1.12 Statistical tables in R
Statistical table functions in R can be used to find p-values for test statistics. See Section 24, User Defined Functions, for an example of creating a function to directly give a two-tailed p-value from a t-statistic.
The standard normal (z) distribution
The pnorm( ) function gives the area, or probability, below a z-value:
> pnorm(1.96)
[1] 0.9750021
To find a two-tailed area (corresponding to a 2-tailed p-value) for a positive z-value:
> 2*(1-pnorm(1.96))
[1] 0.04999579
The qnorm( ) function gives critical z-values corresponding to a given lower-tailed area:
> qnorm(.05)
[1] -1.644854
To find a critical value for a two-tailed 95% confidence interval:
> qnorm(1-.05/2)
[1] 1.959964
The t distribution
The pt( ) function gives the area, or probability, below a t-value. For example, the area below t=2.50 with 25 d.f. is
> pt(2.50,25)
[1] 0.9903284
To find a two-tailed p-value for a positive t-value:
> 2*(1-pt(2.50,25))
[1] 0.01934313
The qt( ) function gives critical t-values corresponding to a given lower-tailed area:
> qt(.05,25)
[1] -1.708141
To find the critical t-value for a 95% confidence interval with 25 degrees freedom:
> qt(1-.05/2,25)
[1] 2.059539
The chi-square distribution
The pchisq( ) function gives the lower tail area for a chi-square value:
> pchisq(3.84,1)
[1] 0.9499565
For the chi-square test, we are usually interested in upper-tail areas as p-values. To find the p-value corresponding to a chi-square value of 4.50 with 1 d.f.:
> 1-pchisq(4.50,1)
[1] 0.03389485