This lesson begins our discussion of randomized block experiments. The purpose of this lesson is to provide background knowledge that can help you decide whether a randomized block design is the right design for your study. Specifically, we will answer four questions:
We will explain how to analyze data from a randomized block experiment in the next lesson: Randomized Block Experiments: Data Analysis.
Note: The discussion in this lesson is confined to randomized block designs with independent groups. Randomized block designs with repeated measures involve some special issues, so we will discuss the repeated measures design in a future lesson.
In a randomized block experiment, a good blocking variable has four distinguishing characteristics:
A blocking variable is a potential nuisance variable - a source of undesired variation in the dependent variable. By explicitly including a blocking variable in an experiment, the experimenter can tease out nuisance effects and more clearly test treatment effects of interest.
Warning: If a blocking variable does not affect the dependent variable or if it is strongly related to an independent variable, a randomized block design may not be the best choice. Other designs may be more efficient.
Blocking is the technique used in a randomized block experiment to sort experimental units into homogeneous groups, called blocks. The goal of blocking is to create blocks such that dependent variable scores are more similar within blocks than across blocks.
For example, consider an experiment designed to test the effect of different teaching methods on academic performance. In this experiment, IQ is a potential nuisance variable. That is, even though the experimenter is primarily interested in the effect of teaching methods, academic performance will also be affected by student IQ.
To control for the unwanted effects of IQ, we might include IQ as a blocking variable in a randomized block experiment. We would assign students to blocks, such that students within the same block have the same (or similar) IQ's. By holding IQ constant within blocks, we can attribute within-block differences in academic performance to differences in teaching methods, rather than to differences in IQ.
A randomized block experiment with independent groups is distinguished by the following attributes:
The table below shows the layout for a typical randomized block experiment.
| T1 | T2 | T3 | T4 | |
|---|---|---|---|---|
| B1 | X1,1 | X1,2 | X1,3 | X1,4 |
| B2 | X2,1 | X2,2 | X2,3 | X2,4 |
| B3 | X3,1 | X3,2 | X3,3 | X3,4 |
| B4 | X4,1 | X4,2 | X4,3 | X4,4 |
| B5 | X5,1 | X5,2 | X5,3 | X5,4 |
In this experiment, there are five blocks ( Bi ) and four treatment levels ( Tj ). Dependent variable scores are represented by X i, j , where X i, j is the score for the subject in block i who received treatment j.
With respect to analysis of variance, a randomized block experiment with independent groups has advantages and disadvantages. Advantages include the following:
Disadvantages include the following:
Problem 1
Which, if any, of the following attributes does not describe a good blocking variable?
(A) It is included as a factor in the experiment.
(B) It is not of primary interest to the experimenter.
(C) It affects the dependent variable.
(D) It affects the independent variable.
(E) All of the attributes describe a good blocking variable.
Solution
The correct answer is (D).
A good blocking variable is not related to an independent variable. When the blocking variable and treatment variable are related, tests of treatment effects may be biased.
Problem 2
Why would an experimenter choose to use a randomized block design?
(A) To test the effect of a blocking variable on a dependent variable.
(B) To assess the interaction between a blocking variable and an independent variable.
(C) To control unwanted effects of a suspected nuisance variable.
(D) None of the above.
(E) All of the above.
Solution
The correct answer is (C).
The blocking variable is not of primary interest to an experimenter, so the experimenter would not choose a randomized block design to test the effect of a blocking variable. A randomized block design assumes that there is no interaction between a blocking variable and an independent variable, so the experimenter would not choose a randomized block design to test the interaction effect. A full factorial experiment would be a better choice to accomplish either of these objectives.
A blocking variable is a potential nuisance variable - a source of undesired variation in the dependent variable. By explicitly including a blocking variable in an experiment, the experimenter can tease out nuisance effects and more clearly test treatment effects of interest. Thus, an experimenter might choose a randomized block design to control unwanted effects of a suspected nuisance variable.
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