## F values and t values, tabulated and probabilities

Often we find that we wish/need to obtain critical F values for
a given probability and numerator and denominator degrees of freedom,
or critical t values for a given probability and denomonator degrees
of freedom.
Obviously, for a limited range of degrees of freedom and probability
levels we can simply use the tabulated values that are given in most
statistics books. However, often the tables do not give the values
we need. We can use SAS (the datastep or IML) to obtain F-values,
or t values,
which we can use to accept/reject a hypothesis. Conversely, with
a given calculated F or t value and the the associated numerator and denominator
degrees of freedom we can obtain the probability associated with this.

The first case, find a F value corresponding to a certain probability
and d.f., uses the SAS function *finv()*. The second case, finding the
probability associated to a given calculated F value and d.f., uses
the SAS function *probf()*. These functions are described in the
SAS Online Documentation, under Base SAS, Language Reference, Functions.

#### Critical F values

If we want to obtain the F value for a certain probability and ndf and ddf,
we can use the finv() function. Suppose that we want to obtain the F value
for a probability of 0.05 (5%), and ndf = 2 and ddf = 27, and the F-value
for a probability of 0.01 (1%) and ndf = 1 and df = 26. We can use the following
data step.

data ftabs;
input prob ndf ddf;
fvalue = finv(1-prob,ndf,ddf);
cards;
0.05 2 27
0.01 1 26
;
proc print data=ftabs;
var prob ndf ddf fvalue;
run;

This will compute the F-value for both cases, producing a SAS dataset with
2 records and 4 variables per record.

### Determining a tabulated t value

Suppose that we wish to determine the cut-off t-value for a probability level
of 5% and ddf (denominator degrees of freedom) = 14, then we can use the
TINV function:

data crittvals;
input pr ddf;
tvalue = tinv(1-(pr/2),ddf);
cards;
0.05 14
;
proc print data=crittvals;
var pr ddf tvalue;
run;

We would obtain the following output from PROC PRINT:

obs pr ddf tvalue
1 0.05 14 2.14479

Which agrees with the tabulated values in STD!

R.I. Cue ©

Department of Animal Science, McGill University

last updated : 2010 April 28