Randomization, or random assignment, provides a way of eliminating all possible systematic differences between conditions all at once. Think of the relation between violent imagery and aggression. Suppose I encourage a group of children to play a violent video game, say GTA 5, for a total of ten hours in one week and I deny another group any access to violent imagery for the same period of time. Suppose I find that children who played the violent game are more aggressive than the control group. Of course there are still many possible alternative explanations for the difference in aggressive behavior other than violent stimuli. Suppose child could volunteer for the violent game play condition, it would not be hard to image that this group would consist of more boys or children more drawn to violence and aggression in the control group. Such systematic differences between the groups, providing alternative explanations for more aggressiveness in the experiential group, would likely have been prevented with random assignment. Okay, let's see why. I could have randomly assigned children to the conditions by flipping a coin, heads for the experimental condition, tails for the control condition. A naturally aggressive child would have a 50-50 chance of ending up in the experimental condition. The same goes for a child of the male sex. A very meek child, a child with impaired eyesight, a child with large feet, any property you can think of, a child with that particular property, will have an equal chance of being assigned to one of the conditions. Put another way, how many boys do we expect in the experimental condition? About half of all boys in this study. Because for the boys on average, the coin will show heads half of the time. How many naturally aggressive children will end up in the experimental condition? Again, about the same number as in the control condition. And the same goes for all other characteristics we can think of. On average, randomization ensures that there is no systematic difference between the groups other than on the independent variable. Of course in any one particular study, it is possible entirely due to chance that we end up for example, with more girls in the control group, possibly explaining why this group is less aggressive. I call this a randomization failure. We rely on the law of large numbers when we flip the coin. But this law doesn't always work out, especially in small groups. Suppose there are only four boys and four girls to assign to the two groups. It's not hard to imagine that the coin toss will come out something like this. First girl heads, second girl tails, first boy heads, second boy heads. Third boy heads, third girl heads, fourth girl tails, fourth boy tails. The experimental group now consists of three boys and two girls, five children in all. The control group consists of one boy and two girls, three children in all. The problem is that the groups are not of equal size which is a nuisance statistically speaking. We also have a systematic difference in terms of sex. One solution is to perform a randomization check. We can measure relevant background or control variables and simply check to see whether randomization worked and the conditions are the same or whether randomization failed and the conditions differ on these variables. There is a way to guarantee randomization works on a select set of variables using restricted randomization procedures. Blocking is the simplest form of restricted randomization. It ensures equal or almost equal group sizes. We pair children up in blocks of two and flip a coin to determine where the first child goes. The second child is automatically assigned the other condition. Repeat for all children and if we have an equal number of participants, equal group sizes are ensured. In stratified restricted random assignment, we use the blocks to ensure not just equal numbers, but also equal representation of a specific subject characteristic, for example, equal numbers of boys and girls in each group. We can arrange this by first pairing up all the girls and for each block of girls, flipping a coin to determine to what condition the first girl is assigned. We then automatically assign the second girl to the other condition. We now have a girl in each condition. We do the same for the second block of girls, end up with two girls in each condition. The same method is applied in assigning the boys so that we end up with two boys and two girls in each condition. Of course, stratified randomization has its limits. You can apply it to several characteristics combined, sex and age, for example, but with more than two or three variables to stratify on, things become complicated. Moreover, there's an endless number of subject characteristics. It's impossible to control them all. I have one final remark about randomization in repeated measures designs, concerning within subjects design, where all subjects are exposed to all of the conditions. In this case, randomization might seem unnecessary, but this is not the case. If all subjects are exposed to the conditions in the same order then any effect could be explained by maturation or some sort of habituation effect that spills over from one condition to the other. So in within subject designs, the order in which subjects are exposed to the conditions should be randomized. We call this counter balancing. Subjects are assigned to one out of all possible orderings of the conditions possibly using blocking to ensure that no one ordering is over represented.