This binomial test calculator determines the probability of a particular outcome (K) across a certain number of trials (n), where there are precisely two possible outcomes.
To use the calculator, enter the values of n, K and p into the table below (q will be calculated automatically), where n is the number of trials or observations, K is number of occasions the actual (or stipulated) outcome occurred, and p is the probability the outcome will occur on any particular occasion.
Things to remember: (a) the binomial test is appropriate only when you've got just two possible outcomes (or categories, etc.); (b) n and K will be frequencies; and (c) the value for p will fall somewhere between 0 and 1 - it's a proportion.
Imagine you want to find out whether you are psychic, so you toss a coin 1000 times, and each time predict whether it will come up heads or tails. You get it right 733 times, which is a lot higher than the 500 times you'd expect by chance. The question is - what's the probability that you'd get a result as extreme as 733 purely by chance?
To find out, enter 1000 as n - that is, the number of coin tosses, or trials, as n; enter 733 as K - that is, the number of times the outcome under consideration, in this case correctly predicting head or tails, actually occurred; and enter 0.5 as p - that is, the proportion of occasions you'd expect, or predict, the outcome to occur (0.5, because given an unbiased coin, and in the absence of psychic abilities, you'd expect a person to guess correctly half the time).