# STATS_BINOMIAL_TEST

Syntax

Description of the illustration ''stats_binomial_test.gif''

Purpose

`STATS_BINOMIAL_TEST` is an exact probability test used for dichotomous variables, where only two possible values exist. It tests the difference between a sample proportion and a given proportion. The sample size in such tests is usually small.

This function takes three required arguments: `expr1` is the sample being examined, `expr2` contains the values for which the proportion is expected to be, and `p` is a proportion to test against. The optional fourth argument lets you specify the meaning of the `NUMBER` value returned by this function, as shown in Table 7-3. For this argument, you can specify a text literal, or a bind variable or expression that evaluates to a constant character value. If you omit the fourth argument, then the default is `'TWO_SIDED_PROB'`.

Table 7-3 STATS_BINOMIAL Return Values

Argument Return Value Meaning

`'TWO_SIDED_PROB'`

The probability that the given population proportion, `p`, could result in the observed proportion or a more extreme one.

`'EXACT_PROB'`

The probability that the given population proportion, `p`, could result in exactly the observed proportion.

`'ONE_SIDED_PROB_OR_MORE'`

The probability that the given population proportion, `p`, could result in the observed proportion or a larger one.

`'ONE_SIDED_PROB_OR_LESS'`

The probability that the given population proportion, `p`, could result in the observed proportion or a smaller one.

`'EXACT_PROB'` gives the probability of getting exactly proportion p. In cases where you want to test whether the proportion found in the sample is significantly different from a 50-50 split, `p` would normally be 0.50. If you want to test only whether the proportion is different, then use the return value `'TWO_SIDED_PROB'`. If your test is whether the proportion is more than the value of `expr2`, then use the return value `'ONE_SIDED_PROB_OR_MORE'`. If the test is to determine whether the proportion of `expr2` is less, then use the return value `'ONE_SIDED_PROB_OR_LESS'`.

STATS_BINOMIAL_TEST Example The following example determines the probability that reality exactly matches the number of men observed under the assumption that 69% of the population is composed of men:

```SELECT AVG(DECODE(cust_gender, 'M', 1, 0)) real_proportion,
STATS_BINOMIAL_TEST
(cust_gender, 'M', 0.68, 'EXACT_PROB') exact,
STATS_BINOMIAL_TEST
(cust_gender, 'M', 0.68, 'ONE_SIDED_PROB_OR_LESS') prob_or_less
FROM sh.customers;
```