G O Wesolowsky Statistical Detection of Cheating on

G. O. Wesolowsky Statistical Detection of Cheating on Multiple Choice Exams: Software, Implementation, and Controversy George O. Wesolowsky Professor Emeritus of Management Science De Groote School of Business Mc. Master University, Hamilton. Ontario,

G. O. Wesolowsky Outline of this Presentation • Introduction: Cheating on multiple choice tests • How I got into this. • Outline of statistical detection methodology • Practical capabilities of SCheck • Common attitudes to detection and prevention • Recommendations

G. O. Wesolowsky Ideal* Writing Conditions * I have seen more than 30% cheating under such conditions

Less than Ideal Writing Conditions G. O. Wesolowsky http: //math. berkeley. edu/~ribet/113/

G. O. Wesolowsky Prevalence of MC Tests and Exams • 30% ? of marks in UG classes given through MC • At Mc. Gill (20000 undergrads) in the Fall Semester of 2002: Finals: 83 courses, 15072 students Midterms: 70+ courses, 14000 students

G. O. Wesolowsky How They Do It: Copying Sampler

G. O. Wesolowsky How They Do It: Types of Cheating not Resulting in Similar Responses I am an impostor Usually not vulnerable to statistical detection

G. O. Wesolowsky A guide to cheating during tests and examinations From Wikibooks, the open-content textbooks collection http: //en. wikibooks. org/wiki/A_guide_to_cheating_during_tests_and_examinations Contents [hide] 1 Preamble 1. 1 A few definitions to consider 1. 2 The rewards/dangers of cheating 1. 2. 1 Rationales of cheating 1. 2. 2 Rationales of prosecuting cheaters 1. 2. 3 Possible Penalties 2 General notes 3 Techniques 3. 1 Copying from a person 3. 1. 1 Application of codes 3. 2 Copying from a pre-written source 3. 2. 1 Directly from textbook/notes 3. 2. 2 Cheat Sheet 3. 3 Precautions 3. 4 Copying from a planted source 3. 5 Locating Cheating Material on the Web 3. 6 Test previewing

G. O. Wesolowsky Some Statistics (CAI) plagiarized text CAI Research Conducted By Don Mc. Cabe (Released In June, 2005) is typical of many studies: As part of CAI’s Assessment Project, almost 50, 000 undergraduates on more than 60 campuses have participated in a nationwide survey of academic integrity since the fall of 2002. The results were disturbing, provocative, and challenging. On most campuses, 70% of students admitted to some cheating. Close to one-quarter of the participating students admitted to serious test cheating in the past year and half admitted to one or more instances of serious cheating on written assignments. Faculty are reluctant to take action against suspected cheaters. In Assessment Project surveys involving almost 10, 000 faculty, 44% of those who were aware of student cheating in their course in the last three years, have never reported a student for cheating to the appropriate campus authority. Students suggest that cheating is higher in courses where it is well known that faculty members are likely to ignore cheating.

G. O. Wesolowsky One Method of Cheating Detection

Questionable Statistical Detection G. O. Wesolowsky It is not infrequent that instructors, when confronted by a suspected cheating situation, invent their own methodology on the spot. This is usually what I call ‘outlier methodology’. The basis is some way of using the number of wrong answers that two students have in common. It could be simply a count of such 'wrong matches', a proportion, a run length, a ratio with other counts, or a multivariate plot of such variables. The idea is to look for outliers and attribute them to cheating.

G. O. Wesolowsky Example Bonnie and Clyde engaged in suspicious behavior. A comparison of responses revealed: “Bonnie and Clyde are surprisingly similar; 23 matches out of 23 wrong. ”. . C. . . B. . . . . C. . . . BD. . . DB. A. . ABD. B. . A. . CB. . . . . ABAC. . A. . C http: //www. astro. washington. edu/fraser/multiple-choice-cheating. html . = correct Both chose C, which is wrong

G. O. Wesolowsky But then: The instructor wrote a program: “My script just returns any match that has a high percentage of matching errors (and sufficient errors to convince you that some thing's up!) “ “Holmes and Watson are surprisingly similar; 8 matches out of 11 wrong. ”. . . D. . . B. . . D. A. . . . BBA. . BD. B. . . CD. . BCC. . BB. . . DC. . CA. . D. EC. . . D. . . AD. . . B. DDAB. . A. AA. . CDB. AA. C. . . BDDBE. B. . Intuitive override: “ I had found by chance (Bonnie and Clyde), but what about the rest? It's very unlikely that Holmes and Watson were cheating, but I think it's likely that the others were”. This instructor then concluded that statistical detection is not really reliable. Bad statistical detection often discredits the good.

G. O. Wesolowsky Aside: A Better “quickie” Index • A better but not good simple index is the Harpp-Hogan index, which is the number of wrong matches divided by the number of differences. One is supposed to be suspicious when it is > 1. For Holmes and Watson this works out to 8/32.

G. O. Wesolowsky Problems with “Simple” Indices or combinations thereof • The value of the indices can depend in an unknown way on class size, number of questions, number of choices, etc. • They use very little information. Capability of students and difficulty of questions are often not incorporated • The risk of “false accusations” is not predictable • Many combinations of indices and plots are possible, and they may point in different directions.

G. O. Wesolowsky How I Got Into This • Request from an administrator • Two students were suspected in another course, how many exactly similar answers did they have in my course? • Probability tree diagrams • Checked the literature Wesolowsky G. O. (2000) "Detecting Excessive Similarity in Answers on Multiple Choice Exams", Journal of Applied Statistics, Vol. 27, 909 -921.

G. O. Wesolowsky pki match Probability correct pji Question i Probability of a match by students j and k on question I = sum of match probabilities Cond. probability wrong 1 - pki w 1 i 1 - pji w 1 i w 2 i w 3 i w 4 i match 1 - pki w 2 i match 1 - pki w 3 i match 1 - pki w 4 i match

G. O. Wesolowsky Assumptions • The probability that a student gets an answer right depends on the ability of the student and the difficulty of the question • The probability of a match on wrong questions depends on the ‘popularity’ of wrong answers • Independencies as implicit in the diagram

G. O. Wesolowsky But how to we estimate wli and pji ?

G. O. Wesolowsky depends on two things Above average student 1 Below average student Proportion of class that answered correctly on question i 0 1

G. O. Wesolowsky Finding cj = proportion of questions answered correctly by student j Find by solving

P value for each pair of students = probability of the observed number of matches or more G. O. Wesolowsky Question 1 M Question j Question q M Compound Binomial Distribution because the probability of a match is different on each question M

Example of SCheck Output G. O. Wesolowsky ** pair = 2 78 ** Harpp-Hogan stat = #wr. mat/#diff = 19. 00 ################################# Zb = 7. 891 'equivalent' z from the BVP model Significance of Zb on a pre-selected pair = 1. 5 E-15 Significance bound (Bonferroni) on program selected pairs = 1. 3 E-11 #matches = 33 | 34 (mu, s)=( 11. 410, 2. 689) prop. right for 2 = 0. 441 prop. right for 78 = 0. 412 Quest. range = [ 1 34 ] #students = 132 --------------------------------. d. abccd. e. e. abedb. . . da. . b. . ea. e -------------------------------. d. abccdee. e. abedb. . . da. . b. . ea. e --------------------------------estimated match probabilities: 0. 423 0. 357 0. 360 0. 324 0. 367 0. 376 0. 232 0. 285 0. 316 0. 237 0. 236 0. 369 0. 283 0. 249 0. 423 0. 254 0. 321 0. 255 0. 483 0. 696 0. 310 0. 371 0. 238 0. 345 0. 536 0. 258 0. 211 0. 460 0. 290 0. 224 0. 326 0. 388 0. 231

G. O. Wesolowsky Data Dredging • The number of student pairs examined is n(n-1)/2. • For 693 students this is 239, 778 pairs suspicious

G. O. Wesolowsky “Unusual” Z’s Depend on Class Size Class size No. of pairs P(Zmax >3) P(Zmax >4) P(Zmax >5) P(Zmax >6) 2 1 0. 00135 3. 167 E-5 2. 8665 E-7 9. 8659 E-10 100 4950 0. 99875 . 145104 . 0014179 4. 8836 E-6 400 79800 1. 00000 . 920134 . 0226151 7. 87297 E-5 1000 499500 1. 00000 . 1334040 . 0004928 5000 12497500 1. 00000 . 9721919 . 0122542

G. O. Wesolowsky Multiply the Pvalue by n(n-1)/2 ** pair = 2 78 ** Harpp-Hogan stat = #wr. mat/#diff = 19. 00 ################################# Zb = 7. 891 'equivalent' z from the BVP model Significance of Zb on a pre-selected pair = 1. 5 E-15 Significance bound (Bonferroni) on program selected pairs = 1. 3 E-11 #matches = 33 | 34 (mu, s)=( 11. 410, 2. 689) prop. right for 2 = 0. 441 prop. right for 78 = 0. 412 Quest. range = [ 1 34 ] #students = 132 A similarity this unusual will occur --------------------------------. d. abccd. e. e. abedb. . . da. . b. . ea. e at most 1. 3 times, on the average, -------------------------------per 100 billion classes. . d. abccdee. e. abedb. . . da. . b. . ea. e --------------------------------estimated match probabilities: 0. 423 0. 357 0. 360 0. 324 0. 367 0. 376 0. 232 0. 285 0. 316 0. 237 0. 236 0. 369 0. 283 0. 249 0. 423 0. 254 0. 321 0. 255 0. 483 0. 696 0. 310 0. 371 0. 238 0. 345 0. 536 0. 258 0. 211 0. 460 0. 290 0. 224 0. 326 0. 388 0. 231

G. O. Wesolowsky Important! • The significance (probability that a similarity that high will occur for an innocent pair) is different for a pair that is pre-selected by, say, suspicious behavior, from that of a pair that was selected purely by the program. In other words, the former case does not need as high a level of similarity evidence. Scheck, therefore, allows pre-selected pairs to be forced into the analysis

Features of SCheck G. O. Wesolowsky Developed from experience with large scale testing, research into cheating psychology, tribunal cases, different data formats, etc. • Up to 30000 students • Up to 200 questions • Up to 27 choices, numbers or letters • True or false or multiple choice in any combination • Select a contiguous block of questions • Option for pre-selected student pairs • Option for similarity scores for all students • Options for removing student identification from input and output files • New: Two Type I methods for setting cutoffs • Adjustment for “speed tests” • Interactive or stored option choice • Batch processing of multiple files • Optional Excel grades output • Files with all components necessary for verification of calculations • Diagnostic graph • Optional fine tuning (T parameter) • Compact and intuitive question diagnostics • Utility programs (format translators)

G. O. Wesolowsky

G. O. Wesolowsky

G. O. Wesolowsky

G. O. Wesolowsky

G. O. Wesolowsky This box and the previous one allow selection of a block of questions. Useful if, say, some questions only gather information.

G. O. Wesolowsky

G. O. Wesolowsky

G. O. Wesolowsky This forces suspect pairs into the output for analysis.

G. O. Wesolowsky

G. O. Wesolowsky

G. O. Wesolowsky

G. O. Wesolowsky • Vertical red line indicates similarity cutoff. Position depends on class size • Straightness = normality • Slope indicates stdev of Z’s • Innocent class is symmetrical within the lines

G. O. Wesolowsky

Forced pairs in NAM file G. O. Wesolowsky

G. O. Wesolowsky Forced pairs in OUT file

G. O. Wesolowsky Diagnostics on questions

It’s Cheating time G. O. Wesolowsky

G. O. Wesolowsky Detected Pairs Summary of significances of identified pairs -------------------pair Z A Priori Bonferroni Signif. --------------------2, 78 7. 891 1. 5 E-15 1. 3 E-11 2, 97 7. 428 5. 5 E-14 4. 8 E-10 36, 69 6. 253 2. 0 E-10 1. 7 E-6 36, 70 4. 755 9. 9 E-7 8. 5 E-3 36, 72 5. 514 1. 8 E-8 1. 5 E-4 60, 119 4. 931 4. 1 E-7 3. 5 E-3 69, 70 6. 527 3. 3 E-11 2. 9 E-7 69, 72 5. 474 2. 2 E-8 1. 9 E-4 70, 72 6. 527 3. 3 E-11 2. 9 E-7 78, 97 7. 067 7. 9 E-13 6. 9 E-9 -------------------- All pairs were found in adjacent seating

G. O. Wesolowsky 36 2 60 69 78 119 70 97 72 132 students teamwork

G. O. Wesolowsky Have you ever seen anything like it? (Contact at a testing agency)

G. O. Wesolowsky Pair Z 16, 39 16, 41 16, 42 16, 44 16, 46 16, 50 16, 65 39, 41 39, 42 39, 43 39, 44 39, 46 39, 50 39, 57 39, 64 39, 65 39, 69 41, 42 41, 43 41, 44 6. 453 5. 453 6. 090 5. 051 5. 089 5. 074 5. 837 7. 385 8. 178 6. 196 6. 061 6. 916 6. 878 5. 662 5. 896 7. 887 5. 515 6. 958 5. 515 5. 043 41, 46 41, 50 41, 57 41, 64 41, 65 42, 43 42, 44 42, 46 42, 50 42, 57 42, 64 42, 65 42, 69 43, 46 43, 64 43, 65 44, 46 44, 50 44, 64 44, 65 6. 196 5. 811 5. 011 4. 907 6. 745 5. 786 5. 614 7. 236 7. 190 5. 293 6. 183 7. 458 5. 786 5. 386 5. 118 5. 660 5. 176 5. 083 4. 941 5. 590 Pair 46, 50 46, 57 46, 64 46, 65 46, 69 49, 65 50, 57 50, 64 50, 65 57, 65 64, 65 65, 69 82, 87 82, 109 82, 110 86, 92 87, 109 87, 110 91, 93 91, 100 Z Pair Z 6. 013 4. 933 5. 786 6. 337 5. 055 4. 964 4. 900 5. 737 6. 314 5. 106 6. 021 5. 660 8. 456 7. 750 8. 945 6. 381 7. 375 8. 456 5. 896 7. 385 91, 107 93, 100 93, 107 100, 107 109, 110 113, 117 113, 119 113, 124 113, 137 117, 119 118, 138 120, 122 120, 124 120, 137 120, 141 122, 137 122, 141 124, 137 7. 385 6. 592 8. 716 7. 750 5. 328 6. 013 5. 386 5. 515 7. 062 8. 415 6. 319 5. 257 7. 054 5. 345 5. 664 7. 419 5. 185

G. O. Wesolowsky Really enthusiastic teamwork! 82 16 49 39 113 87 117 109 50 57 42 86 64 43 92 91 69 46 120 122 124 118 137 65 44 119 110 41 109 141 93 100 107 35 suspects, 79 pairs, 200 students

G. O. Wesolowsky A NEW OPTION SCheck Version 8 a 7. #### 03 -05 -2009 11: 21: 34 Bonferroni program selected significance bound is 0. 01 _______________________________ ** pair = 48 188 ** Harpp-Hogan stat = #wr. mat/#diff = 2. 12 ################################# Zb = 5. 211 'equivalent' z from the BVP model Significance of Zb on a pre-selected pair = 9. 4 E-8 Approximate significance of program selected pair = 3. 7 E-5 Signif. bound (Bonferroni) on program selected pairs = 5. 6 E-3 #matches = 42 | 50 (mu, s)=( 24. 832, 3. 318) prop. right for 48 = 0. 540 prop. right for 188 = 0. 580 Quest. range = [ 1 50 ] NRT = 1. 00 #students = 348 --------------------------------. b. b. . . aa. a. baa. . . cb. . b. c. e. aad. e. . . b. a. b -------------------------------- . b. b. . . aa. a. baa. . . cbb. b. c. . . d. . ce. . . b. . . a --------------------------------estimated match probabilities: 0. 502 0. 542 0. 530 0. 616 0. 558 0. 679 0. 571 0. 499 0. 566 0. 747 0. 568 0. 613 0. 499 0. 536 0. 635 0. 552 0. 652 0. 577 0. 639 0. 609 1. 000 0. 597 0. 253 0. 434 0. 278 0. 555 0. 383 0. 405 0. 524 0. 422 0. 674 0. 297 0. 289 0. 231 0. 429 0. 225 0. 211 0. 661 0. 453 0. 270 0. 825 0. 219 0. 585 0. 705 0. 433 0. 257 0. 562 0. 217 0. 451 0. 295

G. O. Wesolowsky History of Applications • • Early studies for economics department For individual instructors Large assessment organizations National education departments “This is the only instance where separate examination venues have shown up and I have used your analysis on probably about 30, 000 candidates. ”

G. O. Wesolowsky Dallas Morning News Study on Cheating on the TAKS test (June 2007), an Application of SCheck DMN: “ The test scores of more than 50, 000 students show evidence of cheating. Some of those students were the innocent victims of others copying their answers. But experts say most were likely either deliberately copying answers or had their answer sheets doctored by school staff. “ TEA response “Officials at the Texas Education Agency have consistently argued that statistical analysis can't prove cheating and that they must rely on other forms of evidence – like getting teachers to confess to misbehavior – in their investigations. TEA decided not to use data drawn from student answer sheets – even with evidence of widespread copying in a classroom. “

G. O. Wesolowsky Common Objections: We studied together, we are from a similar background, we are twins, etc. Some direct studies have been done. Note that a huge number of pairs is being looked at. 1. We would expect that there would be a large number of highly similar pairs that couldn’t have cheated 2. Would expect that if prevention is implemented the high similarity rate would continue

G. O. Wesolowsky Both expectations have been proven false in thousands of data sets. Prior to electronic cheating methods, no very high similarities lacking the opportunity to cheat (adjacent seating) were found. Multiple versions of exams cause a drastic decrease in the cheating rate.

G. O. Wesolowsky Pitfalls in interpretation • • • High marks make detection difficult* Non-responses can invalidate the model Cheating must be substantial for detection Too much cheating can invalidate the model Hierarchical questions violate assumptions Data sets may be too small *In the extreme, if one student copies from another with a perfect test, there is no way statistical detection can distinguish this case from the case of two brilliant students with perfect papers. Scheck knows this.

G. O. Wesolowsky Effective Prevention Measures • Multiple versions • Randomized or assigned seating • • Seat spacing Invigilation Electronic counter-measures “Education on integrity” & ethics indoctrination

G. O. Wesolowsky December 2002 exams Mc. Gill University. Proper prevention measures are in place. finals midterms 2 17

G. O. Wesolowsky End Part 1

G. O. Wesolowsky Multiple choice tests provide a substantial component of grades in undergraduate courses. Statistical detection of copying or collusion on such tests has proven to be quite successful, and has in turn demonstrated that simple and non-intrusive prevention measures are very effective. Why then is this subject conspicuously absent in most discussions on cheating prevention strategies?

G. O. Wesolowsky The most common general attitudes of student leaders, instructors, and administrators towards cheating are remarkably similar See no Evil, Hear no Evil, Speak no Evil

G. O. Wesolowsky Comments • A “look the other way” strategy is actually the best one if the goal is to protect the integrity reputation of a university • Why? Media assume that the cheating problem is proportional to the number of reported cases or the amount of discussion about cheating. Keeping quiet, therefore, creates the impression that there is no problem. • A university that tries to do something about cheating often gets a reputation for being infested with cheating. (Otherwise, why would they talk about it? )

G. O. Wesolowsky Instructor Attitudes Instructor: Not on my tests you won’t!

#1 G. O. Wesolowsky

G. O. Wesolowsky #2

Instructor: I’m not a Policeman or Prison Guard, I’m an Educator and Researcher G. O. Wesolowsky Translation: I am not going to charge any students with cheating or take any special prevention measures This sounds idealistic and has the added benefit of saving a lot of work and avoiding unpleasant confrontations

G. O. Wesolowsky Comments • Implicit assumption: The university’s main function is to provide an education and grades are merely an unimportant side-issue. • I disagree: The main product of a university is grades and degrees and diplomas. Without these, even if it continued to give a good education, the university would be out of business overnight. On the other hand, degrees without education (diploma mills) are a growing phenomenon. http: //chronicle. com/free/v 50/i 42/42 a 00901. htm • The assumption of a degree is that a required level of academic achievement has been met. Grades and degrees without this level of achievement are defective. • By giving degrees with based on defective grades it is giving the public a defective product.

G. O. Wesolowsky Postscript: Education versus Grades By JANE ARMSTRONG Friday, January 27, 2006 Posted at 5: 20 AM EST From Friday's Globe and Mail “Professor David Weale called it a "January clearance" -- and clear out they did. Dismayed by his crowded classroom, the history teacher at the University of Prince Edward Island offered his students a deal some couldn't resist: Drop this Christianity class and you'll get a B minus. “ “The offer, also dubbed the "Weale deal" worked. The next week, about 20 of the 95 students were gone. So too is Prof. Weale after shocked administrators caught wind of the unorthodox academic transaction. ”

G. O. Wesolowsky Addendum “Vice-president Gary Bradshaw said the school had no choice but to suspend Prof. Weale while a disciplinary probe begins. Offering students a credit without doing the work "strikes at the very heart of the academic principles, " Mr. Bradshaw said. ” • The next week, he sweetened the offer, saying he'd give students who left a mark of 68. Students mulled it over during the break and negotiated the deal up to 70, which is a B minus. Departing students were required to send Prof. Weale an e-mail and pay the $450 for the course.

G. O. Wesolowsky Student Leaders and Instructors

G. O. Wesolowsky Student Leaders and Instructors: A Matter of Trust* Student Leader: “If you take prevention measures you show you don’t trust us and that cheating is expected. This will only increase cheating. Anyway, cheating is very rare. ” Translation: My constituency would feel threatened. Instructor: “Cheating prevention and detection poisons the atmosphere and destroys the vital rapport and atmosphere of trust I have with my students” Translation: My teaching evaluations would go down. *paraphrased

G. O. Wesolowsky Administration

G. O. Wesolowsky Administration: The Best Solution is ‘Ethics Reengineering’ “E-tegrity board members, …, have developed a range of new initiatives to integrate integrity into the college’s culture. ” “… suggest a more broadly focused approach that creates an educational community valuing academic integrity and focusing on the moral and ethical development of students” Sounds good and plays well in the media. Often arises out of bad publicity on cheating incidents. 1) Will it work if it is seriously implemented? Mc. Cabe versus the economists http: //www. arts. ubc. ca/Why_Students_Cheat. 116. 0. html 2) Will it ever be implemented beyond the talk level? Web pages, articles in school newsletters, “integrity officers”, inviting Mc. Cabe. Usual outcomes: a) effort fades away b) majority of students and instructors are not involved. 3) Contrast this with prevention measures on MC tests, which have been shown to virtually eliminate cheating.

G. O. Wesolowsky Comments on Honor Codes

G. O. Wesolowsky Honor Codes* Traditional Honor Codes • Pledge and ceremonies • Proctoring of tests not allowed • Students in charge of tribunals • Students obliged to report infractions (rarely enforced) Modified Honor Codes • Proctoring allowed *Mc. Cabe

G. O. Wesolowsky Quote on Honor codes In this same study that found over 75 percent of students admitting to cheating, Mc. Cabe saw that only 57 percent of students cheated at schools with honor codes. Chronic cheating also seems to reduce with honor codes. At schools without codes, 1 in 5 students admits to cheating more than twice. Only 1 in 16 students admits to the same offense at schools with honor codes. "I think it's a question of making your students understand that academic integrity is important to the school, " Mc. Cabe said. "Just the fact that it's being discussed" can heighten student's awareness and reduce cheating, he concluded.

G. O. Wesolowsky Do Honor Codes Work? Comments • ? Only? 57% • Response bias: ‘Honor’ rhetoric leads to fewer admissions of cheating? Fear of Draconian penalties? • Control for other variables: Types of exams, subject matter etc. • Low response rates → non-response bias “it is clear the response rate is below desired levels, averaging between 10% and 15% and varying from as little as 5% to 10% on some large varying from as little as 5% to 10% campuses to over 50% on a limited number of small, residential campuses” http: //www. ojs. unisa. edu. au/journals/index. php/IJEI/article/view. File/14/9

G. O. Wesolowsky Advantages of Honor Codes • Media friendly • Reduce the number of reported cases of dishonesty Disadvantages of Honor Codes?

G. O. Wesolowsky

G. O. Wesolowsky

G. O. Wesolowsky Recommendations* • Make statistical testing (even without identifying the students involved) a non-optional part of the scanning report. • Institute mandatory or strongly “encouraged” prevention measures: multiple versions, assigned seating, electronic counter-measures, etc. . • As a last and least important step, use statistical testing to support charges of academic dishonesty. In other words, use it this way only after the cheating is cleaned up. Observation: Statistical evidence is very unlikely to be sufficient by itself. Other evidence, such as a proctor’s observations, will be required to make charges stick. * Plan is plagiarized from Mc. Gill

G. O. Wesolowsky End