How calculate probabillity of density plot?

Question

I have following question: Is it possible to calculate a probabillity of a density plot?

So for example, I have following data frame

 test<- data.frame(
  Gruppe = rep(c("Aktien","Aktien"), 
               times=c(136, 37)),
  Zufriedenheit = c(f_keineErf, f_Erf))

and i plot a density plot, with de ggplot function:

 ggplot(test, aes(x=Zufriedenheit)) +geom_density()

How can I calculate the probability for example getting a value above 70?

Thank you!

Answer 1

Your data is not included in the question, so let's make up a small random sample:

library(ggplot2)

set.seed(69)

df <- data.frame(x = rnorm(10))

Now we can create a density plot as per your example:

p <- ggplot(df, aes(x)) + 
  geom_density() +
  xlim(c(-5, 5))

p

Now, we can actually find the x and y coordinates of this line using the base R function density and extracting its x and y components into a data frame:

dens <- density(df$x)
d    <- data.frame(x = dens$x, y = dens$y)

head(d)
#>           x            y
#> 1 -3.157056 0.0009453767
#> 2 -3.144949 0.0010145927
#> 3 -3.132841 0.0010870523
#> 4 -3.120733 0.0011665920
#> 5 -3.108625 0.0012488375
#> 6 -3.096517 0.0013382316

We can see plotting this as a red dashed geom_line it is the same as geom_density:

p + geom_line(data = d, aes(x, y), col = "red", linetype = 2, size = 2) 

Now suppose we want to know the probability of having a value of more than one. We can show the area we are interested in like this:

p + geom_area(data = d[d$x >= 1,], aes(x, y), fill = "red")

Since the x values are all equally spaced in our data frame d, then the red area's proportion of the area under the line is a simple ratio of the sum of all y values at x values greater than one to the grand sum of y:

sum(d$y[d$x > 1])/sum(d$y)
#> [1] 0.1599931

So the probability of getting an x value of > 1 is 0.15999, or 16%

^{Created on 2020-08-17 by the reprex package (v0.3.0)}