Binomial tests assume that data comes from n independent trials and have outcomes in either of two classes, and that the probability (p) of each outcome of each trial is the same.
When each data item has only two possible values, the outcome values come directly from the data.
More commonly, the binomial test applies to the sign of the difference between two values. It reports whether the probability that the sign is positive is a particular p_value, p*.
When p* is 0.5, the test is called the sign test.
Binomial/Z-Test
Each unique set of values in the groupby columns is called a group-by value set, or GBV set.
The test outputs a p value to compare to the specified probability threshold to determine whether to reject the null hypothesis (p=p*, p≤p*, or p>p*) for each GBV set.
When N (the count of value pairs) is over 100, the test outputs only the Z-test result (nP), an approximation more appropriate than the binomial test result. Otherwise, the test outputs both the binomial probability (BP) and Z-test results for all N. BP is the p_value of the one-tailed or two-tailed test, depending on singletail.
Binomial Sign Test
The sign test tests whether one column is positive.