This cheat sheet compares completely randomized designs and randomized block designs in statistics experiments. Students need these designs to plan fair studies, reduce bias, and understand how treatment effects are estimated. It is especially useful when deciding whether subjects should be assigned all at once or first grouped by an important variable.
The goal is to help students recognize, describe, and choose an experimental design correctly.
In a completely randomized design, all experimental units are randomly assigned directly to treatments. In a randomized block design, units are first separated into blocks of similar units, then random assignment occurs within each block. Blocking is used when a variable is expected to affect the response but is not the main explanatory variable.
Both designs rely on random assignment so differences in response can be linked more confidently to the treatments.
Key Facts
- In a completely randomized design, every experimental unit is assigned to one treatment using random assignment across the whole group.
- In a randomized block design, experimental units are divided into blocks first, and treatments are randomly assigned within each block.
- A treatment is a specific condition or combination of conditions applied to experimental units.
- A block is a group of similar experimental units formed using a variable expected to affect the response.
- The basic treatment effect can be compared using a difference in means, such as .
- Blocking reduces unexplained variation by comparing treatments within similar groups instead of across the entire sample.
- Random assignment helps balance unknown variables across treatment groups and supports cause-and-effect conclusions.
- Use a randomized block design when a known variable, such as age, gender, skill level, or location, is likely to influence the response.
Vocabulary
- Experimental Unit
- An experimental unit is the individual person, animal, object, or plot of land that receives a treatment.
- Treatment
- A treatment is the condition or procedure applied to experimental units in an experiment.
- Completely Randomized Design
- A completely randomized design assigns all experimental units directly to treatment groups using random chance.
- Randomized Block Design
- A randomized block design groups similar experimental units into blocks before randomly assigning treatments within each block.
- Block
- A block is a group of experimental units that are similar in a way that may affect the response variable.
- Response Variable
- The response variable is the outcome measured after treatments are applied.
Common Mistakes to Avoid
- Calling any grouped experiment a block design is wrong because blocks must be formed using a variable expected to affect the response.
- Randomly choosing subjects but not randomly assigning treatments is wrong because random assignment is what helps justify cause-and-effect conclusions.
- Blocking after treatments are assigned is wrong because blocks must be created before random assignment within each block.
- Using a completely randomized design when strong natural groups exist can be inefficient because important variation may be left uncontrolled.
- Treating blocks as treatments is wrong because treatments are the conditions being tested, while blocks are used to organize similar units.
Practice Questions
- 1 A teacher has students and wants to compare two review methods. Describe a completely randomized design that assigns students to each method.
- 2 A medical study has patients, with under age and age or older. Describe a randomized block design using age group as the blocking variable.
- 3 In an experiment, the mean score for Treatment A is and the mean score for Treatment B is . Find the difference in means .
- 4 A researcher compares two fertilizers on farms in both dry and wet regions. Explain why region might be used as a blocking variable instead of using a completely randomized design.
Understanding Completely Randomized vs Block Design Reference
The main reason for choosing a design is control of variation. People, plants, machines, and locations rarely begin at the same baseline. A study of a new teaching method may include students with very different prior knowledge.
A study of fertilizer may use soil with different moisture and nutrients. If these differences are large, they can hide a real treatment effect or make a weak effect appear strong.
Good design tries to make the treatment groups comparable before outcomes are measured. This makes the final comparison more informative.
Blocking works best when the blocking variable is known before the experiment begins and has a clear connection to the response. For example, a coach testing two training plans might group athletes by current fitness level. Each fitness group receives both plans through random assignment.
The comparison is then made among athletes who started at similar levels. A school study might block by grade level because older students may have different reading skills.
A farm study might block by field section because one part of the field may get more sunlight. The block should be based on a meaningful source of difference, not a detail chosen after results are seen.
A block is not an extra treatment group. It is a way to organize fairer comparisons. Students often confuse the two because both create groups.
Treatments are the conditions being tested. Blocks describe existing similarities among experimental units. Another common mistake is assigning one treatment to one whole block.
If every advanced student gets one teaching method while every beginner gets another, skill level becomes mixed up with the method. The study cannot separate the effect of skill from the effect of the method. Each block needs random assignment to the treatments whenever possible.
Blocking has limits. Very small blocks may leave too few units receiving each treatment, which makes results unstable. Too many blocking variables can create many tiny groups and make random assignment difficult.
A variable that has little effect on the response may not be worth using for blocks. In some cases, a completely randomized design is more practical because the units are already quite similar or no important grouping variable is known.
When reading an experiment, pay attention to the experimental units, the response measured, the treatments applied, and the exact point where random assignment happened. These details show whether a cause and effect conclusion is justified and whether the design handled important differences fairly.