Teaching · For Teachers · Research and data

When the scores are lopsided,
compare the order.

Rubric ratings, reading times and survey answers rarely make a tidy bell curve. Paste two groups and the calculator ranks every score together, then tests whether one group sits higher than the other, with an exact p-value for small samples.

Run the testWhat you get
$12one-time · every device you sign in on
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Included with Caveat Classroom and Whole-school licenses. Or get it in the For Teachers toolkit, $79 for 72 items.

The Mann-Whitney U calculator

The worked example is made up: chapter reading times with and without audio support. Use codes, not names. Nothing you type leaves this browser.

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What you get

Teaching · For Teachers$12 · included with Classroom and Whole-school licenses

What you finish with
U, the two-tailed p-value (exact or approximate, and which), the rank-biserial correlation, the probability of superiority, medians, rank sums and the Hodges–Lehmann shift, with the steps. It prints as a summary and downloads as a spreadsheet.
Who it is for
Teachers doing action research, data teams and instructional leaders, school psychologists and graduate students in education.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Up to 500 scores a group. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
$12 one-time, yours on every device you sign in on; the tool opens once you are signed in with it. Included with Caveat Classroom and Whole-school licenses. Also in the For Teachers toolkit ($79) and the Teaching Suite pass ($199), and 1 more bundle. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The For Teachers space in Caveat Teaching.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Name the measure and the two groups.
  2. Paste each group’s scores.
  3. Read the p-value with the rank-biserial r and the probability of superiority.
  4. Report the medians and the Hodges–Lehmann shift alongside.
  5. Print the summary or download the spreadsheet.

Run the test

How the test works

Ranks in place of raw scores.

The worked example: reading timesRank all 231 to 23smallest time = rank 1Audio rank sum9112 readersU for audio1391 − 12 × 13 ÷ 2Exact two-tailed< .001of all rank splitsThe worked example: reading timesRank all 231 to 23smallest time = rank 1Audio rank sum9112 readersU for audio1391 − 12 × 13 ÷ 2Exact two-tailed< .001of all rank splits
The test ignores the size of each score and keeps only its order. If the groups did not differ, the low ranks would be shared out evenly; here the audio group took almost all of them.

When to use it

The Mann-Whitney U test (also called the Wilcoxon rank-sum test) compares two independent groups without assuming the scores are normally distributed. It suits ordinal data such as rubric levels and skewed measures such as times or counts, and one extreme score cannot drag the result the way it drags a mean. For paired scores from the same people, use the Wilcoxon signed-rank test instead.

Reading the result

A small p says one group tends to score higher than the other. It is not strictly a test of medians unless the two distributions have the same shape. The probability of superiority is the easiest effect size to explain to a non-specialist: the chance a randomly chosen score from one group beats one from the other. With many ties the approximation is still sound, but say in your report that ties were corrected for.

Sources

  1. Mann, H. B., and Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18(1), 50–60.
  2. Hollander, M., Wolfe, D. A., and Chicken, E. (2014). Nonparametric Statistical Methods (3rd ed.). Wiley. Chapter 4, the two-sample location problem.
  3. Kerby, D. S. (2014). The simple difference formula: an approach to teaching nonparametric correlation. Comprehensive Psychology, 3, 11.IT.3.1.
  4. NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5, quantitative techniques; nonparametric alternatives (itl.nist.gov).

The worked example is made up. Use student codes, not names. Your scores stay in this browser. Support: team@caveatacademic.com.