Differences in class participation among grade 10, 11 and 12 students using Kruskal-Wallis

Nonparametric Tests (Mann-Whitney and Kruskal-Wallis) for Education and Learning

Field: Education and LearningLevel: Undergraduate thesis (S1)Method: Nonparametric Tests (Mann-Whitney and Kruskal-Wallis)

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Comparing participation score across grade level groups with Mann-Whitney and Kruskal-Wallis tests and Spearman correlation with weekly reading hours, illustrated with synthetic data. Nonparametric tests compare distributions or medians across groups without assuming normality: Kruskal-Wallis for three or more groups, Mann-Whitney for two groups, plus Spearman rank correlation. They suit theses with ordinal scores, Likert scales, small samples or heavily skewed data.

Differences in class participation among grade 10, 11 and 12 students using Kruskal-Wallis: result sheet

Project info

Field of studyEducation and Learning
LevelUndergraduate thesis (S1)
Method typeInferential Statistics
Estimated build time± 3 working days
Toolsstats::kruskal.test, stats::pairwise.wilcox.test, stats::wilcox.test, stats::cor.test, ggplot2
PriceUS$16 - US$103

Research goal

Comparing participation score across grade level groups with Mann-Whitney and Kruskal-Wallis tests and Spearman correlation with weekly reading hours, illustrated with synthetic data.

Variables

Role	Variable	Unit
Main	Participation score	score
Supporting 1	Grade level	group
Supporting 2	Weekly reading hours	hours

Example result

46.314Kruskal-Wallis H
<0.001Kruskal-Wallis p-value
0.126Epsilon squared
<0.001Mann-Whitney p-value
0.415Effect size r
0.452Spearman rho

Kruskal-Wallis shows that Participation score differs significantly across Grade level groups (H = 46.31, p < 0.001, epsilon2 = 0.126). Mann-Whitney between Grade 12 and Grade 10 is significant (p < 0.001) with a medium effect (r = 0.41). The Spearman correlation of Participation score with Weekly reading hours is 0.45 (p < 0.001).

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

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

Nonparametric tests compare distributions or medians across groups without assuming normality: Kruskal-Wallis for three or more groups, Mann-Whitney for two groups, plus Spearman rank correlation. They suit theses with ordinal scores, Likert scales, small samples or heavily skewed data.

Steps

1Check normality in each group with Shapiro-Wilk to justify a nonparametric test
2Summarise the median and IQR per group
3Run kruskal.test and compute the epsilon squared effect size
4Run pairwise.wilcox.test comparisons with Holm correction
5Run Mann-Whitney (wilcox.test) between the two most different groups and compute the effect size r
6Compute the Spearman correlation between the outcome and another continuous variable

Assumptions to check

Observations are independent within and between groups
The outcome is at least ordinal
To interpret results as median differences, group distributions have a similar shape

Reading and reporting the results

Report the Kruskal-Wallis H, degrees of freedom, p-value and epsilon squared, then the pairs that differ in the corrected pairwise Wilcoxon tests. For Mann-Whitney report W, p and r (0.1 small, 0.3 medium, 0.5 large), and the Spearman rho with its p-value.

Example R code

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

Show code

# Contoh kode R: Nonparametric Tests (Mann-Whitney and Kruskal-Wallis)
suppressPackageStartupMessages({
  library(ggplot2)
  library(patchwork)
  library(scales)
})
set.seed(42)
# ---- Gaya grafik ----
pal <- c("#1f6feb", "#e8590c", "#2f9e44", "#ae3ec9", "#f59f00")
warna <- list(bg = "#f4f6fa", panel = "#ffffff", teks = "#1f2933", redup = "#5f6b78", grid = "#e3e8ee", bar = "#1d3557")
tata <- 1
theme_set(theme_minimal(base_size = 11) + theme(legend.position = "bottom"))

# ---- Data sintetis: skor menceng pada tiga kelompok + satu variabel kontinu ----
n <- 200
lv <- c("A", "B", "C")
d <- data.frame(grade_level = factor(sample(rep(lv, length.out = n)), levels = lv),
                weekly_reading_hours = round(pmax(rnorm(n, 30, 6), 0), 2))
z2 <- as.numeric(scale(d$weekly_reading_hours))
efek <- c(0, runif(1, 0.3, 0.6), runif(1, 0.6, 1.1))[sample(3)]      # pergeseran lokasi antarkelompok (dalam SD)
bentuk <- runif(1, 1.5, 3)
galat <- (rgamma(n, shape = bentuk) - bentuk) / sqrt(bentuk)          # galat menceng kanan
z <- efek[as.integer(d$grade_level)] - mean(efek) + runif(1, 0.25, 0.5) * z2 + galat * runif(1, 0.7, 0.9)
d$participation_score <- pmax(100 + 15 * z, 0)
d$participation_score <- if (15 >= 3) round(d$participation_score) else round(d$participation_score, 2)    # skor bulat bila skalanya lebar
write.csv(d, "data_contoh.csv", row.names = FALSE)

# ---- Pemeriksaan normalitas (alasan memakai uji nonparametrik) ----
sw <- tapply(d$participation_score, d$grade_level, function(v) shapiro.test(v)$p.value)
print(sw)
print(aggregate(participation_score ~ grade_level, data = d, FUN = function(v) c(median = median(v), IQR = IQR(v), n = length(v))))

# ---- Kruskal-Wallis + ukuran efek epsilon kuadrat ----
kw <- kruskal.test(participation_score ~ grade_level, data = d)
print(kw)
eps2 <- unname(kw$statistic) / (nrow(d) - 1)

# ---- Perbandingan berpasangan Wilcoxon (koreksi Holm) ----
pw <- pairwise.wilcox.test(d$participation_score, d$grade_level, p.adjust.method = "holm", exact = FALSE)
print(pw)

# ---- Mann-Whitney: dua kelompok dengan median paling jauh + ukuran efek r ----
med <- tapply(d$participation_score, d$grade_level, median)
ekstrem <- names(c(which.min(med), which.max(med)))
if (ekstrem[1] == ekstrem[2]) ekstrem <- lv[c(1, 3)]
sub <- droplevels(d[d$grade_level %in% ekstrem, ])
mw <- wilcox.test(participation_score ~ grade_level, data = sub, exact = FALSE)
print(mw)
z_mw <- qnorm(mw$p.value / 2)
r_mw <- abs(z_mw) / sqrt(nrow(sub))

# ---- Korelasi peringkat Spearman ----
sp <- cor.test(d$participation_score, d$weekly_reading_hours, method = "spearman", exact = FALSE)
print(sp)


# ---- Grafik ----
bungkus <- scales::label_wrap(12)
pendek <- function(s, w = 12) ifelse(nchar(s) > w, paste0(trimws(substr(s, 1, w - 1)), "."), s)
dmed <- data.frame(grade_level = factor(names(med), levels = lv), median = as.numeric(med))
p1 <- ggplot(d, aes(grade_level, participation_score)) +
  geom_violin(aes(fill = grade_level), alpha = 0.3, colour = NA, trim = TRUE) +
  geom_boxplot(width = 0.18, outlier.size = 0.8, colour = warna$redup, fill = warna$panel, alpha = 0.8) +
  geom_point(data = dmed, aes(y = median), shape = 21, size = 3, fill = pal[2], colour = warna$teks) +
  scale_fill_manual(values = pal[c(1, 3, 4)], guide = "none") +
  scale_x_discrete(labels = bungkus) +
  labs(title = "Distribution by group (dot = median)", x = NULL, y = "participation_score")
mp <- matrix(NA_real_, 3, 3, dimnames = list(lv, lv))
mp[rownames(pw$p.value), colnames(pw$p.value)] <- pw$p.value
mp[upper.tri(mp)] <- t(mp)[upper.tri(mp)]
dp <- expand.grid(a = 1:3, b = 1:3)
dp$p <- mp[cbind(dp$a, dp$b)]
dp$teks <- ifelse(is.na(dp$p), "-", ifelse(dp$p < 0.001, "<0.001", sprintf("%.3f", dp$p)))
dp$skor <- ifelse(is.na(dp$p), NA, pmin(-log10(dp$p), 6))
dp$a <- factor(pendek(lv)[dp$a], levels = pendek(lv)); dp$b <- factor(pendek(lv)[dp$b], levels = rev(pendek(lv)))
p2 <- ggplot(dp, aes(a, b, fill = skor)) +
  geom_tile(colour = warna$panel, linewidth = 1.2) +
  geom_label(aes(label = teks), fill = warna$panel, colour = warna$teks, size = 3.2, label.size = 0, alpha = 0.85) +
  scale_fill_gradient(low = warna$grid, high = pal[2], na.value = warna$panel, limits = c(0, 6), guide = "none") +
  scale_x_discrete(labels = bungkus) + scale_y_discrete(labels = bungkus) +
  labs(title = "Pairwise Wilcoxon p-values (Holm)", x = NULL, y = NULL) +
  theme(panel.grid = element_blank())
dr <- data.frame(ry = rank(d$participation_score), rx = rank(d$weekly_reading_hours), kelompok = d$grade_level)
p3 <- ggplot(dr, aes(rx, ry)) +
  geom_point(aes(colour = kelompok), alpha = 0.55, size = 1.4) +
  geom_smooth(method = "lm", formula = y ~ x, colour = warna$teks, fill = warna$redup, alpha = 0.2, linewidth = 1) +
  scale_colour_manual(values = pal[c(1, 3, 4)], name = NULL, labels = pendek) +
  labs(title = sprintf("Spearman rank scatter (rho = %.2f)", sp$estimate), x = "Rank of weekly_reading_hours", y = "Rank of participation_score") +
  theme(legend.position = "bottom")
p_hasil <- if (tata == 1) p1 | (p2 / p3) else (p2 / p3) | p1

print(p_hasil)

The project file you can download

The original project file is available. It is not just the picture above: you get the working R project. It can be downloaded after payment, and we send it by WhatsApp or email.

ZIP: analisis.R + data_contoh.csv + BACA-DULU.txt

What is inside the ZIP

The complete analysis script (analisis.R), commented step by step, ready to run in RStudio.
A sample dataset (data_contoh.csv) so the script runs straight away.
A short guide (BACA-DULU.txt): which packages to install, how to run it and how to swap in your own data.

Packages and prices

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

Package 1

Code and Explanation

US$16

excl. 11% VAT

Duration: 3 working days

Output: R files + result figures

Deliverables

Fully commented R code (.R) for Nonparametric Tests (Mann-Whitney and Kruskal-Wallis)
Example data and step-by-step run instructions
Ready-to-use result figures and metrics table
Short explanation of the method, its assumptions and how to read the results

Choose Package 1

Package 2 · most chosen

Your Data Analysis + Interpretation

US$47

excl. 11% VAT

Duration: 7 working days

Output: Code + analysis + interpretation notes

Includes all of Package 1, plus

Adapting the code to your own research dataset (CSV or Excel)
Assumption checks, result validation and data cleaning
Tables and figures formatted for your manuscript
Interpretation notes for the methods and discussion sections, for you to write up in your own words

Choose Package 2

Package 3

Full Guidance

US$103

excl. 11% VAT

Duration: 12-15 working days

Output: Code + analysis + guidance until ready to present

Includes all of Packages 1 & 2, plus

Comparison against one alternative method with the reasoning for the choice
Two 60-minute online coaching sessions so you fully understand the code and results
Revisions following your supervisor feedback (up to 3 rounds)
Practice Q&A to prepare for your seminar and defence
Full documentation (README, R package list (sessionInfo)) so the results can be reproduced

Choose Package 3

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

Do I get the real project file?

Yes. The original project file is a ZIP containing the complete analisis.R script, a data_contoh.csv sample dataset and a BACA-DULU.txt guide. It can be downloaded after payment, and we send it by WhatsApp or email. For your own data (Package 2 and 3) the script is adapted to your dataset.

Is this suitable for a Undergraduate thesis (S1)?

Yes. Nonparametric Tests (Mann-Whitney and Kruskal-Wallis) is commonly used at this level in Education and Learning. We adapt the analysis to your research question, your own data and your supervisor's requirements.

Is the result sheet real data?

No. The sheet is computed from illustrative synthetic data so you can see the kind of output R Studio gives. For your order we run the same method on your own data.

Will I understand the code?

That is the point of the packages. Every script is commented, and Package 3 includes two coaching sessions plus practice questions so you can explain the method and the results at your seminar and defence.

How is the price decided?

Each project has three packages: Package 1 (code and explanation) US$16, Package 2 (your data analysis and interpretation) US$47 and Package 3 (full guidance) US$103, excluding 11% VAT. Larger datasets, extra methods or tight deadlines adjust the quote after a short consultation.

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