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## High school statistics

### Course: High school statistics>Unit 5

Lesson 4: Introduction to experimental design

# Matched pairs experiment design

AP.STATS:
VAR‑3 (EU)
,
VAR‑3.C (LO)
,
VAR‑3.C.9 (EK)
CCSS.Math:
Matched pairs experiment design.

## Want to join the conversation?

• At , Sal defines matched pairs as putting everyone in one round in either the experimental or control group and then switching them. However, in the following practice, I get this question:

"An online retailer wants to study whether more lenient return policies increase purchasing behaviors. They select a random sample of 200020002000 customers who have made purchases in the past year.
The company ranks the customers according to total cost of purchases made the previous year. For every 222 customers, in order, from the list, the online retailer randomly assigns one customer to the treatment group and the other to the control group."

To my thinking, this is simply random, because according to Sal's definition above, you need to follow the 2-step process of assigning two groups and then swapping them. Yet the answer to the above example is also a matched pair. The reasoning given:

"Customers are split into pairs before assignment, matched as nearly as possible on a common trait. Then they are randomly assigned from those pairs into the treatment or control group."

There is no indication that two sets of experiments were run. What am I missing here? If anything, that seems if not random, more like a block. Or is this matched pair definition more expansive than what is mentioned in the video?

I'm not really struggling with the concepts. The video seemed pretty clear, but it also seems that matched pair as a term is being used for what seem to me two different concepts. I am missing something somewhere.
• It looks to me like there may be a mistake in what came through when you typed, correct me if I'm wrong, but should that say "for every 2 customers,"?

If so I think I can help. matched pairs means you are dividing your sample into blocks of size 2. So in your example they are taking that list and blocking by the top 2 purchasers, then the next 2, and so on. That helps mitigate the random chance of more of the top purchasers in one treatment group.

The example Sal uses is matched pairs because each individual is paired up, it's just that they are paired up with themselves. Because if you think about trying to get 2 treatment groups as similar as possible, using all the same individuals is as similar as it gets. You do have to randomize the order of the treatments, however, so that the factor order is not confounding.
• It looks like Sal used a crossover study example for matched pairs experiment. At he says "and then you do another round where you switch, where the people who are in the treatment go to the control, and the people who are in the control go into the treatment". This sounds like a crossover design.

"A crossover design is a repeated measurements design such that each experimental unit (patient) receives different treatments during the different time periods, i.e., the patients cross over from one treatment to another during the course of the trial."
https://onlinecourses.science.psu.edu/stat509/node/123/

In a matched pair design patients would be divided into pairs based on age and gender for example and then assigned different treatment within pairs.

"A matched pairs design is a special case of a randomized block design. It can be used when the experiment has only two treatment conditions; and subjects can be grouped into pairs, based on some blocking variable. Then, within each pair, subjects are randomly assigned to different treatments."
https://stattrek.com/statistics/dictionary.aspx?definition=matched%20pairs%20design
• I believe this is called a cross-over design and not a matched pair design. Am I wrong?
• It really depends on the teacher. For me matched pair is easier to comprehend because you're matching the top two then the next top two and so forth and randomizing from there.
• Can we consider this particular example be incorrect because of the different starting conditions in the 1st and 2nd stages of the experiment? For instance, the 1st stage treatment group might have post-effects caused by the drug.
• nice point

and that might be a whole new direction of research for the drug

i mean you may better design an experiment mainly focusing on that post drug effects, while doing the original experiment under the assumption of no post effects in parallel
(1 vote)
• Is there any reason to do block design with matched pairs? It seems to me like since each individual is going through both treatment groups, it wouldn't matter.
• What is the control group again?
• the group that you give no or fake drug than the real one to test the effect from it
(1 vote)
• I am pretty sure that a matched pairs design is one where an experimental unit receives both treatments
(1 vote)
• Yes, that's what happens in this video. Each person got both the treatment and the placebo. Although, you can also have a matched pairs design where you pair different experimental units together that have similar qualities. Like if you paired up people with similar ages, and gave one person in each pair the placebo, and the other the treatment. Hope this helps! (:
• differences between an experiment and an observational study?
(1 vote)
• An experiment, unlike an observational study, often involves randomly assigning people (or other living things or other objects) to a control group and to one or more treatment groups. A researcher controls the conditions in an experiment, but does not control the conditions in an observational study.