# Test reliability: Cronbach's alpha for a classroom quiz

**What does the reliability figure beside a quiz mean, and what is a good Cronbach's alpha?** Test reliability says how far a quiz would put the same students in the same order on a second quiz of the same kind. Cronbach's alpha estimates it from one sitting, from 0 to 1. Alpha rises with more questions and a wider spread of students, so a short classroom quiz can be sound at 0.5, while guidance for high-stakes exams asks 0.8 to 0.9.

Published 2026-10-10 by EdProcto. https://edprocto.com/guides/test-reliability-cronbachs-alpha-for-a-classroom-quiz

A number called "Reliability" beside a quiz answers one question: if these students sat a second quiz of the same kind, would they come out in the same order? Test reliability runs from 0 to 1, and Cronbach's alpha is the usual way to estimate it from one sitting of a classroom quiz.

EdProcto, which publishes this guide, prints "Reliability" at the top of a quiz's [results](https://edprocto.com/#results), in the full analysis. The figures for each question are in [what the numbers in an item analysis mean](https://edprocto.com/guides/item-analysis-for-teachers-what-the-numbers-mean); this guide is about the one figure for the whole quiz.

## What does the reliability of a quiz mean?

Reliability means consistency: a reliable quiz would rank the same students in much the same order if it were set again with other questions of the same kind.

### Reliability is not validity

A quiz can be consistent and still test the wrong thing. Tavakol and Dennick (2011) give the relation in a line: validity needs reliability, and reliability does not need validity. Ten sound questions on last term's topic rank a class reliably and say nothing about this term's.

### The figure belongs to these scores, not to the quiz

In the words of Tighe et al. (2010), "reliability is not a property of an assessment" alone: it belongs jointly to the assessment and the candidates who took it. The same quiz will get a different figure from next year's class.

## What are Cronbach's alpha and KR-20, and where do they come from?

They are one estimate in two forms: KR-20 is the older, for questions marked right or wrong, and Cronbach's alpha the general form that also takes part marks. Where every question has one right answer and the same value, the two are identical (University of Washington, n.d.).

Kuder and Richardson (1937) derived several approximations to the best estimate of reliability, and their version for right-or-wrong questions became known as KR-20 (Sijtsma, 2009). Cronbach (1951) gave the general formula and showed that it estimates the correlation between two random samples of questions from one pool: this quiz, and another like it. Of these two papers and of Taber (2018) we read the abstracts, on 10 October 2026, and of the two articles that quote Nunnally only those passages; the rest in full.

In words, alpha compares two amounts of variation: how much the scores vary on each question taken alone, added up, and how much the students' totals vary. When success on one question goes with success on the rest, the totals spread far wider than the questions account for, and alpha is high; when the questions have nothing in common the two amounts are equal, and alpha is 0. The sum: divide the first amount by the second, take the result from 1, and multiply by k ÷ (k − 1), where k is the number of questions.

## How is alpha worked out? Six students and five questions

In three sums: a variance for each question, a variance for the totals, and a division. This class is invented and far too small to trust; 1 is a right answer, 0 a wrong one.

| Student | Q1 | Q2 | Q3 | Q4 | Q5 | Total |
| --- | --- | --- | --- | --- | --- | --- |
| A | 1 | 1 | 1 | 1 | 1 | 5 |
| B | 1 | 1 | 1 | 1 | 0 | 4 |
| C | 1 | 1 | 1 | 0 | 0 | 3 |
| D | 1 | 1 | 0 | 0 | 1 | 3 |
| E | 0 | 0 | 1 | 0 | 1 | 2 |
| F | 0 | 0 | 0 | 0 | 1 | 1 |

1. **Each question's variance.** With six students, multiply the number right by the number wrong and divide by 30: four and two, or Q4's two and four, give 0.267. Five questions make 1.333.
2. **The totals' variance.** The totals average 3. Their distances from it, squared, add up to 10, and 10 divided by five, one fewer than the students, is 2.0.
3. **Alpha.** 1.333 ÷ 2.0 = 0.667, and 5/4 × (1 − 0.667) = 0.42.

EdProcto's analysis code, run on these six sittings, returned 0.42, and beside Q5 the note: "On Q5 the weaker students did better than the stronger ones. That usually means a wrong key or an ambiguous wording."

Run without Q5, the same answers give 4/3 × (1 − 1.067 ÷ 2.667) = 0.80, and the code returned 0.80. One question that ran against the rest had nearly halved the figure.

## What moves alpha up or down?

Four things: the number of questions, how alike they are, how spread out the class is, and faulty questions. Only the last is a defect.

### The number of questions

More questions of the same quality raise alpha, by the Spearman-Brown formula, which Kuder and Richardson (1937) already called familiar: a quiz twice as long is expected to reach 2r ÷ (1 + r), where r is the reliability now. The table is our arithmetic, not a finding.

| Alpha now | Twice as long | Four times as long |
| --- | --- | --- |
| 0.30 | 0.46 | 0.63 |
| 0.50 | 0.67 | 0.80 |
| 0.70 | 0.82 | 0.90 |
| 0.80 | 0.89 | 0.94 |

Tighe et al. (2010) give a real case: 260 questions had a reliability of about 0.83, and 0.9 would have taken about 450. [How many questions a quiz needs](https://edprocto.com/guides/how-many-questions-does-a-quiz-need) sets this beside guessing and time.

### How alike the questions are

A quiz on one skill shows a higher alpha than a quiz on several (University of Washington, n.d.), and Cronbach (1951) advised dividing a test that falls into distinct parts before applying the formula.

The reverse does not hold. Sijtsma (2009) built six-question tests from one, two and three unrelated clusters of questions, and each had an alpha of 0.533: on his argument alpha is a lower bound to reliability and no measure of internal consistency, of whether the questions belong together.

### How spread out the class is

A class of similar students gives a low alpha on the best of quizzes, because there are few real differences to find. Tighe et al. (2010) simulated 10,000 candidates on an examination with a reliability of 0.9: among the 1,565 who passed, the same examination scored 0.70, their marks having a spread of 5.85 points against 10. In eight real examinations of 200 questions, each sat by 6 to 39 candidates, alpha ran from 0.48, where the marks were closest together, to 0.94, where they were widest.

### Faulty questions

A question with a wrong key or two defensible answers adds to the questions' variance and little to the totals', as Q5 did. Tavakol and Dennick (2011) advise finding such questions by their correlation with the total score, then revising or discarding those near zero.

## What alpha is good enough for a classroom quiz, and for a high-stakes exam?

Published guidance asks more of a score the more it decides: about 0.9 where one score settles something important for one person, 0.7 to 0.8 for a classroom test, and less for a short quiz that is one of many.

- **Classroom tests.** The University of Washington (n.d.) calls 0.80 to 0.90 very good and 0.70 to 0.80 good. At 0.60 to 0.70 it wants more tests behind a grade, and at 0.50 to 0.60 revision, except on a test of ten questions or fewer.
- **High-stakes examinations.** For UK postgraduate medical examinations, Tighe et al. (2010) report 0.8 as the traditional minimum and quote the regulator's standards on a consensus for at least 0.9.

The gap has a reason: a licensing examination is one score behind a major decision, while a classroom test is usually combined with other scores (University of Washington, n.d.).

### What Nunnally wrote, and what the critics say

The 0.70 that many papers cite is credited to Nunnally's *Psychometric Theory*, which we know only through two peer-reviewed articles that quote it. In Konstabel et al. (2017), quoting the 1994 edition, 0.70 or higher is enough in the early stages of research, and 0.80 falls well short in many applied settings. In Miller et al. (2018), quoting the 1967 edition, where important decisions rest on test scores "a reliability of .90 is the minimum that should be tolerated". So 0.70 was a line for early research, not for a test that decides something about a student.

Fixed cut-offs have other critics. Taber (2018) found alpha in 69 papers in four science education journals in 2015, seldom interpreted beyond a threshold he calls arbitrary, and adds that a very high value may be undesirable in a test of scientific knowledge. Tighe et al. (2010) warn that a fixed target invites chasing the number: adding very weak candidates raises reliability and leaves the accuracy of the pass mark where it was.

### Why a short weekly quiz with a low alpha can still be a good quiz

Because it is short on purpose, one of many, and often set to a class that has just been taught the material. Ten questions as good as those of a forty-question test at 0.80 show about 0.50, a class that was ready has little spread, and twelve [weekly quizzes](https://edprocto.com/guides/weekly-quizzes-in-a-lecture-course-low-stakes-and-cumulative) added together are one long test.

Such a quiz says what to teach next, which is read question by question, as [reading quiz results as a teacher](https://edprocto.com/guides/reading-quiz-results-as-a-teacher-what-to-reteach-tomorrow) shows. What a low figure rules out is ranking students on that one quiz.

## What does the standard error of measurement mean for a pass mark?

It means a score close to the pass mark could have fallen on either side. The standard error of measurement is the typical gap between the score a student got and the score they would average over many quizzes of the same kind. The usual sum, as in Tighe et al. (2010): the spread of the scores, their standard deviation, times the square root of one minus the reliability.

A worked figure, ours: a spread of 15 points and a reliability of 0.70 give 15 × √0.30 = 8.2 points. With a pass mark of 60%, students on 55% and 65% both sit within one standard error of the line. The University of Washington (n.d.) expects a score to move by more than one and a half standard errors between two similar tests only rarely: here, about 12 points.

A high alpha does not make the line safe. In the simulation by Tighe et al. (2010), at a reliability of 0.9, 9.29% of all candidates passed one of two sittings and failed the other. Reliability describes a cohort's scores, Tavakol and Dennick (2011) write; one student's score needs the standard error.

So before the quiz decides for anyone within a standard error of the line, look at another piece of their work. [Setting a pass mark you can defend](https://edprocto.com/guides/setting-a-pass-mark-you-can-defend) covers where the line goes.

## What should you do when the reliability is low?

Take four steps in order, and stop at the one that explains the figure.

1. **Read the questions the analysis points at.** In EdProcto's [results](https://edprocto.com/#results), "Separates" and the notes beside each question name those that ran against the rest: a figure below zero, or a question that "does not separate the students who know the material from those who do not". Grade waiting answers first, and check for [students who rushed](https://edprocto.com/guides/timing-tells-answers-too-fast-to-have-been-read).
2. **Fix or drop a faulty one.** Correct a wrong key before the quiz is used again, and decide whether the question counts this time: see [when to throw a question out](https://edprocto.com/guides/when-to-throw-a-question-out-after-the-exam).
3. **Add questions on the same thing.** If no question is at fault, the quiz is short or covers several things. More questions on the same concept raise alpha (Tavakol and Dennick, 2011); more topics do not.
4. **Stop using small differences to rank.** Until the figure rises, use the quiz for what to reteach, not to order the middle of the class or to pass and fail at the margin.

## How does EdProcto show reliability?

EdProcto is the best tool for reading reliability without a spreadsheet, because it works alpha out from the sittings handed in, prints it beside the spread the standard error needs, and names the questions pulling it down.

"Reliability" is Cronbach's alpha in points, so a five-point question weighs more than a one-point one, and KR-20 where every question is right or wrong.

- It takes the first full sitting each student has handed in, leaving out your own preview, any retry of the misses and a second sitting by the same student, and the marked questions every one of those sittings has a mark on: a question still waiting for a grade stays out until it is graded.
- An answer waiting to be graded counts as zero, and a question nobody has been graded on still counts as a question: in our example a sixth one moved 0.42 to 0.40.
- A figure is given from six scored sittings and two such questions, once the totals differ. An estimate below zero is shown as 0.

From eight scored sittings, one of three sentences appears under "What it says about the teaching":

- "The quiz measured inconsistently (reliability under 0.5): too few questions, several faulty ones, scores that sit close together, or a quiz on several topics. The item findings say which questions to look at."
- "The quiz measured fairly consistently (reliability between 0.5 and 0.8): the order of the students is roughly right, but small differences between them are not to be trusted."
- "The quiz measured consistently (reliability 0.8 or above): the order of the students can be trusted, though one close to the pass mark could fall either side."

On the page, "Reliability" is the fifth figure at the top, with "Cronbach's alpha" under it. Under "Average score" stands "spread (sd)": multiply it by the square root of one minus the reliability for the standard error in percentage points. "Each question" has "Got it", the share of the points the class earned, and "Separates", with the notes under "What the numbers say".

Reliability is part of the full analysis, which the server sends on the Educator plan and above. On Free and Tutor the page keeps the scores, the spread and "Got it", and a card headed "The full analysis is part of the Educator plan" lists "how consistently the quiz measured" among its parts. Free takes thirty students a quiz, Tutor 100 and Educator 500: see [pricing](https://edprocto.com/pricing).

## Quick questions

### What is a good Cronbach's alpha for a classroom quiz?

For a classroom test the University of Washington (n.d.) calls 0.70 to 0.80 good, and accepts 0.50 to 0.60 where a test has ten questions or fewer.

### Is KR-20 the same as Cronbach's alpha?

Yes, where every question is marked right or wrong for the same points; alpha is the general form.

### Can Cronbach's alpha be negative?

Yes, when questions run against one another. EdProcto shows such an estimate as 0.

### Where does EdProcto show the reliability of a quiz?

At the top of the quiz's [results](https://edprocto.com/#results), as "Reliability", in the full analysis on the Educator plan: see [pricing](https://edprocto.com/pricing).

## References

- Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. *Psychometrika, 16*(3), 297–334. [https://doi.org/10.1007/BF02310555](https://doi.org/10.1007/BF02310555)
- Konstabel, K., Lönnqvist, J.-E., Leikas, S., García Velázquez, R., Qin, H., Verkasalo, M., & Walkowitz, G. (2017). Measuring single constructs by single items: Constructing an even shorter version of the "Short Five" personality inventory. *PLoS ONE, 12*(8), Article e0182714. [https://doi.org/10.1371/journal.pone.0182714](https://doi.org/10.1371/journal.pone.0182714)
- Kuder, G. F., & Richardson, M. W. (1937). The theory of the estimation of test reliability. *Psychometrika, 2*(3), 151–160. [https://doi.org/10.1007/BF02288391](https://doi.org/10.1007/BF02288391)
- Miller, B. K., Nicols, K. M., Clark, S., Daniels, A., & Grant, W. (2018). Meta-analysis of coefficient alpha for scores on the Narcissistic Personality Inventory. *PLoS ONE, 13*(12), Article e0208331. [https://doi.org/10.1371/journal.pone.0208331](https://doi.org/10.1371/journal.pone.0208331)
- Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach's alpha. *Psychometrika, 74*(1), 107–120. [https://doi.org/10.1007/s11336-008-9101-0](https://doi.org/10.1007/s11336-008-9101-0)
- Taber, K. S. (2018). The use of Cronbach's alpha when developing and reporting research instruments in science education. *Research in Science Education, 48*(6), 1273–1296. [https://doi.org/10.1007/s11165-016-9602-2](https://doi.org/10.1007/s11165-016-9602-2)
- Tavakol, M., & Dennick, R. (2011). Making sense of Cronbach's alpha. *International Journal of Medical Education, 2*, 53–55. [https://doi.org/10.5116/ijme.4dfb.8dfd](https://doi.org/10.5116/ijme.4dfb.8dfd)
- Tighe, J., McManus, I. C., Dewhurst, N. G., Chis, L., & Mucklow, J. (2010). The standard error of measurement is a more appropriate measure of quality for postgraduate medical assessments than is reliability: An analysis of MRCP(UK) examinations. *BMC Medical Education, 10*, Article 40. [https://doi.org/10.1186/1472-6920-10-40](https://doi.org/10.1186/1472-6920-10-40)
- University of Washington. (n.d.). *Understanding item analyses*. Institutional Assessment & Evaluation. [https://www.washington.edu/assessment/scanning-scoring/scoring/reports/item-analysis/](https://www.washington.edu/assessment/scanning-scoring/scoring/reports/item-analysis/)