mpg)),
mean.log.trans = 10^mean.log,
mean.plus.se = mean + sqrt(var(mpg)/length(mpg)),
se.log = sqrt(var(log10(mpg))/length(mpg)),
mean.log.plus.se = mean.log + se.log,
mean.log.plus.se.trans = 10^mean.log.plus.se)
#> am vs mean mean.log mean.log.trans mean.plus.se se.log
#> 1 0 0 15.05000 1.170219 14.79853 15.85090 0.02457101
#> 2 0 1 20.74286 1.314225 20.61699 21.67683 0.01956814
#> 3 1 0 19.75000 1.288104 19.41353 21.38661 0.03606088
#> 4 1 1 28.37143 1.447286 28.00826 30.16967 0.02893993
#> mean.log.plus.se mean.log.plus.se.trans
#> 1 1.194790 15.65992
#> 2 1.333793 21.56718
#> 3 1.324165 21.09431
#> 4 1.476226 29.93823
And we can also see that coord_trans(y="log10") calculates means and error bars before the log transformation:
p3 = p1 + coord_trans(y="log10")
p3dat = ggplot_build(p3)$data[[3]]
p3dat %>% select(y, ymin, ymax)
#> y ymin ymax
#> 1 15.05000 14.24910 15.85090
#> 2 20.74286 19.80888 21.67683
#> 3 19.75000 18.11339 21.38661
#> 4 28.37143 26.57319 30.16967