Units of Study

Finally, in addition to ambiguities in what constitutes a ``treatment'' and which treatments should be administered, there may be substantial ambiguity about what constitues a ``unit of study'' in an experiment or observational study.

The ``units of study'' are the rows in the Y vector and X matrix in the matrix form of the regression equations.

Example.

In a study of a new method of teaching mathematics, school district officials were able to get 60 students in each of nine schools to participate. In each school, 30 children were randomly assigned to the ``current'' method, and 30 were assigned to the ``new'' method. Three teachers taught three classes each of the ``current'' method classes , and three more taught three classes each of the ``new'' method classes.

In the example, children participated in the study, with 270 children experiencing each teaching method. We might think of these children as the experimental units. However,

• Because the children interact with one another in the classroom (in both methods), their responses to the end-of-semester test will be dependent on one another within each classroom (even if no one cheats on the exam!). Thus perhaps we should think of the classrooms as the experimental units; now there are only 9 units in the ``current'' method and 9 units in the ``new'' method.
• Finally, perhaps the teacher also has an influence on the outcome of the students; then all the children who have the same teacher will have dependent responses, so perhaps classes within teacher should be the units of study; now there are only 3 units in the ``current'' method, and 3 units in the ``new'' method.

Nevertheless, identifying and clearly stating what the units of study are is an important point in both communication and in understanding what the data are telling us.