## Applied Statistics Lesson of the Day – The Matched Pairs Experimental Design

The matched pairs design is a special type of the randomized blocked design in experimental design.  It has only 2 treatment levels (i.e. there is 1 factor, and this factor is binary), and a blocking variable divides the $n$ experimental units into $n/2$ pairs.  Within each pair (i.e. each block), the experimental units are randomly assigned to the 2 treatment groups (e.g. by a coin flip).  The experimental units are divided into pairs such that homogeneity is maximized within each pair.

For example, a lab safety officer wants to compare the durability of nitrile and latex gloves for chemical experiments.  She wants to conduct an experiment with 30 nitrile gloves and 30 latex gloves to test her hypothesis.  She does her best to draw a random sample of 30 students in her university for her experiment, and they all perform the same organic synthesis using the same procedures to see which type of gloves lasts longer.

She could use a completely randomized design so that a random sample of 30 hands get the 30 nitrile gloves, and the other 30 hands get the 30 latex gloves.  However, since lab habits are unique to each person, this poses a confounding variable – durability can be affected by both the material and a student’s lab habits, and the lab safety officer only wants to study the effect of the material.  Thus, a randomized block design should be used instead so that each student acts as a blocking variable – 1 hand gets a nitrile glove, and 1 hand gets a latex glove.  Once the gloves have been given to the student, the type of glove is randomly assigned to each hand; some may get the nitrile glove on their left hand, and some may get it on their right hand.  Since this design involves one binary factor and blocks that divide the experimental units into pairs, this is a matched pairs design.

## Applied Statistics Lesson of the Day – Blocking and the Randomized Complete Blocked Design (RCBD)

A completely randomized design works well for a homogeneous population – one that does not have major differences between any sub-populations.  However, what if a population is heterogeneous?

Consider an example that commonly occurs in medical studies.  An experiment seeks to determine the effectiveness of a drug on curing a disease, and 100 patients are recruited for this double-blinded study – 50 are men, and 50 are women.  An abundance of biological knowledge tells us that men and women have significantly physiologies, and this is a heterogeneous population with respect to gender.  If a completely randomized design is used for this study, gender could be a confounding variable; this is especially true if the experimental group has a much higher proportion of one gender, and the control group has a much higher proportion of the other gender.  (For instance, purely due to the randomness, 45 males may be assigned to the experimental group, and 45 females may be assigned to the control group.)  If a statistically significant difference in the patients’ survival from the disease is observed between such a pair of experimental and control groups, this effect could be attributed to the drug or to gender, and that would ruin the goal of determining the cause-and-effect relationship between the drug and survival from the disease.

To overcome this heterogeneity and control for the effect of gender, a randomized blocked design could be used.  Blocking is the division of the experimental units into homogeneous sub-populations before assigning treatments to them.  A randomized blocked design for our above example would divide the males and females into 2 separate sub-populations, and then each of these 2 groups is split into the experimental and control group.  Thus, the experiment actually has 4 groups:

1. 25 men take the drug (experimental)
2. 25 men take a placebo (control)
3. 25 women take the drug (experimental)
4. 25 women take a placebo (control)

Essentially, the population is divided into blocks of homogeneous sub-populations, and a completely randomized design is applied to each block.  This minimizes the effect of gender on the response and increases the precision of the estimate of the effect of the drug.