We'll often want to find

For example, the upper 5% point of

(Note that we have to convert back and forth between probabilities and percentages.)

We will denote other percentage points by the name of the distribution
(so, *t*, χ^{2} 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 *t _{3}(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:

*t*_{3}(1%) = 4.541*t*_{40}(1%) = 2.423*t*_{45}(1%) ≈ 2.413*F*_{4, 5}(5%) = 5.192

In `R`

, the commands `qnorm, qchisq, qt`

, and
`qf`

will get percentage points of the normal, *χ ^{2},
t*, and

> qt(0.01, df=3, lower.tail=F) [1] 4.540703 > qt(0.01, df=40, lower.tail=F) [1] 2.423257 > qt(0.01, df=45, lower.tail=F) [1] 2.412116 > qf(0.1, df1 = 4, df2 = 5, lower.tail = F) [1] 3.520196 > qf(0.05, df1 = 4, df2 = 5, lower.tail = F) [1] 5.192168 > qf(0.01, df1 = 4, df2 = 5, lower.tail = F) [1] 11.39193The following are some examples of getting percentage points of the normal distribution from

`R`

.
> qnorm(0.05, lower.tail = F) [1] 1.644854 > qnorm(0.05, mean = 0, sd = 1, lower.tail = F) [1] 1.644854 > qnorm(0.05, mean = 0, sd = 1) [1] -1.644854Note that we supply the probability

`R`

that we are interested in `R`

command above.
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Last modified: Wed Sep 26 18:40:49 BST 2007