The t-Distribution

Particularly since the t-distribution table is complicated to use, it is helpful to be able to have R do the computation for us. R provides a procedure, qt, that behaves much like that table. However, qt, given an area, computes a t-value with that area to the left (rather than to the right, as shown in the table).

For a 95% confidence interval, we call qt with .975. (Why .975? Because there's 0.025 to the right, and therefore 0.975 to the left.) More generally, we can average the confidence level and 1. Of course, qt expects a second parameter, which represents the degrees of freedom. Most generally, we write

qt(confidence_level+1)/2, df)

For example, to compute t^* for a 95% confidence interval with a sample size of 30, we would write

qt(.975, 29)

Similarly, to compute t^* for a 90% confidence interval with a sample size of 100, we would write

qt(.95, 99)