The t-test assumes that scores, or the changes in scores, are roughly normally distributed. In a class of a dozen learners, or when one learner’s score is far from the rest, that assumption is hard to check and easy to break. The Wilcoxon signed-rank test and the Mann-Whitney U test do the same jobs as the paired and independent t-tests using ranks instead of the scores themselves, so a single extreme value cannot swing the result. Below, both tests are run in Excel on the Action Research Toolkit’s practice data (the same data as our t-test guide), on a real DepEd example, and on a small class where the two kinds of test disagree.

It is written for teachers analyzing action research with small groups, and for school heads and research committees reviewing it.

Key points

  • Wilcoxon signed-rank test: for the same learners measured twice (pretest and posttest), in place of the paired t-test.
  • Mann-Whitney U test: for two different groups, such as two sections, in place of the independent t-test.
  • Use them for small groups with skewed scores, for outliers, or for ranked data such as reading levels and single rating-scale items.
  • Excel has no built-in function for either, but RANK.AVG and a few sums do the work; free programs such as JASP and jamovi give exact p-values.
  • They cannot rescue a tiny sample. With 5 pairs, the Wilcoxon test cannot reach p < 0.05 even if every learner improves; with 3 learners per group, neither can the Mann-Whitney test.
  • Report an effect size, such as r = z ÷ √n, with every result.

Which test to use

Your design Usual test Rank-based alternative
One group, pretest and posttest Paired t-test Wilcoxon signed-rank test
Two independent groups Independent t-test Mann-Whitney U test (also called the Wilcoxon rank-sum test)
Three or more groups One-way ANOVA Kruskal-Wallis test

The toolkit’s rule of thumb is at least 30 learners per group for experiments. Many action research classes are smaller, and the toolkit itself notes that in action research “the sampling should be purposive and accessible”: the learners you teach.

When the t-test misleads: a small example

Nine learners in a small remedial group (invented data) took a pretest and a posttest. Eight gained 1 to 3 points; one gained 25.

Learner L1 L2 L3 L4 L5 L6 L7 L8 L9
Pretest 12 9 15 11 8 14 10 13 6
Posttest 14 10 18 13 10 15 13 15 31
Gain 2 1 3 2 2 1 3 2 25
  • Paired t-test: mean gain 4.56, SD 7.70, t(8) = 1.78, p = 0.114. Not significant.
  • Wilcoxon signed-rank test: all nine learners improved, so T = 0, p = 0.004. Significant.

The one large gain inflates the standard deviation so much that the t-test misses what is plain in the table: every learner improved. Without that learner, the t-test gives t(7) = 7.48, p < 0.001. The Wilcoxon test is not fooled either way, because it looks only at the direction and the order of the changes. The median gain, 2 points, describes the group better than the mean, 4.56.

The Wilcoxon signed-rank test in Excel

The toolkit’s practice data: Math scores of 12 girls before and after a strategy (Teacher’s Guide 5.3).

Step 1. Compute each learner’s difference (posttest − pretest) in column D: =C2-B2.

Step 2. Drop zero differences. Learners who scored the same twice tell you nothing about direction; two girls did, so n = 10.

Step 3. Rank the absolute differences from smallest to largest, giving tied values the average of their ranks. For the ten non-zero rows, put the absolute difference in column E (=ABS(D2)), then rank it: =RANK.AVG(E2, $E$2:$E$11, 1). The final 1 ranks from smallest to largest.

Step 4. Give each rank the sign of its difference, then add the positive ranks and the negative ranks.

Learner Pretest Posttest Difference Rank of |difference| Signed rank
G1 9 6 −3 6.5 −6.5
G2 7 7 0 dropped
G3 8 4 −4 8 −8
G4 6 5 −1 1.5 −1.5
G5 11 6 −5 9.5 −9.5
G6 8 8 0 dropped
G7 9 4 −5 9.5 −9.5
G8 10 8 −2 4 −4
G9 8 5 −3 6.5 −6.5
G10 7 6 −1 1.5 −1.5
G11 5 7 +2 4 +4
G12 8 6 −2 4 −4

Sum of positive ranks W⁺ = 4; sum of negative ranks W⁻ = 51. As a check, the two add up to n(n + 1) ÷ 2 = 55.

Step 5. Decide. The test statistic T is the smaller sum, 4.

  • With a table (small n): the critical value of T for n = 10 at 0.05, two-tailed, is 8. Since 4 ≤ 8, the change is significant.
  • With the normal approximation (larger n, about 20 or more): z = (W⁺ − n(n+1)/4) ÷ √(n(n+1)(2n+1)/24) = (4 − 27.5) ÷ 9.81 = −2.40, and the two-tailed p-value is =2*(1-NORM.S.DIST(ABS(-2.40),TRUE)) = 0.017.

The girls’ scores fell, T = 4, z = −2.40, p = 0.017, which agrees with the toolkit’s paired t-test (t(11) = −3.25, p = 0.008). For the boys, all 12 improved: T = 0, z = 3.06, exact p < 0.001, again in line with the t-test.

Critical values of T (0.05, two-tailed; reject when T is at or below the value), computed from the exact distribution:

n 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Critical T 0 2 3 5 8 10 13 17 21 25 29 34 40 46 52

The Mann-Whitney U test in Excel

The question: did the boys and girls differ on the posttest? Each group has 12 learners.

Step 1. Put all 24 scores in one column (C2:C25), with the group in the next column.

Step 2. Rank all the scores together, smallest first, with ties averaged: =RANK.AVG(C2, $C$2:$C$25, 1).

Step 3. Add the ranks of each group. The boys’ ranks sum to R₁ = 222 and the girls’ to R₂ = 78 (check: the total is 24 × 25 ÷ 2 = 300).

Step 4. Compute U for each group: U₁ = R₁ − n₁(n₁ + 1) ÷ 2 = 222 − 78 = 144, and U₂ = n₁n₂ − U₁ = 144 − 144 = 0. The test statistic U is the smaller, 0.

Step 5. Decide.

  • With a table: the critical value of U for 12 and 12 at 0.05, two-tailed, is 37. Since 0 ≤ 37, the groups differ.
  • With the normal approximation: z = (U₁ − n₁n₂/2) ÷ √(n₁n₂(n₁ + n₂ + 1)/12) = (144 − 72) ÷ 17.32 = 4.16, p < 0.001.

U = 0 means that every boy scored higher than every girl on the posttest. The pretests, by contrast, did not differ: U = 50, z = −1.27, p = 0.204, matching the t-test’s p = 0.201.

Critical values of U for equal groups (0.05, two-tailed; reject when U is at or below the value):

Learners per group 4 5 6 7 8 9 10 11 12
Critical U 0 2 5 8 13 17 23 30 37

For unequal groups, use a published table or a free program such as JASP or jamovi.

Effect sizes

  • r = |z| ÷ √n, where n is the number of non-zero pairs (Wilcoxon) or all learners (Mann-Whitney). Cohen’s rough guide calls 0.1 small, 0.3 medium and 0.5 large. For the girls, r = 2.40 ÷ √10 = 0.76; for the posttest comparison, r = 4.16 ÷ √24 = 0.85.
  • Rank-biserial correlation, which reads like a share: for Wilcoxon, (W⁺ − W⁻) ÷ (W⁺ + W⁻) = (4 − 51) ÷ 55 = −0.85; for Mann-Whitney, (U₁ − U₂) ÷ (n₁n₂) = 144 ÷ 144 = 1.00, meaning that the boys outscored the girls in every possible boy-girl pair.

Report the medians too: rank-based tests compare the distributions, and the median describes a skewed group better than the mean.

A real example: Candon City’s Grade 1 readers

Our t-test guide compared the share of Grade 1 struggling readers in 22 public schools of the Schools Division of Candon City at the start and end of School Year 2025-26 (Comprehensive Rapid Literacy Assessment). The end-of-year shares are badly skewed: 13 of the 22 schools ended at 0%, and the median fell from 85.2% to 0.0%.

The share fell in every school, so W⁺ = 0 and W⁻ = 253: z = −4.11, p < 0.001, r = 0.88. The paired t-test gave the same verdict (t(21) = −16.26). Here the two tests agree; with skewed data like these, the Wilcoxon test is the safer one to report, and the conclusion does not depend on the normality assumption. As our t-test guide explains, the drop also happened without any special intervention, so it shows growth over a school year, not the effect of a program.

The trap: some samples are too small for any test

Rank-based tests have a floor. With very few learners, even the most extreme possible result is not significant:

Pairs (Wilcoxon) 3 4 5 6 7 8
Smallest two-tailed p 0.250 0.125 0.063 0.031 0.016 0.008
Learners per group (Mann-Whitney) 2 and 2 3 and 3 4 and 4 5 and 5
Smallest two-tailed p 0.333 0.100 0.029 0.008

A study of five learners who all improved cannot reach p < 0.05 with the Wilcoxon test. If your group is this small, report each learner’s results and describe the pattern, or treat the study as qualitative; do not present “not significant” as evidence that the intervention failed.

How to report

The girls’ Math scores decreased from pretest (Mdn = 8.0) to posttest (Mdn = 6.0), Wilcoxon signed-rank test, T = 4, z = −2.40, p = 0.017, r = 0.76, n = 10 non-zero differences.

The boys (Mdn = 14.5) scored higher than the girls (Mdn = 6.0) on the posttest, Mann-Whitney U = 0, z = 4.16, p < 0.001, r = 0.85.

Give the medians, the test statistic, z when used, the p-value, the effect size, and the number of learners, and say how many zero differences were dropped.

Common mistakes

  • Using a rank test to dodge a weak result. Choose the test from the design and the data before you look at the p-value.
  • Forgetting to drop zero differences in the Wilcoxon test.
  • Ranking each group separately in the Mann-Whitney test; rank all scores together.
  • Ranking from largest to smallest. Use RANK.AVG(..., 1); Excel’s default ranks from the largest.
  • Reporting means with a rank test; report medians.
  • Expecting significance from five learners. Check the floor table first.

Frequently asked questions

When should I use the Wilcoxon signed-rank test instead of a paired t-test?

When the same learners are measured twice and the group is small with skewed changes, when there are extreme values, or when the scores are ranks, such as reading levels. With 30 or more learners and roughly symmetric changes, the paired t-test is fine.

Is the Mann-Whitney U test the same as the Wilcoxon rank-sum test?

Yes. They are two forms of the same test for two independent groups, and they give the same p-value.

Can I do the Wilcoxon test in Excel?

Excel has no built-in function, but you can compute it: take each learner’s difference, drop the zeros, rank the absolute differences with RANK.AVG, add the positive and negative ranks, and compare the smaller sum with a table of critical values or use the normal approximation for larger groups.

What is the minimum sample size for the Wilcoxon signed-rank test?

To reach p < 0.05 two-tailed at all, at least 6 non-zero pairs, and only if every learner changed in the same direction. In practice, aim for 10 or more.

More on DepEd research

Sources

  • Department of Education and the Basic Education Sector Transformation (BEST) Program. (2019). Action Research Toolkit: Teacher’s Guide, sections 4.1 (sampling) and 5.3 (inferential statistics; practice data), with support from the Australian Government.
  • CRLA results: EDCOM II dashboard data on the Comprehensive Rapid Literacy Assessment at the end of SY 2025-26 and DepEd’s CRLA file for selected schools (DepEd does not say which round it covers, but its date and results point to the start of the year), cleaned by NASH Reviewer.
  • Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83. https://doi.org/10.2307/3001968
  • Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), 50–60. https://doi.org/10.1214/aoms/1177730491
  • Microsoft. RANK.AVG function.

Analysis by Mark Anthony Llego for NASH Reviewer. The nine-learner example is invented. NASH Reviewer is not affiliated with DepEd.