Mann-Whitney and Kruskal-Wallis Tests on 100 m swim time by swimming stroke in student swimming clubs

Project info

• Field of studySports and Kinesiology
• LevelMaster's thesis (S2)
• Method typeInferential Statistics
• Estimated build time± 5 working days
• Toolsscipy.stats mannwhitneyu, kruskal, shapiro
• PriceUS$22 - US$144

Research goal

Compare 100 m swim time by swimming stroke in student swimming clubs with nonparametric tests when the normality assumption is not met.

Variables

Example result

• 521Mann-Whitney U
• 0.001Mann-Whitney p-value
• 11.148Kruskal-Wallis H
• 0.004Kruskal-Wallis p-value
• 0.409Rank-biserial r
• 23.437Median diff G3-G1

Because 100 m swim time is skewed, nonparametric tests are used: Kruskal-Wallis H = 11.148 (p = 0.004) and Mann-Whitney G1 vs G3 is significant (p = 0.001), rank-biserial r 0.409.

Computed from illustrative synthetic data, not from a real study.

About Nonparametric Tests (Mann-Whitney and Kruskal-Wallis)

The Mann-Whitney test compares two independent groups and Kruskal-Wallis compares three or more, both rank-based without a normality assumption. They suit ordinal data, Likert scales, or numeric data that deviate from normality.

Steps

1. 1Check normality to justify a nonparametric test
2. 2Run Mann-Whitney U for two groups
3. 3Run Kruskal-Wallis H for three or more groups
4. 4Run pairwise post-hoc tests (Dunn or Mann-Whitney with Bonferroni correction)
5. 5Compute an effect size
6. 6Plot boxplots per group

Assumptions to check

• Observations are independent
• The variable is at least ordinal
• Group distributions have similar shape if interpreted as a difference in medians

Reading and reporting the results

Report the median of each group, the U or H statistic, p-value, and effect size. Use medians and interquartile ranges, not means, when describing the data.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as st

rng = np.random.default_rng(29)
swimming_stroke = rng.exponential(2.0, 40)
body_height = rng.exponential(3.0, 40)
x3 = rng.exponential(4.0, 40)
y = np.concatenate([swimming_stroke, body_height, x3])

print("Shapiro p (group 1):", round(st.shapiro(swimming_stroke).pvalue, 4))

u = st.mannwhitneyu(swimming_stroke, body_height, alternative="two-sided")
rbc = 1 - 2 * u.statistic / (len(swimming_stroke) * len(body_height))
print("Mann-Whitney U =", round(u.statistic, 1), "p =", round(u.pvalue, 4),
      "rank-biserial r =", round(rbc, 3))

h = st.kruskal(swimming_stroke, body_height, x3)
eps2 = h.statistic * (len(y) + 1) / (len(y) ** 2 - 1)
print("Kruskal-Wallis H =", round(h.statistic, 3), "p =", round(h.pvalue, 5),
      "epsilon2 =", round(eps2, 3))

pairs = [(0, 1), (0, 2), (1, 2)]
groups = [swimming_stroke, body_height, x3]
for i, j in pairs:
    pv = st.mannwhitneyu(groups[i], groups[j]).pvalue * len(pairs)
    print("Pair", i + 1, j + 1, "Bonferroni p =", round(min(pv, 1), 4))

plt.boxplot(groups)
plt.xticks([1, 2, 3], ["G1", "G2", "G3"])
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions