Effectiveness of problem-based, cooperative and lecture methods on physics test scores

ANOVA, ANCOVA and Tukey Post Hoc Test for Education and Learning

Field: Education and LearningLevel: Undergraduate thesis (S1)Method: ANOVA, ANCOVA and Tukey Post Hoc Test

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Comparing mean physics test score across teaching method groups with ANOVA, ANCOVA adjusted for pretest score, and Tukey tests using synthetic data for demonstration. One-way ANOVA compares the mean of a numeric outcome across three or more groups, while ANCOVA makes the same comparison after adjusting for a covariate such as a pretest score. It suits experimental or quasi-experimental theses comparing treatments, methods or varieties, with the Tukey post hoc test showing which pairs differ.

Effectiveness of problem-based, cooperative and lecture methods on physics test scores: result sheet

Project info

Field of studyEducation and Learning
LevelUndergraduate thesis (S1)
Method typeInferential Statistics
Estimated build time± 3 working days
Toolsstats::aov, stats::TukeyHSD, car::leveneTest, car::Anova, emmeans::emmeans, ggplot2
PriceUS$19 - US$125

Research goal

Comparing mean physics test score across teaching method groups with ANOVA, ANCOVA adjusted for pretest score, and Tukey tests using synthetic data for demonstration.

Variables

Role	Variable	Unit
Main	Physics test score	score
Supporting 1	Teaching method	group
Supporting 2	Pretest score	score

Example result

<0.001ANOVA p-value
0.168Eta squared
<0.001ANCOVA group p-value
0.231Partial eta2 (ANCOVA)
0.084Levene p-value
0.705Slope homog. p-value

ANOVA shows that Physics test score differs significantly across levels of Teaching method (F = 19.86, p < 0.001, eta2 = 0.168); Tukey finds 2 of 3 pairs different. Adjusting for Pretest score (ANCOVA), the group effect remains significant (p < 0.001, partial eta2 = 0.231), highest in Lecture; Levene p = 0.084.

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

About ANOVA, ANCOVA and Tukey Post Hoc Test

One-way ANOVA compares the mean of a numeric outcome across three or more groups, while ANCOVA makes the same comparison after adjusting for a covariate such as a pretest score. It suits experimental or quasi-experimental theses comparing treatments, methods or varieties, with the Tukey post hoc test showing which pairs differ.

Steps

1Prepare the data with a group factor and the outcome, then summarise the mean and standard deviation per group
2Run one-way ANOVA with aov() and compute eta squared
3Check assumptions: homogeneity of variance with car::leveneTest and residual normality with shapiro.test
4Run the TukeyHSD post hoc test for all pairs of groups
5Test homogeneity of regression slopes (covariate x group interaction) before ANCOVA
6Run ANCOVA with type II car::Anova and compute partial eta squared
7Obtain covariate-adjusted means with emmeans and their pairwise comparisons

Assumptions to check

Observations are independent and each unit belongs to one group only
Residuals are approximately normal within each group
Group variances are homogeneous (non-significant Levene test)
For ANCOVA: the covariate relates linearly to the outcome with equal slopes across groups

Reading and reporting the results

Report the ANOVA F, degrees of freedom, p-value and eta squared, then the pairs that differ according to Tukey with their differences and confidence intervals. For ANCOVA report the group effect after adjusting for the covariate, partial eta squared, the adjusted group means and the slope homogeneity test.

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: ANOVA, ANCOVA and Tukey Post Hoc Test
suppressPackageStartupMessages({
  library(ggplot2)
  library(patchwork)
  library(car)
  library(emmeans)
  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: tiga kelompok perlakuan dengan satu kovariat ----
n <- 200
lv <- c("A", "B", "C")
d <- data.frame(teaching_method = factor(sample(rep(lv, length.out = n)), levels = lv),
                pretest_score = round(rnorm(n, 30, 6), 2))
z2 <- as.numeric(scale(d$pretest_score))
efek <- c(0, runif(1, 0.25, 0.6), runif(1, 0.55, 1.1))[sample(3)]   # beda rata-rata antarkelompok (dalam SD)
b_kov <- runif(1, 0.35, 0.7)                                         # pengaruh kovariat
d$physics_test_score <- round(100 + 15 * (efek[as.integer(d$teaching_method)] - mean(efek) + b_kov * z2 +
                                    rnorm(n, 0, runif(1, 0.55, 0.8))), 2)
write.csv(d, "data_contoh.csv", row.names = FALSE)

# ---- Analisis 1: ANOVA satu arah ----
fit_aov <- aov(physics_test_score ~ teaching_method, data = d)
tab_aov <- summary(fit_aov)[[1]]
print(tab_aov)
print(aggregate(physics_test_score ~ teaching_method, data = d, FUN = function(v) c(rerata = mean(v), sd = sd(v), n = length(v))))

# ---- Uji asumsi ANOVA ----
lev <- car::leveneTest(physics_test_score ~ teaching_method, data = d, center = median)   # homogenitas varians (Levene/Brown-Forsythe)
sw <- shapiro.test(residuals(fit_aov))                              # normalitas residual
print(lev); print(sw)
eta2 <- tab_aov[1, "Sum Sq"] / sum(tab_aov[, "Sum Sq"])             # eta kuadrat (= partial eta2 pada ANOVA satu arah)

# ---- Uji lanjut Tukey HSD ----
tk <- TukeyHSD(fit_aov, conf.level = 0.95)
print(tk)
tkd <- as.data.frame(tk[[1]])
names(tkd) <- c("selisih", "bawah", "atas", "p_adj")

# ---- Analisis 2: ANCOVA (kovariat pretest_score) ----
fit_slope <- lm(physics_test_score ~ pretest_score * teaching_method, data = d)                  # uji homogenitas kemiringan regresi
a_slope <- car::Anova(fit_slope, type = 2)
print(a_slope)
p_slope <- a_slope[3, "Pr(>F)"]
fit_anc <- lm(physics_test_score ~ pretest_score + teaching_method, data = d)
a_anc <- car::Anova(fit_anc, type = 2)
print(a_anc)
p_anc <- a_anc[2, "Pr(>F)"]
peta2 <- a_anc[2, "Sum Sq"] / (a_anc[2, "Sum Sq"] + a_anc["Residuals", "Sum Sq"])   # partial eta kuadrat kelompok
em <- emmeans::emmeans(fit_anc, specs = "teaching_method")                   # rata-rata terkoreksi kovariat
print(em)
print(pairs(em, adjust = "tukey"))
emd <- as.data.frame(summary(em))
names(emd)[1:6] <- c("kelompok", "rerata", "se", "db", "bawah", "atas")


# ---- Grafik ----
bungkus <- scales::label_wrap(12)
pendek <- function(s, w = 12) ifelse(nchar(s) > w, paste0(trimws(substr(s, 1, w - 1)), "."), s)
rata <- aggregate(physics_test_score ~ teaching_method, data = d, FUN = mean)
p1 <- ggplot(d, aes(teaching_method, physics_test_score)) +
  geom_boxplot(aes(fill = teaching_method), alpha = 0.25, outlier.shape = NA, colour = warna$redup, width = 0.6) +
  geom_jitter(aes(colour = teaching_method), width = 0.15, alpha = 0.5, size = 1.3) +
  geom_point(data = rata, shape = 23, size = 3.2, fill = warna$panel, colour = warna$teks, stroke = 1.1) +
  scale_fill_manual(values = pal[1:3], guide = "none") +
  scale_colour_manual(values = pal[1:3], guide = "none") +
  scale_x_discrete(labels = bungkus) +
  labs(title = "Distribution by group (diamond = mean)", x = NULL, y = "physics_test_score")
pasangan <- combn(lv, 2)
tkd$pasangan <- factor(paste(pendek(pasangan[2, ]), "-", pendek(pasangan[1, ])),
                       levels = rev(paste(pendek(pasangan[2, ]), "-", pendek(pasangan[1, ]))))
tkd$nyata <- ifelse(tkd$p_adj < 0.05, "p < 0.05", "n.s.")
p2 <- ggplot(tkd, aes(selisih, pasangan, colour = nyata)) +
  geom_vline(xintercept = 0, linetype = "dashed", colour = warna$redup) +
  geom_errorbarh(aes(xmin = bawah, xmax = atas), height = 0.25, linewidth = 0.9) +
  geom_point(size = 2.8) +
  scale_colour_manual(values = c("p < 0.05" = pal[2], "n.s." = warna$redup), name = NULL, drop = FALSE) +
  labs(title = "Tukey HSD: mean differences (95% CI)", x = "Difference in physics_test_score", y = NULL) +
  theme(legend.position = "bottom")
garis <- expand.grid(pretest_score = seq(min(d$pretest_score), max(d$pretest_score), length.out = 30), teaching_method = factor(lv, levels = lv))
garis$prediksi <- predict(fit_anc, newdata = garis)
p3 <- ggplot(d, aes(pretest_score, physics_test_score, colour = teaching_method)) +
  geom_point(alpha = 0.45, size = 1.3) +
  geom_line(data = garis, aes(y = prediksi), linewidth = 1.1) +
  scale_colour_manual(values = pal[1:3], name = NULL, labels = pendek) +
  labs(title = "ANCOVA: parallel fitted lines", x = "pretest_score", y = "physics_test_score") +
  theme(legend.position = "bottom")
mentah <- aggregate(physics_test_score ~ teaching_method, data = d, FUN = function(v) c(m = mean(v), se = sd(v) / sqrt(length(v))))
dm <- rbind(data.frame(kelompok = factor(lv, levels = lv), rerata = mentah$physics_test_score[, "m"],
                       bawah = mentah$physics_test_score[, "m"] - 1.96 * mentah$physics_test_score[, "se"],
                       atas = mentah$physics_test_score[, "m"] + 1.96 * mentah$physics_test_score[, "se"], jenis = "Raw mean"),
            data.frame(kelompok = emd$kelompok, rerata = emd$rerata, bawah = emd$bawah, atas = emd$atas,
                       jenis = "Adjusted mean"))
dm$jenis <- factor(dm$jenis, levels = c("Raw mean", "Adjusted mean"))
p4 <- ggplot(dm, aes(kelompok, rerata, colour = jenis)) +
  geom_pointrange(aes(ymin = bawah, ymax = atas), position = position_dodge(width = 0.5), size = 0.45, linewidth = 0.9) +
  scale_colour_manual(values = c("Raw mean" = warna$redup, "Adjusted mean" = pal[4]), name = NULL) +
  scale_x_discrete(labels = bungkus) +
  labs(title = "Raw vs covariate-adjusted means", x = NULL, y = "physics_test_score") +
  theme(legend.position = "bottom")
p_hasil <- if (tata == 1) (p1 | p2) / (p3 | p4) else (p1 | p3) / (p4 | p2)

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$19

excl. 11% VAT

Duration: 3 working days

Output: R files + result figures

Deliverables

Fully commented R code (.R) for ANOVA, ANCOVA and Tukey Post Hoc Test
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$56

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$125

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. ANOVA, ANCOVA and Tukey Post Hoc Test 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$19, Package 2 (your data analysis and interpretation) US$56 and Package 3 (full guidance) US$125, excluding 11% VAT. Larger datasets, extra methods or tight deadlines adjust the quote after a short consultation.

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The result sheet uses illustrative synthetic data. R is a programming language of the R Foundation project; RStudio and Posit are trademarks of Posit PBC.

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