Cheating on electronic exams Use of Data Science

Suppose Students F1 and F2 cheated Student A – 93 average deserves A  B Student B – 85 average deserves B  C Student C – 77 average deserves C  F Student F1 – 99 average deserves F  A Student F2 – 96 average deserves F  A Suppose student F1 and F2 cheated. Deserve F’s but their grades show A and the teacher curves the course grades. For simplicity there are no +/- grades just A,B,C, and F

Cheating prior to a test. If a professor gives exams over and over semester after semester (or year after year), students can Makes copies of the exam. If professor gave correct answers in previous semesters, students save those answers. Have an expert answer the exam as best as possible and post the answered exam on the internet for all who need it. Post the previous exams on the internet with questions answered correctly for future students to have.

Cheating prior to a test - Solutions Professor can give many tests. Some contain questions from previous semesters Some contain only brand new questions. If students do extremely well on the tests where the answer key may be available to students from previous answered exams but do statistically worse on exams where the test questions are brand new (never appeared anywhere), then it would be obvious that the student is cheating.

True and False Exams Knowledge = (Grade – 50) * 2 Knowledge % Number Grade Letter Grade 100 A+ 90 95 A- 84 92 B 72 86 C- 64 82 F 50 75

True Story

Cheating during test During an exam where students can chat with each other during the test (in the classroom or in the bathroom or via cell phones etc.) and all the questions are identical, the students will give the same answers (correct and incorrect) to all questions.

True story Students answered a question with the same exact wrong answer, then crossed off that wrong answer, and gave the same exact new answer, which was also wrong. 28 out of 32 students did this

28 students gave 2 sets of identical wrong answers to the same question.

Detecting same answers The grader would have to notice that the same wrong answer is being given from a group of students. For example, if a grader grades 32 exams in order (1 to 32) and students 3, 16 and 27 submitted identical answers it may not be noticed being mixed in with so many other exams. Sometimes there are several graders for an exam and they would never notice it.

Cheating during online test During an online exam students are taking an exam anywhere in the world and can sit with each other, chat with each other during the test can submit the same answers. If the questions are identical, Data Science software can compare all exam answers of all students in seconds looking for exams where students submit identical (correct and incorrect) answers.

Statistical Significance Ex) if 2 students are asked 2 True or False questions and they both got question 1 correct and question 2 wrong, did they cheat? If you have 2 students who got one correct and one wrong, what is the probability that they would have the same exact answers? Answer 50%

Statistical Significance Ex) if 2 students are asked 14 True or False questions and they both get the same exact 11 questions correct and the same 3 wrong, did they cheat? Assume all questions are equally difficult. What is the probability they would have the same exact answers but didn’t cheat? Answer: 1∗2∗3 12∗13∗14 = 1 364 = 0.002747%

Birthday Paradox In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people

Statistical Significance Ex) if 200 students are asked 14 True or False questions and 23 student got 11 questions correct and the same 3 wrong. Of the 23 students, there is a pair of student whose answers matched identically, did those students cheat? What is the probability that they would have the same exact answers? Answer: 50% (See the birthday paradox) Enough to indict but not convict.

Statistical Significance Ex) if 200 students are asked 14 True or False questions and 23 student got the same 11 questions correct and the same 3 wrong. Of the 23 students there is a pair of student whose answers matched identically. Then give those 2 students another 14 question exam and again they both got the same exact 11 correct and 3 wrong. What is the probability they would have the same exact answers on both tests? Answer: same as finding 2 students with matching birthdays and asking both when is your mother’s birthday and the mothers also have matching birthdays. Enough to indict and convict. = 99.73% after indicting.

Probabilities 2 students take a True or False test and get the same exact correct and incorrect answers: Probability of hitting Powerball Jackpot = 3.42229781 E-9 Questions correct incorrect Probability 14 11 3 0.0027472 28 22 6 0.0000075474 48 40 8 3.18008 E-9 39 9 7.33865 E-10 72 69 1.75 E -5 66 7.41 E-10

What can/should a professor do? If 1 student cheats: University policy is the students gets a F in the course Student goes before the ethics board and possible expelled. What is 85% of the class is cheating (deserve F but average is A) Do nothing and curve good student’s grades down? Fail 85% of the class?