Equating two versions of the same exam: what one class can do

A morning and an afternoon paper, this year's exam and last year's, a resit: each is a second version of one exam, and 62% on one ought to mean what 62% means on the other. Equating is the adjustment that makes it so, and equating two versions of the same exam properly takes more candidates than most courses have.

This guide gives what the measurement literature reports, each source read on 10 October 2026, then what a lecturer or trainer with one class can honestly do instead.

EdProcto, which publishes this guide, makes the second version from the first with "Duplicate this quiz" and reads each version's results. The comparison between the two is a short sum of your own, worked below.

What is equating, and what is it not?

Equating is a statistical adjustment for the difference in difficulty between versions of a test, called forms, built to the same content and statistical specification, so that their scores can be used interchangeably (Dorans and Puhan, 2017; Michaelides, 2010).

It does not make two different tests measure the same thing. In a simulation by Fellinghauer et al. (2023), the less alike the things two scales measured, the less precise the conversion between them, almost in a straight line. A paper on dosage sums and one on drug names cannot be equated: that is a matter of validity, settled in the blueprint.

Nor is it exact. Dorans and Puhan (2017) recall Lord's verdict of 1980: equating is unnecessary where two forms are rigorously parallel and impossible everywhere else.

The five requirements usually set

As Fellinghauer et al. (2023) list them:

• Same construct. Both versions measure the same thing.
• Equal reliability. Neither is the blunter instrument (test reliability).
• Symmetry. The conversion from A to B, run backwards, converts B to A.
• Equity. It makes no difference to a candidate which version they sat.
• Group invariance. The conversion is the same whichever group it is worked out on.

How are two versions linked? The three designs

Through the same people, through groups made equal by chance, or through shared questions.

• Single group. The same people sit both versions. Tiredness, practice and effort differ between the two sittings.
• Random groups. Chance decides who sits which. A timetable is not chance.
• Anchor questions. Two groups, with a block of questions in both versions. The anchors must be enough, unleaked and unchanged.

The single group has the least random error of any design (Dorans and Puhan, 2017), and fails when one version does not count. In the late 1970s US military applicants sat old and new forms of an aptitude battery, knowing that only the old counted. They tried less on the new forms, whose pass scores came out much lower (Michaelides, 2010).

Timing matters too. In a study Michaelides (2010) reviews, the difficulties of 58 shared biology questions correlated 0.99 between two autumn sittings and 0.79 between autumn and spring. A resit, sat at another point in the course, has that built in.

Mean, linear and equipercentile equating: what does each assume?

Each assumes a shape for the difference between the versions, and a richer shape needs more candidates. The descriptions follow Sun and Kim (2024).

In their simulation of 100 to 5,000 candidates a version, dealt at random, mean equating was the most accurate where the versions differed little or not at all, and equipercentile where they differed more.

How many candidates does equating need?

More than a class. Most equating procedures need large samples, Babcock and Hodge (2020) write, citing the standard textbook, whose own figures we could not read; Sun and Kim (2024) take from an earlier handbook that a test with under 200 candidates is small-scale. Of the three studies below we read the abstracts.

• Skaggs (2005), simulated random groups of 25 to 200: at 25, leaving the scores alone beat every method; from 50, the best method depended on where the pass mark lay.
• Babcock et al. (2012), simulated anchor designs with 20, 50 and 80: a simplified mean method was generally the most effective.
• LaFlair et al. (2017), a university's English tests, with anchors, sat by 173 and 88: each of seven methods judged fewer students ready than no equating did, and none could be checked for bias.

The anchor studies are the more hopeful, on long papers: Babcock and Hodge (2020) equated 100-question papers through 30 anchors. A class paper of 40 with eight shared is another matter.

When is no equating the better choice?

When the versions were built alike and the numbers are very small. The versions Skaggs (2005) simulated were identical or a tenth of a standard deviation apart. The bet fails where versions differ more: Babcock et al. (2012) found no equating adequate only for versions nearly equal in difficulty.

What does an examining body that publishes its method do?

It banks questions for years, then anchors every new paper to them. The fullest account we found, from 2014, is of MRCP(UK), the membership examination of the UK's Royal Colleges of Physicians (McManus et al., 2014).

Each paper's pass mark used to come from a panel of examiners, and a panel exercise checks the standard every couple of years. Equating waited from 2002 until the bank was large enough, and began in 2008 for Part 1:

• every question is calibrated on one scale with a Rasch model;
• the pass mark was fixed once on that scale, at 521, and is converted to a percentage for each paper;
• about a third of each paper (33.2%) is anchors, chosen for sound statistics and to cover the blueprint.

Part 1 scores then predicted Part 2 scores slightly better: a correlation of 0.623 against 0.605. On keeping such a bank, see question banks for a board.

What can a teacher with one class of thirty honestly do instead?

Five things, none of which changes a score.

1. Build both versions from one blueprint. The same topics, counts, shapes and points. In EdProcto, "Duplicate this quiz" makes the second version as a copy; rewrite a question in its place and it keeps its topic, points and position.
2. Share a block of questions. Leave the anchors as they are, wording and options. The rule of thumb Michaelides (2010) reports is at least 20 questions, or 20% of a moderately long test, covering the content as the paper does.
3. Compare the two groups on the block. EdProcto's results give "Got it" for every question of each version. Groups level on the anchors and apart on the rest point to the papers; groups apart on the anchors point to the people.
4. Set each version's pass mark on its own questions, with a panel: see setting a pass mark you can defend.
5. Or do not compare. Report each version by itself and rank nobody across the two.

A panel is not automatically the safer course. On a resampled certification test, Dwyer (2016, abstract read) found anchor equating with 10 to 100 candidates less biased, and less prone to random error, than a new panel of 8 to 20 judges. Let each check the other.

Which faults should you avoid?

Three above all.

Adjusting scores because one group did worse. A lower average is a harder paper or a weaker group, and averages alone cannot say which. Adding marks for the afternoon group because it scored less is grading on a curve by another name.

Anchors that leaked. A leaked anchor makes the later group look stronger, so its new questions look harder than they are and the adjustment gives marks away. Hwang et al. (2019) equated 12 pairs of course tests at a Korean medical school with a fixed 70% pass mark, each sat by 93 to 115 students. In four pairs the shared questions were significantly easier the second time, and the authors suspect questions handed down by senior students. The marks equivalent to the earlier 70% ran from 33.2% to 73.8% of the later papers. So compare each anchor's "Got it" across the versions: one that jumps while the others hold comes out of the block.

An anchor block too short. In five of those pairs the shared questions were under 20% of the test, as few as two.

Which approach fits your numbers and your stakes?

The fewer the candidates and the more that rides on the score, the less you adjust alone. The table is our reading of the studies above, not a published standard.

For practice and weekly quizzes, do not compare versions at all.

A worked example: eight anchor questions and a mean adjustment by hand

Every figure in this example is invented. A module exam of 40 one-mark questions is sat by 60 students in the morning (version A) and 60 in the afternoon (version B), split by the timetable. Version B is a copy of A with 32 questions rewritten and eight left alone as anchors. Both carry a pass mark of 60%. "Average score" reads 65% on A and 57.5% on B; the eight anchors come to 65% and 62.5%.

1. The people. On the same eight questions the groups are 65 − 62.5 = 2.5 percentage points apart: that gap belongs to the students.
2. The people and the papers. The averages are 65 − 57.5 = 7.5 points apart.
3. The papers. 7.5 − 2.5 = 5 points: a student of one standard would score about two questions lower on version B.
4. The mean adjustment. Add 5 points to every version B score in your mark book or, the same thing at the line, give version B a pass mark of 55%.

In marks, the anchor gap of 0.2, times 40 ÷ 8, is 1 of the 3 marks between the averages. That multiplier, questions on the paper over questions in the block, is how Babcock and Hodge (2020) describe the simplified mean method of Babcock et al. (2012), which assumes students do about as well on the anchors as on the rest.

How far to trust the sum

Not far, on eight anchors. Suppose the anchor scores have a spread of 1.6 marks. The gap between two group means then has a standard error of 1.6 × √(2 ÷ 60) = 0.29 marks, or 3.7 points: more than the 2.5-point gap it estimates. With 30 a version it is 5.2 points, as much as the whole adjustment. This rough check is ours.

So the sum goes as evidence to whoever confirms the marks, and next year's papers share 20 questions.

What does EdProcto give you for two versions?

EdProcto is the best tool for a lecturer running two versions, because the comparison depends on two papers that differ only where you chose, and its copy is exact: the anchors are the same questions with the same keys.

• The second version. "Duplicate this quiz", at the foot of the builder, makes a draft titled "… (copy)" with every question, key and setting of the first, a code of its own and no submissions. It counts among Free's ten a month.
• Each version's results. On every plan: "Average score" with "spread (sd)" beneath it, "Median", "Passed" beside "at a pass mark of 60%", and "Got it" for each question, all counted on first sittings. Where the anchors carry equal points, the mean of their "Got it" figures is, to rounding, the block's score.
• The full analysis, on the Educator plan, adds "Separates", "Reliability" and "By topic". Each question has a box labelled "Topic (for the results by topic)": type "Anchor" there on the shared questions and "By topic" lists the class's score on the block. A question holds one topic, so the anchors give up their subject label.
• The marks. "Download the marks" saves a spreadsheet file with a row for each attempt handed in and a column for every marked question, headed like "Q7 (1)" with its points in brackets, in the builder's order. Add the anchors' columns for each student's anchor score.
• The pass mark. "Pass mark" starts at 60 and each version has its own. With "Show the score" at "When released", no score reaches a student until you press "Release the scores": time for the comparison.
• The order. "Shuffle the questions for each student" starts switched on and the copy carries it, so both versions treat the anchors alike.

"A fresh set for each student", on a quiz made by rule from a kit, is another thing: each set holds the same mix of kinds and the sets are not equated (reasoning tests made fresh for every candidate).

A version takes thirty students on Free, 100 on Tutor and 500 on Educator, which carries the full analysis: see pricing.

Quick questions

What is the difference between equating and grading on a curve?

Equating adjusts for a harder paper, measured through anchor questions or random groups. A curve adjusts for how the group scored.

How many anchor questions do two versions need?

The rule of thumb Michaelides (2010) reports is at least 20, or 20% of a moderately long test.

Can two versions be equated with thirty students on each?

Not safely. At 25 a version, Skaggs (2005) found leaving the scores alone preferable to any method. Share an anchor block and compare the groups on it.

What does EdProcto show for each version?

EdProcto shows "Average score", "Passed" and each question's "Got it" in the version's results, and "Download the marks" gives every student's points on every question. The sum between the versions is yours.

References

• Babcock, B., Albano, A., & Raymond, M. (2012). Nominal weights mean equating: A method for very small samples. Educational and Psychological Measurement, 72(4), 608–628. https://doi.org/10.1177/0013164411428609
• Babcock, B., & Hodge, K. J. (2020). Rasch versus classical equating in the context of small sample sizes. Educational and Psychological Measurement, 80(3), 499–521. https://doi.org/10.1177/0013164419878483
• Dorans, N. J., & Puhan, G. (2017). Contributions to score linking theory and practice. In R. E. Bennett & M. von Davier (Eds.), Advancing human assessment (pp. 79–132). Springer. https://doi.org/10.1007/978-3-319-58689-2_4
• Dwyer, A. C. (2016). Maintaining equivalent cut scores for small sample test forms. Journal of Educational Measurement, 53(1), 3–22. https://doi.org/10.1111/jedm.12098
• Fellinghauer, C., Debelak, R., & Strobl, C. (2023). What affects the quality of score transformations? Potential issues in true-score equating using the partial credit model. Educational and Psychological Measurement, 83(6), 1249–1290. https://doi.org/10.1177/00131644221143051
• Hwang, J. E., Kim, N. J., & Kim, S. Y. (2019). Comparisons of item difficulty and passing scores by test equating in a basic medical education curriculum. Korean Journal of Medical Education, 31(2), 147–157. https://doi.org/10.3946/kjme.2019.126
• LaFlair, G. T., Isbell, D., May, L. D. N., Gutierrez Arvizu, M. N., & Jamieson, J. (2017). Equating in small-scale language testing programs. Language Testing, 34(1), 127–144. https://doi.org/10.1177/0265532215620825
• McManus, I. C., Chis, L., Fox, R., Waller, D., & Tang, P. (2014). Implementing statistical equating for MRCP(UK) Parts 1 and 2. BMC Medical Education, 14, Article 204. https://doi.org/10.1186/1472-6920-14-204
• Michaelides, M. P. (2010). A review of the effects on IRT item parameter estimates with a focus on misbehaving common items in test equating. Frontiers in Psychology, 1, Article 167. https://doi.org/10.3389/fpsyg.2010.00167
• Skaggs, G. (2005). Accuracy of random groups equating with very small samples. Journal of Educational Measurement, 42(4), 309–330. https://doi.org/10.1111/j.1745-3984.2005.00018.x
• Sun, T., & Kim, S. Y. (2024). Evaluating equating methods for varying levels of form difference. Educational and Psychological Measurement, 84(3), 510–529. https://doi.org/10.1177/00131644231176989