PCRM - Cheating

                                                       Chapter 26

Experience during the past few years with multiple-choice tests scored by only counting right marks has made it clear that cheating occurs at all levels from student to state house. The usual method for detecting this activity is to compare observations with probabilistic models. The down side of this approach is that the models are generally too simplistic to match the real world. Also, school administrators value “catching them in the act” (a very difficulty thing to do) far more than “statistics” applied to individual students.

An alternative is to make use of the information content in each student answer string. Answer strings can be matched by collating, filtering and sorting. Presumptive cheating is then a marked departure from the class norm. Confirmed cheating usually requires additional information that is accepted by students and administrators.

The PUP copy detector shows a suspect pair on Part 1&2 involving student 11 and 29 with a standardized index (Z) value of 3, a marginal level of detection. This individual pairing shows a string of 14 identical marks followed by strings of 2 and 7 identical marks. This is presumptive cheating.

The student counseling matrixes show identical strings within unfinished (-A@D@EE-) and within misconception and guessing (D@EE-A). No other of the fifty students marked in this fashion. Question 9 was flagged by Ministep as most unexpected right. Only two students with the lowest scores shared this classification.

I would not call this a confirmed case of copying, as six of the seven identical pairs were non-critical, that is the identical wrong marks were too common on the test. In my judgment, this pair did not fail the test for independent marking. Failure would require additional information. There is also no noticeable marked departure from the class norm.

A record of presumptive cheating is easy to keep on mark matrixes sorted by student ID and question number, PUP 3b, or by score and difficulty, PUP 3c. Answer sheets were coded with three spaces each, for test number and seat number. Students filled in their three-digit student number. This information generally permitted confirming cheating, without resorting to multiple test forms (a negative, time wasting, procedure). Relying on their written record (answer sheets), just as scientists do, modeled the ethics of science as these students explored and developed their ability and desire to make sense of biological literature for the rest of their lives. (On the Internet, it is even more important to have formed the habit of questioning and confirming the information encountered.) 

The most successful classroom policy I used to manage copying was to clearly state that answer sheets would be checked for cheating to protect honest students. Any answer sheet that failed the check would receive a score of zero. I would help any student who wanted to protest this decision to student affairs (no student every protested, which was, in itself, a further confirmation of cheating). Two students were detected twice over a nine-year period. They readily admitted copying but were both unhappy with themselves over finding their “fool proof” methods in other courses did not work here.

PCRM - Guessing

                                                              Chapter 25

The Rasch model does not include guessing. This does not make it go away. Multiple-choice, by design, has a built in average random guessing score of one part for the printed set of answer options. Active scoring starts at 25% for 4-option questions scored by counting right marks. This scores and rewards the lowest levels of thinking. Active scoring starts at 50% for Knowledge and Judgment Scoring where higher levels of thinking are assessed and rewarded. If a student elects to mark all questions, both methods of scoring, included in PUP, yield the same score. The two methods of scoring respond the same to guessing.

Knowledge and Judgment Scoring, however, gives students the responsibility to learn and to report what they trust they know and can do. It is one form of “student-centered” instruction. This is critical in developing high quality self-correcting students, and as a result, high scoring students.

Five guessing items were found on Part 1&2 and six on Part 3&4 of the biology fall 88 test. These are items that fewer students, than the average score on the test, elected to mark, but less than that portion who marked, were right. A few students believed they knew but they did not know.  

The four [unfinished] items on Part 3&4 were also among the six guessing items. Most of the Ministep “most unexpected right responses” (dark blue) occurred on these items on Part 1&2 and 3&4. Are they guessing (chance or good luck) or just marking error that also occurs among the other groups of items?

Assuming that the most unexpected responses involve carelessness, guessing, and marking error, these then play a small part in determining a student’s score. The rate tends to increase as student performance decreases. Many unexpected wrong and right answers tend to occur in pairs. One cancels the effect of the other. Only consistent analysis is required to obtain comparable results.

If I interpret the above correctly, the partial credit Rasch model (PCRM) can ignore guessing in estimating person and item measures. However, a teacher or administrator cannot ignore the active starting score of a multiple-choice test in setting cut scores. A cut score set a few points above the range of random guessing is a bogus passing standard even if the test contains “difficult” items.

PCRM - Misconception

                                                                 Chapter 24

Knowledge and Judgment Scoring allows students the option of reporting what, in their own judgment, they know, can do, and find meaningful and useful. This generates four options instead of the usual two (right and wrong) obtained from multiple-choice items by the traditional count of right marks.

A misconception is a question that most students believe they know a right answer to, and mark, when in fact they do not know (more students, than the average score on the test, elected to mark, but less than that portion who marked, were right). Only one item was flagged as a misconception, item 6, on both halves of the biology fall 88 test. This can be compared to four on an earlier test.

Top students who rushed through the test marked “A” as a “most unexpected wrong response” on item 6 on Part 1&2. Other students gave a mixed response on Part 1&2. Only two top students who took their time marked “A” on Part 3&4. Most of the remaining students marked “A” wrong on Part 3&4. This observation gives rise to several stories.

Did top students in a hurry pick the same answer as lower scoring students who took their time? Did students functioning at higher levels of thinking and taking their time reason out the correct answer?  Is this just sampling error?

Misconceptions make for good class discussions. Lectures seem to have little effect on changing student misconceptions. One misconception question repeated in several bi-weekly exams stabilized by most students omitting. The one thing they did know was that they did not understand something that would allow them to trust marking an answer to the question correctly (nor did they have in mind a meaningless right answer that matched an option on the question as the answer options were not always the same and were always randomized).

The combined report from Ministep and PUP opens a new window of inquiry into the behavior of students and test items. In my experience, these student-counseling matrixes provided a better insight into how a class and students were performing than reading “blue book” essays. Winsteps adds predictive measures to otherwise descriptive classroom data.

  

PCRM - Item Discrimination

                                                              Chapter 23

Item discrimination identifies the items that separate a group of students that know and can do from a group that cannot. The Rasch model identifies the estimated measure at which students with an ability that matches the item difficulty will make a right mark 50% of the time. Item discrimination is not a part of the partial credit Rasch model (PCRM), however, Winsteps and PUP both print out the point biserial r (pbr) that estimates item discrimination.

About 10 discriminating items are needed in a classroom test to produce a good range of scores with which to set grades. The two halves of the biology fall 88 test (Part 1&2 and 3&4) show 11 and 16 discriminating items in PUP Table 7. All 11 discriminating items in Part 1&2 are found among the 16 in Part 3&4 (average pbr of 0.29 and 0.33, and average alpha of 0.62 and 0.77). A test composed of 50 items with this discrimination ability is expected to have an average alpha of 0.92. This puts it into a standardized test range of test reliability. A practical standardized test uses fewer items with more discrimination ability.

Dropping down from averages of groups of items and students to individual items and students restricts the validity of PUP Table 3a printouts to descriptive statistics for each test. (The Rasch model printouts from Ministep for individual estimated person and item measures are valid predictions as well as descriptions.)  What needs to be re-taught and what can students do to correct their errors?

A teacher can mix students who marked discriminating items correctly with a set of students who did not know, or marked wrong, to sort out their errors. This is in contrast to an unfinished item. Here is a problem in instruction, learning, and/or assessment. Here the teacher must take the lead. These are the only items I reviewed in a class that promoted the use of higher levels of thinking by way of Knowledge and Judgment Scoring.

End of course standardized tests scored at the lowest levels of thinking (only counting right marks) have only one valid use, ranking. There is no way for current students to benefit from the testing. New designs for 2011 will use “through-course” assessment. Even in low level of thinking environments there is time for meaningful corrections at the individual student and classroom levels. One plan (August 2010) spaces parts of the test evenly through the course, the other spaces parts over the last 12 weeks of the course.

Neither plan replaces the good teaching practice of periodic assessment in such detail that students cannot fall so far behind that they cannot catch up with the class. Self-correcting students find the student counseling matrixes helpful. Most of these biology students were functioning at and above an 80% right high-quality score by the end of the semester. 

PCRM - Stability

Next     Back    Start                        Chapter 22

Data stability has a different meaning for classroom tests and standardized tests. Standardized tests seek predictive statistics based on more than 300 answer sheets. Classroom tests seek descriptive statistics based on 20 to 50 answer sheets. Standardized tests need to find the fewest questions that will produce the desired test reliability. Classroom tests need to find a rank for grading (summative assessment) or to reveal what each student knows and needs to know to be successful in the current instructional environment (in a formative-assessment process). 

If the instructional environment is functioning at lower levels of thinking, the test must be given shortly after training to expect the highest scores. If functioning at higher levels of thinking, meaningful test results must be returned to the student shortly after the test to develop the highest scoring performance. Both timing and level of thinking influence data stability.

A bi-weekly general studies remedial biology course test with 100 students has been divided into four parts. This is roughly 25 answer sheets turned in after 20, 30, 40 and 50 minutes (Part 1, 2, 3, and 4). 

Two 50-answer-sheet groups are labeled Part 1&2 and 3&4 (download answer files below). 

The four Ministep bubble charts show Part 1, 3, and 4 to be very similar. Part 2 has measures with larger bubbles, lower reliability. When 25-answer-sheet files were combined into 50-answer-sheet files, the bubbles, in general, shrank, reliability increased. Items 19 and 20, 100% right, were edited into the Part 1, 2, and 1&2 charts as the Rasch model ignores all right and all wrong responses.  

  

Scatter plots between Part 1&2 and 3&4 show practical stability for classroom descriptive results for both item scores (percent right) and item measures with two exceptions. Items 12 and 23 measures are outliers. The first received only right and omit marks; the second only unexpected wrong and omit marks. 

PUP descriptive statistics show that the bubble chart for Part 2 had the lowest item discrimination (0.28 pbr) of the four parts. This low item discrimination resulted in the lowest test reliability (0.47 alpha) for the four parts. This effect then carried over into Part 1&2 (0.29 pbr discrimination and 0.62 alpha test reliability). 

Winstep item measures reliability (0.91) was identical for Part 1&2 and 3&4 even though the person measures reliability varied from 0.55 to 0.71. Here is the evidence, in part, that, “Rasch measures represent a person’s ability as independent of the specific items, and item difficulty as independent of specific samples within standard error estimates.” (Bond & Fox, 2007, page 280)

Next    Back    Start                   Answer Files: 1&2 PUP, Winsteps; 3&4 PUP, Winsteps

Partial Credit Rasch Model

Next     Back    Start                        Chapter 21

The bubble charts for the nursing school test, used in the first 20 posts, and for a general studies biology test are strikingly different. The nursing test had a cut score of 75%, was right count scored, and only three of the 24 students failed. The biology test had a cut score of 60%, was knowledge and judgment scored, and only one of the 24 students passed.

 

The active starting score on the nursing test was set at zero with one point for right and zero for omit and wrong. The active starting score for the biology test was set at 50% (knowledge, and the judgment to use that knowledge, had equal value) with one point for right, ½ point for omit, and zero for wrong. (Partial credit analysis used 2, 1, and 0.)

The averages scores were 84% for nursing and 50% for biology. Nursing students were preparing for a licensure test. Remedial course biology students only needed credit for the course. (It is customary for these freshman students to take this first test without studying to determine if attending lecture will suffice, a case of high school lag.)

The overfit students (1 and 8, for example) tended to omit (good judgment to not make a wrong mark) more than other students. The underfit students (17 and 24, for example) tended to not use good judgment (GJ) as often as other students.

Winsteps flagged four of the six omits on item 24 as unexpected. Rasch model analysis provides an indication of students omitting when the odds were more in favor of getting a right answer than a wrong answer, 4/576, or less than 1% of the time. This rate is less than the average marking error on paper tests.

Only two students, with test scores of 56.3% and 64.6%, are predicted to pass the biology course on PUP Table 3a. Neither student earned scores of 70% or higher (cut score plus one letter grade when using right count scoring). Instead both students demonstrated their ability to use what they knew with quality scores of 100% and 73%.

Ministep estimates the person ability of 21000053 (21) and 25000059 (25) at 0.17 measures. PUP test scores for both are 56.3%. Student 21 may pass because of a quality score of 100%. Student 25 is predicted to fail because of a quality score of only 60%. The quality score was used to break ties in the annual NWMSU Science Olympiad.

PUP Table 3 EGMD makes a selection more interesting. This table of student judgment is unique to Knowledge and Judgment Scoring. It guides students along the path from passive pupil to self-motivated high achiever (average quality score of 90%, always above 80%). Students 21 and 25 differ markedly among the four categories of items. Student 21 unexpectedly marked a misconception right. Student 25 marked three of the four misconceptions wrong. Student 21 omitted all three discriminating items, but student 25 marked all three right. These descriptive data, at the individual level, can yield many stories with unknown reliability. Reliability comes with repeated performance.

Partial credit Rasch model analysis and Knowledge and Judgment Scoring together produce a more meaningful and easy to use classroom and proficiency report than either alone. Caveat: This small sample size was used for illustrative purposes.

Next    Back    Start                        Download BioSci2a.txt, Winsteps;  BioSci2a.ans, PUP

Scaled Scores

Next     Back    Start                        Chapter 20

A variety of ways has evolved to report standardized test results with the “Lake Wobegon” goal of all schools being above average or improving each year: percent right score, ranked score, scaled score, standardized scaled score, and percent improvement.

The percent right score is the number of right marks divided by the number of questions on the test. It cannot be manipulated, however, Ministep calculates the number of right marks divided by the total number of marks when estimating student ability and item difficulty measures. 

Ranked scores are obtained by sorting right mark scores.

Scaled scores are positive and arbitrary. In general, the central scaled score corresponds to zero logits. Scaling involves a multiplier and a constant. A logit scale running from -5 to +5 can be scaled by multiplying by 10 (-50 to + 50) and then adding a constant of 50 (0 to 100). The multiplier spreads out the scale. The constant sets the value related to zero logits. Winsteps Table 20.1 prints a logit scale (default) and a percent (0 to 100 point) scale. Table 20.2 prints a 500 point scale. 

Standardized scaled scores go one step farther in adjusting the result to fit a predefined range. The central scaled score may not correspond to zero logits. The scaling multiplier and constant must be published to obtain the original logit scale and the original raw scores.

Percent improvement compares scaled scores from one year to the next. When the scaled score and the percent right scores are not published, there is no way to know the basic test results.

Each “improvement” in reporting test results, over the past few years, makes the output from Winsteps less transparent. The Rasch model and traditional CTT analyses provide data for these methods of reporting but are not responsible for the end uses. Most disturbing is a recent report that, in general, there is no way to audit the judgments made in developing annual reported school values.

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