Probability plays a role in ALL statistical inference. Before we dive into this idea, we will investigate a real court case. In this case the prosecution used an argument based on probability (statistical inference), as well as an argument based only on data analysis (not statistical inference.)

Using inference to detect cheating?a real case

How can a prosecutor use data to detect cheating? The details of this case appeared in Chance magazine in 1991.

Overview of the case:

The Case:During an exam at a university in Florida in 1984, the proctor suspected that one student, whom we will call Student C, was copying answers from another student, whom we will call Student A. The proctor accused Student C of cheating, and the case went to the university's supreme court.

The Evidence:At the trial, the prosecution introduced evidence based on data. Here is the evidence: On the 16 questions missed by both Student A and Student C, 13 of the wrong answers were the same.

The Argument:The prosecutor used the data to draw an inference based on probability. He asked the question: Could 13 out of 16 matches be due to chance?

He argued that a match of 13 out of 16 was very unlikely with random guessing; therefore, there had to be another explanation besides chance, and the prosecutor said the explanation was cheating. Based on this evidence, Student C was found guilty of academic dishonesty.

The Role of Random Chance

Using Simulation to Produce a Probability Distribution

To decide if we agree with this argument, we need to determine if it would be unusual to get 13 matches on 16 questions by chance alone if students just guess. Let's assume that each question had four options: A, B, C, or D.

We use a computer program to randomly assign answers to each question, which mimics what happens when someone randomly guesses. Using software to imitate chance behavior is called simulation.

The table lists the 16 questions missed by both students and shows how each student answered the 16 questions. Answers with a check mark (

\f-00000000000 10000000 10000000 10000000 -00000 10000 O O 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 proportion_of matches to_Student A100 random answer sets 1025 random answer sets 250 200 150 CO800803080080030 100 50 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 proportion_of_matches proportion_of_matchesStudents' wrong answers, together with simulated random answers 16 Questions Student A's Student C's missed by wrong Random wrong Random Random both students answers answers #1 answers answers #2 answers #3 1 A Av B D Av 2 C B D A B 3 B BY By A By 4 B BY A C D B BY C C C D DV B B C D DV DV B B 8 C CV CV B B 9 B BY D BY A 10 C A CV B A 11 A Av Av C Av 12 B BY D BY A 13 B By BY BY BY 14 B BY D D By 15 D DV B C A 16 B A A D D