The t Distribution

The following code will generate a t density curve with 20 degrees of freedom.

curve(dt(x, df=20), main="t Distribution", xlab="t", ylab="density", type="l", xlim=c(-4,4) );

The following will calculate the probability for a t-statistic, q = 1.23, with 20 degrees of freedom.

pt(q=1.23, df=20); # for P(T ≤ q)

## [1] 0.8835151

pt(q=1.23, df=20, lower.tail=FALSE); # for P(T ≥ q)

## [1] 0.1164849

The following will calculate the t-statistic, t, with 20 degrees of freedom for a specified probability p.

qt(p = .85, df = 20); # for P(T ≤ q) = p

## [1] 1.064016

qt(p = .85, df = 20, lower.tail=FALSE); # for P(T ≥ 1) = p

## [1] -1.064016