We will denote other percentage points by the name of the distribution (so, t, χ2 or F) with ``degrees of freedom'' parameters given as subscripts and the percentage value given in brackets. So the upper 1% point of a t distribution with 3 degrees of freedom is denoted by t3(1%) and so on.
We get percentage points either from statistical tables (like those on
handout 1) or using
R. For example, from handout 1 we can
find the following:
R, the commands
qnorm, qchisq, qt, and
qf will get percentage points of the normal, χ2,
t, and F distributions respectively. For example, we
can get the percentage points given above, and some others, as follows.
> qt(0.01, df=3, lower.tail=F)  4.540703 > qt(0.01, df=40, lower.tail=F)  2.423257 > qt(0.01, df=45, lower.tail=F)  2.412116 > qf(0.1, df1 = 4, df2 = 5, lower.tail = F)  3.520196 > qf(0.05, df1 = 4, df2 = 5, lower.tail = F)  5.192168 > qf(0.01, df1 = 4, df2 = 5, lower.tail = F)  11.39193The following are some examples of getting percentage points of the normal distribution from
> qnorm(0.05, lower.tail = F)  1.644854 > qnorm(0.05, mean = 0, sd = 1, lower.tail = F)  1.644854 > qnorm(0.05, mean = 0, sd = 1)  -1.644854Note that we supply the probability P/100 rather than P and then supply parameters of the distribution. We have to tell
Rthat we are interested in upper percentage points, otherwise it assumes we are after lower percentage points --- that is what has happened with the last