Adaptive Quiz

Activities ::: mod_adaptivequiz
Maintained by Adam Franco, Vitaly Potenko
Create tests that efficiently measure users' abilities by adapting the questions difficulty to the estimation of user's ability.
Latest release:
230 sites
319 downloads
61 fans
Current versions available: 5

The Adaptive Quiz activity enables a teacher to create tests that efficiently measure the takers' abilities. Adaptive tests are comprised of questions selected from the question bank that are tagged with a score of their difficulty. The questions are chosen to match the estimated ability level of the current test-taker. If the test-taker succeeds on a question, a more challenging question is presented next. If the test-taker answers a question incorrectly, a less-challenging question is presented next. This technique will develop into a sequence of questions converging on the test-taker's effective ability level. The test stops when the test-taker's ability is determined to the required accuracy.

The Adaptive Quiz activity uses the "Practical Adaptive Testing CAT Algorithm" by B.D. Wright published in Rasch Measurement Transactions, 1988, 2:2 p.24 and discussed in John Linacre's "Computer-Adaptive Testing: A Methodology Whose Time Has Come." MESA Memorandum No. 69 (2000).

This Moodle activity module was created as a collaborative effort between Middlebury College and Remote Learner. Later on it was adopted by Vitaly Potenko to keep it compatible with new Moodle versions and enhance with new features.

Below you'll find short documentation on the plugin to explain its essential concepts and flows.

The Question Bank

To begin with, questions to be used with this activity are added or imported into Moodle's question bank. Only questions that can automatically be graded may be used. As well, questions should not award partial credit. The questions can be placed in one or more categories.

This activity is best suited to determining an ability measure along a unidimensional scale. While the scale can be very broad, the questions must all provide a measure of ability or aptitude on the same scale. In a placement test for example, questions low on the scale that novices are able to answer correctly should also be answerable by experts, while questions higher on the scale should only be answerable by experts or a lucky guess. Questions that do not discriminate between takers of different abilities on will make the test ineffective and may provide inconclusive results.

Take for example a language placement test. Low-difficulty vocabulary and reading-comprehension questions would likely be answerable by all but the most novice test-takers. Likewise, high-difficulty questions involving advanced grammatical constructs and nuanced reading-comprehension would be likely only be correctly answered by advanced, high-level test-takers. Such questions would all be good candidates for usage in an Adaptive Test. In contrast, a question like "Is 25¥ a good price for a sandwich?" would not measure language ability but rather local knowledge and would be as likely to be answered correctly by a novice speaker who has recently been to China as it would be answered incorrectly by an advanced speaker who comes from Taiwan -- where a different currency is used. Such questions should not be included in the question-pool.

Questions must be tagged tagged with a 'difficulty score' using the format 'adpq_n' where n is a positive integer, e.g. 'adpq_1' or 'adpq_57'. The range of the scale is arbitrary (e.g. 1-10, 0-99, 1-1000), but should have enough levels to distinguish between question difficulties.

The Testing Process

The Adaptive Test activity is configured with a fixed starting level. The test will begin by presenting the test-taker with a random question from that starting level. As described in Linacre (2000), it often makes sense to have the starting level be in the lower part of the difficulty range so that most test-takers get to answer at least one of the first few questions correctly, helping their moral.

After the test-taker submits their answer, the system calculates the target question difficulty it will select next. If the last question was answered correctly, the next question will be harder; if the last question was answered incorrectly, the next question will be easier. The system also calculates a measure of the test-taker's ability and the standard error for that measure. A next random question at or near the target difficulty is selected and presented to the user.

This process of alternating harder questions following correct answers and easier questions following wrong answers continues until one of the stopping conditions is met. The possible stopping conditions are as follows:

  • there are no remaining easier questions to ask after a wrong answer
  • there are no remaining harder questions to ask after a correct answer
  • the standard error in the measure has become precise enough to stop
  • the maximum number of questions has been exceeded


Attempt graph


Test Parameters and Operation

The primary parameters for tuning the operation of the test are:

  • the starting level
  • the minimum number of questions
  • the maximum number of questions
  • the standard error to stop

Relationship between Maximum Number of Questions and Standard Error

As discussed in Wright (1988), the formula for calculating the standard error is given by:

Standard Error (± logits) = sqrt((R+W)/(R*W))

where R is the number of right answers and W is the number of wrong answers. This value is on a logit scale, so we can apply the inverse-logit function to convert it to an percentage scale:

Standard Error (± %) = ((1 / ( 1 + e^( -1 * sqrt((R+W)/(R*W)) ) ) ) - 0.5) * 100

Looking at the Standard Error function, it is important to note that it depends only on the difference between the number of right and wrong answers and the total number of answers, not on any other features such as which answers were right and which answers were wrong. For a given number of questions asked, the Standard Error will be smallest when half the answers are right and half are wrong. From this, we can deduce the minimum standard error possible to achieve for any number of questions asked:

  • 10 questions (5 right, 5 wrong) → Minimum Standard Error = ± 15.30%
  • 20 questions (10 right, 10 wrong) → Minimum Standard Error = ± 11.00%
  • 30 questions (15 right, 15 wrong) →  Minimum Standard Error = ± 9.03%
  • 40 questions (20 right, 20 wrong) →  Minimum Standard Error = ± 7.84%
  • 50 questions (25 right, 25 wrong) →  Minimum Standard Error = ± 7.02%
  • 60 questions (30 right, 30 wrong) →  Minimum Standard Error = ± 6.42%
  • 70 questions (35 right, 35 wrong) →  Minimum Standard Error = ± 5.95%
  • 80 questions (40 right, 40 wrong) →  Minimum Standard Error = ± 5.57%
  • 90 questions (45 right, 45 wrong) →  Minimum Standard Error = ± 5.25%
  • 100 questions (50 right, 50 wrong) →  Minimum Standard Error = ± 4.98%
  • 110 questions (55 right, 55 wrong) →  Minimum Standard Error = ± 4.75%
  • 120 questions (60 right, 60 wrong) →  Minimum Standard Error = ± 4.55%
  • 130 questions (65 right, 65 wrong) →  Minimum Standard Error = ± 4.37%
  • 140 questions (70 right, 70 wrong) →  Minimum Standard Error = ± 4.22%
  • 150 questions (75 right, 75 wrong) →  Minimum Standard Error = ± 4.07%
  • 160 questions (80 right, 80 wrong) →  Minimum Standard Error = ± 3.94%
  • 170 questions (85 right, 85 wrong) →  Minimum Standard Error = ± 3.83%
  • 180 questions (90 right, 90 wrong) →  Minimum Standard Error = ± 3.72%
  • 190 questions (95 right, 95 wrong) →  Minimum Standard Error = ± 3.62%
  • 200 questions (100 right, 100 wrong) →  Minimum Standard Error = ± 3.53%

What this listing indicates is that for a test configured with a maximum of 50 questions and a "standard error to stop" of 7%, the maximum number of questions will always be encountered first and stop the test. Conversely, if you are looking for a standard error of 5% or better, the test must ask at least 100 questions.

Note that these are best-case scenarios for the number of questions asked. If a test-taker answers a lopsided run of questions right or wrong the test will require more questions to reach a target standard of error.

Minimum Number of Questions

For most purposes this value can be set to 1 since the standard of error to stop will generally set a base-line for the number of questions required. This could be configured to be greater than the minimum number of questions needed to achieve the standard of error to stop if you wish to ensure that all test-takers answer additional questions.

Starting Level

As mentioned above, this usually will be set in the lower part of the difficulty range (about 1/3 of the way up from the bottom) so that most test takers will be able answer one of the first two questions correctly and get a moral boost from their correct answers. If the starting level is too high, low-ability users would be asked several questions they can't answer before the test begins asking them questions at a level they can answer.

Scoring

As discussed in Wright (1988), the formula for calculating the ability measure is given by:

Ability Measure = H/L + ln(R/W)

where H is the sum of all question difficulties answered, L is the number of questions answered, R is the number of right answers, and W is the number of wrong answers.

Note that this measure is not affected by the order of answers, just the total difficulty and number of right and wrong answers. This measure is dependent on the test algorithm presenting alternating easier/harder questions as the user answers wrong/right and may not be applicable to other algorithms. In practice, this means that the ability measure should not greatly affected by a small number of spurious right or wrong answers.

As discussed in Linacre (2000), the ability measure of the test taker aligns with the question-difficulty at which the test-taker has a 50% probability of answering a question correctly.

For example, given a test with levels 1-10 and a test-taker that answered every question 5 and below correctly and every question 6 and up wrong, the test-taker's ability measure would fall close to 5.5. Remember that the ability measure does have error associated with it. Be sure to take the standard error amount into account when acting on the score.

Screenshots

Screenshot #0

Contributors

Adam Franco (Lead maintainer)
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  • Tue, Feb 15, 2022, 1:11 AM
    Ah, sorry, Andrew, I mislead you in fact - the required Moodle version, 3.11, is set in the plugin's settings. So you have to install it on 3.11.4+ only, it'll not work on 3.10. Sorry for the confusion! The version for 3.10 (and probably even for earlier Moodle versions) should be definitely released for this plugin. Hope, this will happen soon.
  • Tue, Feb 15, 2022, 4:01 AM
    All good! Thanks Vitaly!
  • Wed, Feb 23, 2022, 4:43 PM
    Hi Vitaly Potenko, can this adaptive quiz be given a time limit to complete the quiz like the classic quiz on Moodle where you can adjust the length of time for a quiz.

    Thank you
  • Thu, Feb 24, 2022, 4:28 AM
    Hi Abdul, at this moment the plugin doesn't have such functionality. But from my point of view it's also debatable if an adaptive quiz, which is aimed at ability measuring, should have any time limits... Would be happy to get any opinions on that.
  • Thu, Feb 24, 2022, 9:30 AM
    It would be better to add a time limit option in completing the adaptive quiz if it is in measuring ability. The time limit option can be activated when an adaptive quiz is used to measure ability, as is the case with the time limit in the classic Moodle quiz.

    Thanks to Vitaly Potenko, I've run the previous version of the adaptive quiz and the latest version has a lot of maintenance so it's much better 😊
  • Thu, Mar 24, 2022, 6:51 PM
    Hey folks! The new version has been released - 2.1.0. It mainly aims at user experience of the reporting part of the plugin. Please, check the release notes for more info. As usual, feel free to report any plugin issues in the plugin's GitHub repo (check the link in the plugin's description). A big thank you to all who helps to make this plugin better!
  • Thu, Mar 24, 2022, 9:13 PM
    @Vitaly Potenko,hi,Vitaly,it seems that 2.1.0 requies Moodle 3.11.6, is it possible to work on older version?
  • Thu, Mar 24, 2022, 10:45 PM
    Hi @synnac song, at this moment it does support 3.11.6 only, that's because it was essentially tested on this version. But in the nearest future the compatibility will be ensured with the 3.11's earlier versions as well. Stay tuned!
  • Fri, Mar 25, 2022, 3:07 AM
    The latest plugin version now is 2.1.1 and besides improvements from 2.1.0 it also ensures compatibility with Moodle 3.11 branch starting from 3.11.2. Enjoy!
  • Fri, Mar 25, 2022, 9:19 AM
    Thank you, @Vitaly Potenko . This makes thing much easier for us!
  • Fri, Mar 25, 2022, 4:24 PM
    Hi @Vitaly Potenko. Slightly in need of repair. On the Review Attemp page --> Question Details, when you will see the summary on the next page by clicking the number 2, it does not go to the next page but will go to the Attemp Summary.
  • Fri, Mar 25, 2022, 6:28 PM
    Hi Abdul, thanks for trying the new version out! Please, feel free to create an issue in the plugin's GitHub repository with the bug description - https://github.com/vtos/moodle-mod_adaptivequiz/issues.
  • Wed, Mar 30, 2022, 2:18 AM
    I'd really like to use this plugin, and although I understand the rationale behind not using a time limit as that would restrict the adaptive process, if we are to use the system, we'd still need to set some boundaries for time limits so they can't take e.g. 10 hours to complete their test (in which they can search for their answers).
    Is there any kind of add on or work around which would allow for a time limit to be added to this?
  • Wed, Mar 30, 2022, 9:41 AM
    Hi Theodore! This really is an awesome plugin and I can't express sufficient gratitude to Vitaly for keeping it updated after the original developers declined to do so anymore. My previous organizations uses it and has given literally tens of thousands of English language placement tests using it. All was fine pre-Covet when we gave the test in our computer labs where time could be monitored and reminders given to students to finish up. But once we had to go to an off-site modality without any oversight, there was no way to be sure students weren't looking up answers or spending hours on the test (although the latter can be checked when reviewing the results). Putting a time limit will affect the outcome, however, since the algorythm would stop sooner than the proper score/level is determined. So, although we considered doing that, it really isn't an acceptable solution. I suppose one could add a time clock as a reminder to students, but again they could still continue the test. Another option might be to put a time limit on each question where if it isn't answered within a minute or two, it is marked wrong. This would, of course, require some serious coding which may not be feasible. I wish I could offer an optimal solution but there doesn't seem to be a way to get an accurate score any other way than the way the test is currently designed. Maybe others have suggestions.

    Dave
  • Mon, Apr 4, 2022, 11:11 PM
    The new version has just been released, and the essential goal was to make the plugin compatible with Moodle 3.8, 3.9, 3.10 and all minors of 3.11.
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