Plot multiple line graphs on one graph - r

Question

I can get a single power curve shown below but I want to create a power analysis graph. I want to change my delta value (to .6, .7, and .8) and plot those 3 other lines on that same r curve in a different color. I provided an example of what I kinda want it to look.
n_participants <- c(5, 10, 20, 30, 40)
npercluster <- 20
n_tot <- n_participants*npercluster
icc <- 0.6 # assumption
deff <- 1 + icc*(npercluster - 1)
ess <- n_tot / deff
mydelt <- 0.5
mypowers <- power.t.test(n=ess, delta=mydelt)$power
plot(n_participants, mypowers, type='l',
main=paste('Power based on', npercluster, 'volumes per participants'),
xlab='Number of participants', ylim=c( 0, 1),
ylab='Power')

Answer 1

If you are planning to use R a lot I would recommend investing in learning ggplot2. Base R plotting solutions get very limited very quickly.
To solve your problem I would make a data frame with every combination of effect size and sample size.
dat <- expand.grid(mydelt=c(0.5,0.6,0.7,0.8), ess=n_tot / deff)
Then add a column for the power:
dat$mypowers = power.t.test(n=dat$ess, delta=dat$mydelt)$power
Then I can use ggplot to easily make a nice graph of the power curves:
library(ggplot2)
ggplot(dat, aes(x=ess, y=mypowers, color=factor(mydelt))) + geom_point() + geom_line()
You can easily change the overall graph look and add appropriate labels:
ggplot(dat, aes(x=ess, y=mypowers, color=factor(mydelt))) +
geom_point() +
geom_line() +
theme_bw() +
labs(x="Effective sample size", y="Power", color="Effect size" )
In response to the comment.. there was a mistake in the code above in that I plotted the effective total sample size on the x axis not the sample size per cluster. So instead we should make sure we have n_participants in the dataset for plotting, then calculate the powers and plot:
So the whole script is now:
n_participants <- 5:40
npercluster <- 20
icc <- 0.6 # assumption
deff <- 1 + icc*(npercluster - 1)
dat <- expand.grid(mydelt=c(0.5,0.6,0.7,0.8), npart=n_participants)
dat$n_tot <- dat$npart*npercluster
dat$ess <- dat$n_tot / deff
dat$mypowers <- power.t.test(n=dat$ess, delta=dat$mydelt)$power
library(ggplot2)
ggplot(dat, aes(x=npart, y=mypowers, color=factor(mydelt))) +
geom_line()+
theme_bw() +
labs(x="Number of participants", y="Power", color="Effect size" )
Which gives this graph:

Answer 2

You may put the logic in a function f, sapply over desired deltas and - as also suggested in comments - use matplot without having to bother with any new packages.
f <- \(mydelt=.5, n_participants=c(5, 10, 20, 30, 40), npercluster=20, icc=.6) {
n_tot <- n_participants*npercluster
deff <- 1 + icc*(npercluster - 1)
ess <- n_tot/deff
power.t.test(n=ess, delta=mydelt)$power
}
deltas <- seq(.5, .8, .1)
res <- t(sapply(deltas, f))
matplot(res, type='l', main=paste('Power based on 20 volumes per participants'),
xlab='Number of participants',
ylab='Power')
legend('topleft', legend=deltas, col=seq_along(deltas), lty=seq_along(deltas),
title='delta', cex=.8)
It's also possible pipe it directly into matplot:
t(sapply(deltas, f)) |>
matplot(res, ...)
See ?matplot for easy customizing of colors, linetypes etc.
Note: R >= 4.1 used.