Completely Randomized Design & Completely Randomized Design

Completely Randomized Design

A completely randomized design is probably the simplest experimental design, in terms of data analysis and convenience. With this design, subjects are randomly assigned to treatments.

Treatment
Placebo	Vaccine
500	500

A completely randomized design layout for a hypothetical medical experiment is shown in the table to the right. In this design, the experimenter randomly assigned subjects to one of two treatment conditions. They received a placebo or they received a cold vaccine. The same number of subjects (500) are assigned to each treatment condition (although this is not required). The dependent variable is the number of colds reported in each treatment condition. If the vaccine is effective, subjects in the "vaccine" condition should report significantly fewer colds than subjects in the "placebo" condition.

A completely randomized design relies on randomization to control for the effects of extraneous variables. The experimenter assumes that, on averge, extraneous factors will affect treatment conditions equally; so any significant differences between conditions can fairly be attributed to the independent variable.

Randomized Block Design

With a randomized block design, the experimenter divides subjects into subgroups called blocks, such that the variability within blocks is less than the variability between blocks. Then, subjects within each block are randomly assigned to treatment conditions. Compared to a completely randomized design, this design reduces variability within treatment conditions and potential confounding, producing a better estimate of treatment effects.

The table below shows a randomized block design for a hypothetical medical experiment.

Gender	Treatment
	Placebo	Vaccine
Male	250	250
Female	250	250

Subjects are assigned to blocks, based on gender. Then, within each block, subjects are randomly assigned to treatments (either a placebo or a cold vaccine). For this design, 250 men get the placebo, 250 men get the vaccine, 250 women get the placebo, and 250 women get the vaccine.

It is known that men and women are physiologically different and react differently to medication. This design ensures that each treatment condition has an equal proportion of men and women. As a result, differences between treatment conditions cannot be attributed to gender. This randomized block design removes gender as a potential source of variability and as a potential confounding variable.

Reference 

http://stattrek.com/statistics/dictionary.aspx?definition=Completely%20randomized%20design