#### 15.9.1 Binomial test

[ /BINOMIAL[(`p`)]=`var_list`[(`value1`[, `value2`)] ] ]

The `/BINOMIAL`

subcommand compares the observed distribution of a dichotomous
variable with that of a binomial distribution.
The variable `p` specifies the test proportion of the binomial
distribution.
The default value of 0.5 is assumed if `p` is omitted.

If a single value appears after the variable list, then that value is
used as the threshold to partition the observed values. Values less
than or equal to the threshold value form the first category. Values
greater than the threshold form the second category.

If two values appear after the variable list, then they will be used
as the values which a variable must take to be in the respective
category.
Cases for which a variable takes a value equal to neither of the specified
values, take no part in the test for that variable.

If no values appear, then the variable must assume dichotomous
values.
If more than two distinct, non-missing values for a variable
under test are encountered then an error occurs.

If the test proportion is equal to 0.5, then a two tailed test is
reported. For any other test proportion, a one tailed test is
reported.
For one tailed tests, if the test proportion is less than
or equal to the observed proportion, then the significance of
observing the observed proportion or more is reported.
If the test proportion is more than the observed proportion, then the
significance of observing the observed proportion or less is reported.
That is to say, the test is always performed in the observed
direction.

pspp uses a very precise approximation to the gamma function to
compute the binomial significance. Thus, exact results are reported
even for very large sample sizes.