Dr. Johnson conducted a research study in which he investigated the effect of three different methods of teaching mathematics to three different classes of fifth grade students. However, one of the classes had smarter students than the other two and as a result this class demonstrated the most improvement in their mathematics scores. In spite of this problem, he concluded that the method used to teach mathematics to this class of students was the most effective. In this experiment, the intellectual ability of the students in the various classes was:

Just a quick reminder: a dependent variable is what is being studied or researched. An independent variable is the factor that is introduced or changed in order to affect the dependent variable.

Extraneous variables are factors that may affect the results of a study. These variables may lead a researcher to think that there is indeed an association between the other variables in the study when, in fact, there is not. A type of extraneous variable is the confounding variable, which is connected to both, the dependent and the independent variable. A confounding variable affects the results of the study because it affects how the independent variable affects the dependent one.

In the study described in the question, the confounding variable is the intellectual ability of the students. If the students in a class are smarter than the others, their results will be different. As we can see, because they did better, Dr. Johnson concluded that his method was effective. However, that may not be true. They might have done better because of the fact they their intellectual ability was already better.