The matched pairs design is a unique type of the randomized blocked design in experimental design. It has only 2 treatment levels (i.e. there’s 1 factor, and this factor is binary), and a blocking factor divides the n experimental units to n/2 pairs. Within every group (i.e. every block), the experimental components have been randomly assigned to both treatment groups (e.g. with a coin flip). The experimental components are broken into pairs such that homogeneity is maximized within each pair.
For instance, a laboratory safety officer wants to compare the durability of nitrile and latex gloves for chemical experiments. She wishes to run 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 all of them play the same organic synthesis using the same procedures to see which kind of gloves lasts more.
She could use a completely randomized design to ensure a random sample of 30 hands get the 30 nitrile gloves, along with the other 30 hands get the 30 latex gloves. However, since lab habits are unique to every individual, this poses a perplexing factor — durability can be impacted by both the material and a student’s lab customs, along with the laboratory safety officer just wishes to study the impact of the substance. Thus, a randomized block design should be used rather so that every student functions as a blocking variable — 1 hand receives a nitrile glove, and 1 hand gets a latex glove. Once the gloves have been given to the student, the kind of glove is randomly assigned to each hand; a few may find the nitrile glove on their left hand, and a few may put it in their own right hand. Since this design involves one binary variable and blocks that divide the experimental components to pairs, this is a matched pairs design.
The word “experiment” can mean many different things in various contexts. In science and statistics, it has a very particular and subtle definition, one that is not immediately familiar to many people who work outside of the field of experimental design. This is the first of a series of blog posts to clarify what an experiment is, how it is conducted, and why it is so central to science and statistics.
Experiment: A procedure to determine the causal relationship between 2 variables – an explanatory variable and a response variable. The value of the explanatory variable is changed, and the value of the response variable is observed for each value of the explantory variable.
– An experiment can have 2 or more explanatory variables and 2 or more response variables.
– In my experience, I find that most experiments have 1 response variable, but many experiments have 2 or more explanatory variables. The interactions between the multiple explanatory variables are often of interest.
– All other variables are held constant in this process to avoid confounding.
Explanatory Variable or Factor: The factor whose values are determined by the experimenter. This factor is the cause in the hypothesis. (*Many people call this the individual factor. I discourage this use, because “independent” means something quite different in statistics.)
Response Variable: The variable whose values have been detected by the experimenter as the explanatory variable’s value is altered. This variable is the effect from the hypothesis. (*Many people call this the dependent variable. Further to my previous point about “independent variables”, dependence means something very different in numbers, and I discourage using this use.)
Factor Level: Each possible value of the factor (explanatory variable). A factor must have at least 2 levels.
Treatment: Each possible combination of factor levels.
– If the experiment has only 1 explanatory variable, then each treatment is simply each factor level.
– If the experiment has 2 explanatory variables, X and Y, then each treatment is a combination of 1 factor level from X and 1 factor level from Y. Such combining of factor levels generalizes to experiments with more than 2 explanatory variables.
Experimental Unit: The object on which a treatment is applied. This can be anything – person, group of people, animal, plant, chemical, guitar, baseball, etc.
Basic Terminology in Experimental Design #2: Controlling for Confounders
A well designed experiment must have good control, which is the reduction of effects from confounding variables. There are several ways to do so:
– Include a control group. This group will receive a neutral treatment or a standard treatment. (This treatment may simply be nothing.) The experimental group will receive the new treatment or treatment of interest. The response in the experimental group will be compared to the response in the control group to assess the effect of the new treatment or treatment of interest. Any effect from confounding variables will affect both the control group and the experimental group equally, so the only difference between the 2 groups should be due to the new treatment or treatment of interest.
– In medical studies with patients as the experimental units, it is common to include a placebo group. Patients in the placebo group get a treatment that is known to have no effect. This accounts for the placebo effect. For example, in a drug study, a patient in the placebo group may get a sugar pill.
– In experiments with human or animal subjects, participants and/or the experimenters are often blinded. This means that they do not know which treatment the participant received. This ensures that knowledge of receiving a particular treatment – for either the participant or the experimenters – is not a confounding variable. An experiment that blinds both the participants and the experimenters is called a double-blinded experiment.
– For confounding variables that are difficult or impossible to control for, the experimental units should be assigned to the control group and the experimental group by randomization. This can be done with random number tables, flipping a coin, or random number generators from computers. This ensures that confounding effects affect both the control group and the experimental group roughly equally. For example, an experimenter wants to determine if the HPV vaccine will make new students immune to HPV. There will be 2 groups: the control group will not receive the vaccine, and the experimental group will receive the vaccine. If the experimenter can choose students from 2 schools for her study, then the students should be randomly assigned into the 2 groups, so that each group will have roughly the same number of students from each school. This would minimize the confounding effect of the schools.