How Much of a Problem is Guessing on a Criterion-Referenced (Mastery) Test?*
by Steven Just Ed.D.

Anyone who gives multiple choice tests worries about the effects of guessing on student scores. After all, for a four choice per item test even a student who knows absolutely nothing will, on average, get a score of 25%. Of course that’s not even close to a passing score so we don’t worry too much about students at the low end of the distribution. The more important question is: For students at the higher end of the distribution (at or above the passing score), how dramatic are the effects of guessing? How many students who otherwise would not have passed the test will actually pass because they guessed some number of correct answers? Surprisingly, on a mastery test with a high cut score, the problem is not as serious as you might think. Let’s look at why.

Most of our clients somewhat arbitrarily set test passing scores at 90% (that’s a separate problem, worthy of a separate article). Since almost all students pass each test, the average test score tends to be quite high (above 90%). So, let’s look at the “average” student with a test score of 94% and the consequences of guessing on that student’s score. To make our calculations easy let’s assume the student took a 100 question multiple-choice test, with four choices per question, so each question is worth 1 point. This means that on this test this student got 6 questions wrong. Since the student did not know the correct answer to these questions, it’s reasonable to assume that he/she “guessed” on these questions.

So we know that the “average” student guessed incorrectly on six questions. But the student must also have guessed correctly on some questions, artificially raising his/her score. How many correct guesses did this student have? Well, it’s pretty easy to calculate. If we know that guessing provides the incorrect answer 75% of the time and the correct answer 25% of the time (on a four-choice item) and the average student guessed incorrectly 6 times on this test, then that student must have guessed on a total of 8 questions (6 incorrect guesses, 2 correct guesses). So even removing the “correct guesses” and counting them as incorrect the “average” student would still have passed the test with a score of 92%.

What about the student who “just passed” with a score of 90%? This student guessed incorrectly on 10 questions. Using our 75% formula this means that he/she guessed correctly on 3.3 questions (let’s say 4) meaning his/her “guess-adjusted" score would have been 86%. Doing the math on scores of 91%, 92% and 93% gives “guess-adjusted” scores of 88%, 89.4%, and 90.7%, respectively. So the bottom line is that those students who received scores of 90%, 91% or 92% (this could go either way) passed, at least in part by guessing.

Is this a big problem? I think not. No test is a “true” score; there is always a measurement error. And having been through a number of cut score setting processes using the Angoff method I can guarantee you that the cut score arrived at is always a somewhat subjective process. So I think it is unlikely that you can discern the difference between an employee with a “guess-adjusted” score of 86% and one with a “guess-adjusted” score of 90% (someone who would have passed even if he/she had not artificially inflated his/her score by guessing.)

Let’s take a look at three other cases of “guess-adjusted” scores:

• A test composed of all true-false questions
• A test composed of four choice multiple-choice questions, but where one distractor can be easily eliminated (in effect a three choice question) on all the questions.
• A test composed of five choice multiple-choice questions where all choices are plausible

The results, along with our original four plausible choice calculations, are summarized in the table below:

*Note: The gray shaded area of the table shows scores that would be classified as failing if “correct guesses” are reclassified as incorrect responses.

There are four lessons here:

1. Do not use True/False questions. For a test of True/False questions a score of 95% would be “guess adjusted” to just passing (90%) and anything below that would be failing.
2. Make sure all distractors are plausible. The ability to eliminate even one distractor significantly raises the probability of a correct guess.
3. Consider using five-choice questions (assuming you can come up with four plausible distractors for each question). They further reduce the “guessing effect.”
4. Except for all True/False tests the “guessing effect” for high-average score mastery tests is smaller than you might think.

*Note: This article is a result of a calculation I saw in Thalheimer, W. (2004, October). Simulation-like questions: How and why to write them. Retrieved March 2007 from http://www.work-learning.com/ma/PP_WP002.asp. It extends a note in that paper on the effects of guessing to a number of other scenarios.