Matched Pairs Design

Matched pairs design is one of the experimental designs of a randomized block design which is used when the experiment has only two treatments. Additionally, as the name suggests, the subjects are grouped into pairs based on blocking variable such as gender and age. Being a randomized design, the two treatments are randomly assigned to the subjects.

Matched Pairs Design Advantages and Disadvantages

Advantages Disadvantages
Each treatment has people with similar characteristics hence fewer participant variables If one participant opts out,2 PPS data is lost
No counterbalancing since there is no order effects. Matching is a quagmire and time-consuming
Materials/tests can be reused across the conditions It is impossible to match people exactly unless participants are twins.

Matched Pairs Diagram

Below is a good example of a matched pair experimental design

matched pairs design diagram

Group design Example

The table shows a matched pairs example for a hypothetical clinical experiment in which 100 subjects were involved. Each of the subjects received either a placebo or a Malaria Vaccine. The subjects were grouped into two each with 50 subjects matched pairs. Each pair was matched on gender and age. For instance, Pair 1 was two males both age 20 while Pair two was two women both age 21 and Pair 3 was two women both age 23 etc.

  Treatment
Pair Placebo Vaccine
1 1 1
2 1 1
3 1 1
49 1 1
50 1 1

Matched pairs analysis/matched-pair t-test

Matched-pair t test is used to test if there is a difference in mean between two matched/related pairs. The matched –pair t test is also referred to as the paired samples t-test of the dependent t-test. The test is a parametric test whose assumptions are

  1. The dependent variable must be continuous
  2. Observations should be independent of each other
  3. Dependent variable should be approximately normal.
  4. There should be no outliers in the dependent variable.

The matched-pair t test statistic is calculated as below;

matched-pair t test formula

The calculated value is compared to the tabulated value with n-1 degrees of freedom.

Example

#ID x1 x2 X1-X2 (X1-X2)²
1 5.24 7.53 -2.29 5.2441
2 6.28 9.06 -2.78 7.7284
3 7.09 12.61 -5.52 30.4704
4 8.21 14.76 -6.55 42.9025
5 11.27 17.66 -6.39 40.8321
Sum -23.53 127.1775
n 5 Mean -4.706
df=n-1: 4 sd 2.027641
matched-pair t test example

At 0.05 level, the t value with 4 degrees of freedom is 2.78.Since the calculated value is greater than the tabulated then there is no significance claimed.

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