My thanks to the many people who have responded to my
query for their swift, informative and helpful replies. What I
had in mind was something like the tables of the Standard
Normal distribution that are commonly available. However
everyone favoured the use of a computer for calculating exact
p-values, and it is certainly true that to deal with degrees of
freedom from 1 to 50 (say) one would need a large number of
pages, while over 100 could take a volume in itself. Multiply
this by the number of tests for which the number of degrees of
freedom (even more than one number, eg F-test) are required,
and this recommendation becomes only too understandable!
A summary of particular comments follows, although in cases
of repetition I may not have quoted everybody:
>From Martin Bland:
There are several programs which will give you P values for
any t and
any degrees of freed, e.g. Iain Buchan's ARCUS.
>From J. Penzer and Phil McShane:
The Minitab command cdf will calculate probability below a
given point for a given distribution. Probability in the tails can
then be calculated easily.
>From Brad Manktelow:
You can calculate exact p-values using Excel. I have a
spreadsheet to do
>From Ted Harding:
If you use books of tables, you end up having to interpolate
between tabulated values which is inconvenient.
One option would be to obtain and use the StaTable program
from Cytel (you can find their advert in RSS News & Notes,
for instance). This is an extremely useful utility program.
Alternatively, for specific distributions which arise you can
usually write your own program.
>From Sytse Knypstra:
You could download the program PQRS (Probabilities,
Quantiles and Random Samples), which gives you p-values
for some 25 distributions, including the t-distribution.
You can download it from
>From Nick Taub:
If it is just values from the cumulative t distribution that you
want - maybe with fractional degrees of freedom - then you
can get them with the tdist function in Excel.
>From Robert Newcombe:
The 7th edition of Documenta Geigy Scientific Tables (1970 -
my copy is a 1972 reprint) gives critical values of t for two-
tailed hypothesis tests at selected alpha levels i.e. 10%, 5%,
2.5%, 2%, 1%, 0.5% and 0.1%, for df = 1, 2, ..., 200. But
that is all. A table giving exact p-values for a fine grid of
values of t, for each df, would be very cumbersome. Your
best bet would be to find software that does this sort of thing.
A useful start is to use minitab, which will give you the
cumulative distribution function for specified t and df.
Thus if you key in cdf 2.00; t 60. it returns the value 0.9750.
But it only gives 4 dp, you just might need more, especially
way out in the tails.(Incidentally - maybe not directly relevant
here - something it is very useful to know is that for large df,
the critical value of t for a two-sided 5% level test is 1.96 +
2.4/df to a close approximation - certainly close enough for
most practical applications.)
>From Philip Sedgwick:
For every degree of freedom between 1 and 200, Documenta
Geigy Scientific tables provide the t-statistics for
pre-specified p-values (both one- and two-tailed p).
Other statistical tables (eg Murdoch and Barnes published
by Macmillan) give similar tabulations but after approximately
30 degress of freedom, they jump by 10 up to about 100. At
that point I approximate to the Normal distribution.
>From Barry W. Brown:
The following free program provides exact (to six or more
places) p-values for a wide variety of statistics. There are
also libraries in Fortran and C for performing the calculations
at the same site.DSTATTAB calculates the cumulative
distribution functions, inverses, and values of parameters for
the statistical distributions listed below.
1 - Incomplete Beta 2 - Binomial
3 - Negative Binomial 4 - Chi-square
5 - Non-central Chi-square 6 - F
7 - Non-central F 8 - Incomplete Gamma
9 - Normal 10 - Poisson
11 - T 12 - Non-central T
This program can be obtained from URL
Department of Epidemiology and Public Health
University of Leicester