Question

How would I go about creating a line from the t-table in R, after running a simulation for a t distribution? In essence, I want to perform the qt function using only values calculated from a random sample from the normal distribution, rather than using the confidence levels as inputs.

I have run a simulation on a t(degrees of freedom “df”) distribution 5000 times, and I want to take these values and use them to recreate the line in the t-table corresponding to the df. Having trouble trying to figure it out.

Any help is greatly appreciated!

Answer 1

The quantile function will give you the values equivalent to those in the t-tables I have used:

quants <- 1-c(0.2, 0.1, 0.05, 0.025, 0.01, 0.005, 0.001)
n <- 15

sims <- replicate( 5000, {x <- rnorm(n); sqrt(n)*mean(x)/sd(x)} )

(t.table <- quantile(sims, quants) )

## compare

rbind( t.table, qt( quants, n-1 ) )

pt(t.table, n-1)

These are the areas to the left, the common t-tables give the area to the right, we can change the labels to match this with names(t.table) <- 1-quants. Change quants to match your particular table (and increase the number of simulations if you want closer matches).

The simulation in this case could possibly be sped up by simulating a whole matrix of normals in 1 step then using tools like rowMeans.