Random Assignment vs Random Variable
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Random assignment
Collecting data and study design
Random assignment uses chance to sort experimental units into treatment groups, so the groups start out similar and confounding is balanced out.
Random assignment is how an experiment builds comparable groups. Because a coin flip or random number decides who gets which treatment, no systematic difference in age, health, or motivation piles up in one group, so a later difference in outcomes can be credited to the treatment. For example, flipping a coin for each of 40 patients to assign a drug or a placebo balances the other traits across the two groups on average. Random assignment builds the groups, while random selection picks the sample; assignment supports cause-and-effect claims, and selection supports generalizing to a population.
Random variable
Random variables and distributions
A random variable assigns a numerical value to each outcome of a chance process, so its value is determined by the result of a random event.
A random variable turns the outcomes of a random process into numbers you can average and analyze. For example, if is the number of heads in two coin flips, then can equal 0, 1, or 2, each with its own probability. Random variables are discrete when their values are countable and continuous when they can take any value in an interval. Its long-run average is the expected value (E of X, each value times its probability, summed).