It seems that often what someone really wants to plot is a confidence interval of some kind, but using SE for this purpose I think only ends up comprising something like a 68% confidence band. Therefore, plotting SE for error bars instead of a wider band more representative of the significance level of your analysis visually suggests significance in your data that may not actually be there.
Consider the following concrete example:
set.seed(123) X <- rnorm(100, 0, 1) Y <- rnorm(100,1.7,5) df = data.frame(X,Y) boxplot(df) se.x = sd(X)/sqrt(length(X)) se.y = sd(Y)/sqrt(length(Y)) X.err.CI = 1.96*se.x Y.err.CI = 1.96*se.y plot(1:2, colMeans(df), ylim=c(-1,3), xlim = c(0.5,4.5), col="dark green" , main="Comparison of SE bars vs 95% CI") lines(c(1,1), c(mean(X) + X.err.CI, mean(X) - X.err.CI), col="dark green") lines(c(2,2), c(mean(Y) + Y.err.CI, mean(Y) - Y.err.CI), col="dark green") text(1:2 + .2, colMeans(df), c("X","Y")) points(3:4, colMeans(df), col="blue") lines(c(3,3), c(mean(X) + se.x, mean(X) - se.x), col="blue") lines(c(4,4), c(mean(Y) + se.y, mean(Y) - se.y), col="blue") text(3:4 + .2, colMeans(df), c("X","Y")) abline(v=2.5, lty=2) legend("topright" ,c("95% CI", "+/- SE") ,lty=c(1,1) ,pch=c(1,1) ,col=c("dark green", "blue") )
If we just base our analysis on SE (the image on the right), visually it appears that there is significance between the means of X and Y because we don't have overlap in our error bars. But if we're testing at a 5% significance level, plotting the 95% confidence bands shows that this is clearly not the case.
Since we can expect that a test at the 32% level will never be appropriate, why even show the SE bars since they will probably be interpreted as though they represent a confidence interval? Do people use SE bars instead of more meaningful CIs because it's moderately easier to calculate (e.g. using a built-in function in Excel)? It seems that we're paying a pretty high cost in terms of the interpretability of our graphic in exchange for a few minutes' less work. Is there some value/utility in SE bars that I'm missing?
For context, I was prompted to write this after skimming this article. I was frustrated by the lack of confidence intervals in the plots provided by the authors, and then when they did finally provide them, it turned out they were just SE bars.