How long did I work? A psychologist wants to know if the difficulty of a task influences our estimate of how long we spend working at it. She designs two sets of mazes that subjects can work through on a computer. One set has easy mazes and the other has hard mazes. Subjects work until told to stop (after $6$ minutes, but subjects do not know this). They are then asked to estimate how long they worked. The psychologist has $30$ students available to serve as subjects.

(a) Describe an experiment using a completely randomized design to learn the effect of difficulty on estimated time.

(b) Describe a matched pairs experimental design using the same $30$ subjects.

(c) Which design would be more likely to detect a difference in the effects of the treatments?

Explain.

Number of students are $30$

The random assignment method assigns subjects to treatments based on chance. Before the treatments are applied, random assignment establishes treatment groups that are comparable (except for chance variance). In experiments, randomization and comparison combined prevent bias or systematic favoritism.

There are $30$ pupils in total.

There are two types of maze treatments: easy and challenging.

Assign a number between one and thirty pupils. Give 15 pupils an easy maze and the remaining 15 students tougher mazes. The results of the two therapy groups should then be compared.

Make $15$ slips and write a simple maze on each one. Similarly, make $15$ more slips and write a difficult maze on them. Now shuffle all of the slips and assign them to the pupils to choose from. Compare their times now.

Because it is controlling the differences among the $30$ participants, the matched pair is likely to detect the difference.