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# The Matched-Pairs Design for Comparing Two Treatment Means Study Guide

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Updated on Oct 5, 2011

## Introduction to The Matched-Pairs Design for Comparing Two Treatment Means Study Guide

Thus far, we have only attempted to set confidence intervals on proportions or means based on a sample from a single treatment or population. Now we want to conduct studies that will allow us to compare the means of two treatments. First, we will think about how best to design a study. In this lesson, after introducing the basic ideas behind matched pairs and two-group designs, we will focus on the analysis of data from the paired design. In the next lesson, we will consider the two-group design.

## Two-Group versus Matched-Pairs Design

Suppose we are going to conduct a study to compare two methods of production, a standard method and a new method, that cause children's dress shoes to shine. Fifty children have been randomly selected to participate in the study. Each child will be given a new pair of dress shoes that shine. But first we need to decide how to assign the treatments (or production methods) to the children's shoes. One approach is to randomly select 25 (half) of the children and give them shoes made using the standard production process; the other half will receive shoes that were made using the new production process. Thus, each child would have a pair of shoes made by one of the two processes. A second approach is to have one shoe of each pair made with the standard process and the other shoe with the new process. Whether the right or left shoe is made with the first process would be randomly determined. In this second approach, each child would wear a dress shoe made using each process.

Regardless of which approach of assigning treatments is used, the children will wear the shoes whenever they wear dress shoes for six months. At the end of the six months, an evaluator who does not know which shoe received which treatment will score the shine quality of each shoe.

Which method of assigning treatments is better? In this case, having each child wear shoes made by both processes is better. Children differ in their activities while wearing dress shoes. Some may wear them only for special occasions, and their shoes will continue to shine no matter what process was used. Other children run and play in their dress shoes. Their shoes are less likely to continue to shine so the process could make a big difference. By having each child wear a shoe made from each process, both processes are subjected to the same environment (level of play). The difference in shine after six months is due more to the differences in the processes and not to differences in the children. This is an example of a paired experiment.

The other design in which half of the children wore dress shoes made by the standard process and half by the new process is a two-group design. Although this is a reasonable design, it is not the best for this study. The differences we observe in the shine of the shoes after six months are not due only to differences in processes, but also due to differences in children. This would lead to more variation in the estimated mean differences, making it more difficult to determine which, if either, shine process is better.

In the planning stages of a study, it is always important to consider the best way to randomize treatments to the study units. Pairs should be formed if, by pairing, we can eliminate some of the variability in the response that would otherwise be present. In the blinking study presented first in Lesson 4, for each study participant, the number of blinks in a two-minute time period was measured during normal conversation and while playing a video game. Those participants who tended to blink less than average during normal conversation also tended to blink less than average while playing a video game. Similarly, those who tended to blink more than average during normal conversation tended to blink more than average while playing a video game. By recording the difference in the number of blinks under each treatment for each person, we could eliminate the differences among people, allowing us to more accurately measure the differences between treatments, that is, between normal conversation and video playing.

Sometimes, it is not reasonable for both treatments to be applied to the same person. In this case, we may want to pair by some factor that will help explain the variability in the response. For example, suppose we want to compare two treatments for cholesterol. We could pair patients by their initial cholesterol levels. Those with the highest cholesterol level would be in the first pair. Those with the next highest cholesterol level would be in the next pair, and so forth. Then, within each pair, one of the patients would be randomly assigned to the first treatment, and the other would get the second treatment.

Whether or not to use pairing is an important consideration. Matched pairs should be formed only if the researcher believes that significant difference in the response variable can be explained, allowing differences in the treatments to be detected more readily. As an illustration, suppose we decided to pair patients in the cholesterol study on the basis of the length of their feet. The two with the longest feet would be in the first pair, the two with the next longest feet would be in the second pair, and so on. We have no reason to believe that foot length is in any way related to cholesterol level. Pairing in such a situation provides no benefit and is not as effective for assessing whether or not the treatment means are different as the two-group design.

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