An analogy between an experiment and drawing numbered tickets "at random" from a box with replacement. For example, suppose we are trying to evaluate a cold remedy by giving it or a placebo to a group of n individuals, randomly choosing half the individuals to receive the remedy and half to receive the placebo. Consider the median time to recovery for all the individuals (we assume everyone recovers from the cold eventually; to simplify things, we also assume that no one recovered in exactly the median time, and that n is even). By definition, half the individuals got better in less than the median time, and half in more than the median time. The individuals who received the treatment are a random sample of size n/2 from the set of n subjects, half of whom got better in less than median time, and half in longer than median time. If the remedy is ineffective, the number of subjects who received the remedy and who recovered in less than median time is like the sum of n/2 draws with replacement from a box with two tickets in it: one with a "1" on it, and one with a "0" on it. This page illustrates the sampling distribution of random draws with or without from a box of numbered tickets.