Experimental Design

Types of Designs by how units are randomized to treatments

• Completely Randomized

• Block

• Matched Pair

Completely Randomized Comparative Design

When all experimental units are allocated at random among all treatments

Diagram for CRD

Diagram for a simple Comparitive Randomized Experimental Design

Group 1 treatment Random Compare Allocation Responses Group 2 treatment

Example

I wish to know from the population of this classroom, if running in place for 1 min. increases pulse rate. I randomly select 10 people to participate in the study. I then randomly select which students will run for 1 min and which students will not run. After 1 min we take the pulse rates of each student. We might make the mean pulse rate of each group my response variable.

Diagram for this example

5 people run Randomly Compare allocate 5 mean pulse people to run rate and 5 to remain 5 people sit stationary

Blocked Design

• The randomized complete block design is a design in which the subjects are matched according to a variable which the experimenter wishes to control. The subjects are put into groups (blocks) of the same size as the number of treatments. The members of each block are then randomly assigned to different treatment groups.

Blocked design Example 1

• Using the previous example with pulse rate, suppose I thought that whether or not you exercised on a regular basis might effect pulse rate. I then assign you to groups of 2…because I have 2 treatment groups…as to how much you exercise. Then within each group of two I randomly select one to be in the control group and one to be in the “run” group. I then compare means of pulse rates of the two groups.

Example 2

• A researcher is carrying out a study of the effectiveness of four different skin creams for the treatment of a certain skin disease. He has eighty subjects and plans to divide them into 4 treatment groups of twenty subjects each. Using a randomized blocks design, the subjects are assessed and put in blocks of four according to how severe their skin condition is; the four most severe cases are the first block, the next four most severe cases are the second block, and so on to the twentieth block. The four members of each block are then randomly assigned, one to each of the four treatment groups

Matched Pair Design

• Type of blocked design• Must compare only two treatments• We choose blocks of two units that are as closely

matched as possible• Twin studies, left/right hand from the same person….• Same person before and after studies• Each subject (unit) serves as his/her own control• Randomization occurs when assigning treatments to

unit or from assigning the order of treatments to a single unit.

Are cereal leaf beetles more strongly attracted by

the color yellow or by the color green? • Agriculture researches want to know,

because they detect the presence of the pests in farm field using sticky boards to trap insect that land on them. The board color should attract beetles as strongly as possible. We must design an experiment to compare yellow and green by mounting sticky boards on poles in a large field of oats.

Using a block design; design an experiment.

• What are the experimental units?• What type of design are we employing?• What is the response variable?•  What is the treatment or explanatory variable•  How have we used randomization?•  How is control being used?

 

• Experimental Units: locations within the field• design: matched pair each location will get a yellow and a green on

one pole• randomize to decide if yellow will go first or

green (toss coin)•  Response variable: how many beetles on each

color•  Factors or explanatory variable: colors of

sticky boards•  Treatment: Subjecting insects to two color of

sticky board.  

Example of matched pair

• http://www.amstat.org/publications/jse/java/v9n1/anderson-cook/GoodExpDesignApplet.html

• Improved Experimental Design Applet

Vocabulary

• double blind: subjects are not aware who is getting the placebo and who is getting the real treatment

• Placebo effect: a dummy treatment such as a sugar pill

• bias: systematically favors one outcome