Determine the probability of an event occurring. If a coin is flipped, the probability of it landing with the head up is 0.5. If a die is tossed, the probability of rolling a six is .167. With the die toss, the only successful event is the rolling of a six. Any other result would be a failure.
Multiply the probability of the successful event occurring by the number of total (successful and unsuccessful) events in the experiment, to get the predicted mean of the number of successes. If a coin is to be tossed 20 times, the predicted number of heads will be 0.5 x 20 = 10. If a die is rolled 20 times, the predicted number of sixes will be 0.167 x 20 = 3.33.
Find the standard deviation for the predicted number of successes. The standard deviation for a binomial distribution is the square root of n x p x q, where n is the number of attempts, p is the number of successes and q is the number of failures. If a coin is tossed 20 times, the standard deviation would be the square root of 20 x .5 x .5, or the square root of 5, which is roughly 2.36. If a die is rolled 20 times, the standard deviation for rolling a six would be the square root of 20 x .167 x .833, or roughly 1.67.
Compare the actual number of successes in the set of trials with the predicted number of successes. The actual outcome should be within two standard deviations of the predicted mean outcome. With the coin toss, the actual number of heads in 20 trials should be between between 5.28 and 14.72 (10 plus or minus 2 x 2.36). With the die toss, the actual number of sixes should be between 0 and 6.67. Any results that are more than two standard deviations from the mean are evidence that something may be skewing the results.