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Completely Randomized Design

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Source: NCSSM Statistics Leadership Institute Notes

Hi. This tutorial covers a specific type of experimental design called the completely randomized design.

So let's start by defining it. A completely randomized design is a method of experimental design that uses a type of randomization scheme where treatments are assigned to experimental units completely by chance. So remember what a treatment is, it's just a specific value of your explanatory variable. And your experimental units are either your participants or your subjects in the experiment. And, of course, with the completely randomized design, that assignment needs to be done by chance.

So let's take a look at a situation where a completely randomized design might be appropriate. So suppose we have four different diets on which we want to compare. The diets are labeled Diet A, Diet B, Diet C, and Diet D. We're interested in how the diets affect the coagulation rates of rabbits. The coagulation rate is the time in seconds that it takes for a cut to stop bleeding.

We have 16 rabbits available for the experiment. So we will use four rabbits on each diet. The 16 rabbits arrive and are placed in a large compound until you're ready to begin the experiment, at which time they will be transferred to cages.

So how should we use randomization to assign the rabbits to the four treatment groups? So in this case, the rabbits are experimental units. And the four diets are our four treatment groups.

We're going to look at two different methods for possibly assigning the treatments to the rabbits. So let's start with Method 1 and try to decide if this is a completely randomized design.

So, Method 1-- we assume that the rabbits will be caught at random. Catch four rabbits and assign them to Diet A. Catch the next four rabbits and assign them to Diet B. Continue with Diet C and D. So is this a completely randomized design? Were those diets assigned to the rabbits totally by chance?

And I would like to make the argument that no, this isn't a completely randomized designed. So Method 1 is faulty. The first rabbits caught could be the slowest and weakest rabbits, those least able to escape capture. This would bias the results. If the experimental results came out to the disadvantage of Diet A, there would be no way to determine if the results were a consequence of Diet A or the fact that they were the weakest rabbits placed on that diet by our randomization process. So since this would not be a completely randomized design, this would not fulfill the requirements that we set out in our original definition.

So let's take a look at now a second method of random assignment. So, Method 2-- catch all the rabbits and label them one to 16. Select four numbers, one to 16 at random, without replacement. And put each rabbit in a separate cage and provide them with Diet A. Then select another four numbers at random, again, without replacement. And put them in cages to receive Diet B.

Continue until you have 16 rabbits in 16 cages. So at the end of it, four rabbits should be receiving Diet A, four should be receiving Diet B, et cetera. So now we want to think about, is this a completely randomized design? And what I would argue is yes. Method 2 is completely randomized because the diet treatments were randomly assigned to the rabbits. So we had this completely by chance since we were just generating random numbers.

So one thing to consider is that sometimes a completely randomized design has flaws. Say if male and female rabbits had different eating habits, randomization may put a disproportionate amount of male rabbits in one of the diet groups. So although completely randomized design does usually provide good experimental groups and good randomization, it's not perfect. So this is one example where we would get some flaws in our completely randomized design.

So that is the tutorial on completely randomized design Thanks for watching.