# Instructions

In this simulation, a group of students takes a test made up of 100 true/false questions. Each student knows the answers to a specific number of questions and guesses at the remaining. For simplicity, it is assumed that there is no partial knowledge and therefore a guess has a 0.5 chance of being correct. Students get one point for each question they answer correctly and lose one point for each question they answer incorrectly.

Students take two versions of the test. It is assumed that a given student knows the answers to exactly the same number of questions on both tests. This number is called the student's "true score." The student's scores on the the two tests will generally be different because the number of correct guesses will differ for the two tests.

Some test scores will be above the "true scores" and some will be below the true scores. If a student is correct on exactly half the questions he or she guesses on, the true score and the test score will be equal.

The two graphs shown when the simulation begins plot observed scores as a function of true scores for the two tests. For the upper figure, test scores that are above the "true score" are shown in blue ,test scores below the true score are shown in green, and scores that equal the true score are shown in magenta. The colors in the lower figure are based on scores on the first test. Therefore, if someone scored above their true score on the first test and below their true score on the second test, the data point for that person would be blue in both figures. In the upper figure, the point would be above the black diagonal line; in the lower figure the point would be below the line.

The default is for true scores to be sampled from a normal distribution with at mean of 60 and a standard deviation of 5. With a sample size of 1,000, the sample mean true score can be expected to be quite close to 60 (95 times out of 100 it should be be between 59.7 and 60.3). The expected score for an item that is guessed at is 0 since students are penalized by one point if they guess wrong. Therefore, the mean test scores should also be close to 60.

The simulation is designed to show the characteristics of a group selected on the basis of test scores. Drag the black horizontal bar at the bottom of the first figure upwards to set the criterion for selecting students. Only students as high or higher than the bar are selected.

The upper graph uses colors to show which students:

1. Had true scores above the cutoff, had good luck, and were selected (dark blue)
2. Had true scores below the cutoff, had good luck, and were selected (light blue).