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Completely Randomized Design
Common Core: S.IC.3

Completely Randomized Design

Author: Jonathan Osters

Describe completely randomized design experiments.

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Source: Male Bathroom Symbol, Public Domain: Female Bathroom Symbol, Public Domain:

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This tutorial is going to talk to you about completely randomized design of an experiment. Now, completely randomized design means that you're going to assign treatments to individual participants in the experiment randomly. So here's an example of a completely randomized design.

A researcher wants to identify whether the new acid reflux drug that they've developed is going to be more effective than the one that's currently available. So he gets 500 volunteers and he writes on 500 slips of paper. He writes 1 on 250 of them and 2 on the other 250. Places the numbers into a hat, mixes them up, has the volunteers pull them out. And the ones who selected 1 receive the new drug. And the ones who selected 2 receive the old drug that's currently available.

And that's all there is to it. I mean, it's a random assignment of people to groups. Now, this is the simplest way to assign subjects to treatments. However, it's not necessarily ideal for every scenario.

Now, it's possible that the acid reflux drug is say, more effective for men than it is for women. Well, that's not really a problem if we divide the treatment control groups like this. In this particular case, there were nine males and 14 females that I pictured, which was a little different than what we had on the previous slide-- but I didn't draw 500 people.

But here you can see there's roughly the same amount of females and roughly the same amount of males in the treatment group and the control group. Here, if the treatment is more effective for males and for females we'll see that because of the about equal assignment. Now, it might have been even more beneficial to essentially run two experiments side-by-side. One that contains only females and one that contains only males. But that's not exactly how we did it.

Where we run into problems with a completely randomized design is if the random assignment doesn't match the proportions of the population equally, like if this had happened-- if we had assigned 10 of the 14 women to the treatment group and only four of the women to the control group. Notice, these have 12 and 11 people in them, so they're roughly the same size. It's just the proportions are way out of whack. And that happens from time-to-time with random assignment. Here if the drug was more effective for men and than women, we actually wouldn't see that because there aren't that many men in the treatment group-- most of men went to the control group.

So let's take another look. Let's take another example and see what a completely randomized design would look like. Suppose a tire company is considering rolling out-- pun entirely intended-- a new type of rubber for its bicycle tires. It as 300 bikes that it can use, and we want to do a completely randomized design. So pause the video for a little bit. Scribble down some ideas about what a completely randomized design would look like for this experiment.

All right, what you should have come up with is something like this. They could place the numbers one through 300 in a hat and have each rider select out one number. The numbers one through 150 receive the tire's made of old rubber. And the ones 151 to 300 receive the tire's made of new rubber. The cyclist wouldn't necessarily know which type of tire there receiving.

Problem again arises here, what if all 300 riders don't ride their bikes the same way? What if all the people that commute to work are in the same group? Or most of the people who commute to work are in the same group? They might wear their tires out faster regardless if their on the new tires or the old tires. And so the comparison of where between the two groups wouldn't make a whole lot of sense.

So there's lots of things to consider. And actually, each of these two scenarios-- the acid reflux drug scenario and the bicycle rubber company scenario-- both of these actually have better ways that we could go about them then a completely randomized design. However, a completely randomized design is the simplest.

So to recap, in a completely randomized design, which is the simplest way of assigning individuals, the subjects are assigned using some random process like numbers in a random number generator, random number table, numbers in a hat, names in a hat. The problem is it's not always the best way to assign treatments. Although, a lot of the times it is and it works just fine. And again, the terminology that we used was completely randomized design.

Good luck. See you next time.

Terms to Know
Completely Randomized Design

An experimental design where the assignment of subjects to treatments is done entirely at random.