Ce TP bonus explore les notes d’algèbre sur trois années (2022, 2023, 2024) pour analyser s’il existe une différence significative entre les résultats des étudiants selon le sexe (M/F).
Nous utiliserons les outils vus dans les TPs précédents :
alg22 = read.csv2("alg22.csv")
alg23 = read.csv2("alg23.csv")
alg24 = read.csv2("alg24.csv")
cat("=== 2022 ===\n")
head(alg22)
cat("\n=== 2023 ===\n")
head(alg23)
cat("\n=== 2024 ===\n")
head(alg24)=== 2022 ===| Sexe | note22 | |
|---|---|---|
| <chr> | <dbl> | |
| 1 | F | 0.0 |
| 2 | M | 0.0 |
| 3 | M | 2.5 |
| 4 | M | 3.0 |
| 5 | M | 3.0 |
| 6 | M | 3.0 |
=== 2023 ===| Sexe | note23 | |
|---|---|---|
| <chr> | <dbl> | |
| 1 | F | 3.5 |
| 2 | M | 4.0 |
| 3 | M | 4.5 |
| 4 | M | 5.0 |
| 5 | F | 5.0 |
| 6 | M | 5.0 |
=== 2024 ===| Sexe | note24 | |
|---|---|---|
| <chr> | <dbl> | |
| 1 | M | 0.0 |
| 2 | M | 3.5 |
| 3 | M | 7.5 |
| 4 | M | 8.0 |
| 5 | F | 9.0 |
| 6 | F | 9.0 |
cat("Effectifs 2022 :", nrow(alg22))
cat("\nEffectifs 2023 :", nrow(alg23))
cat("\nEffectifs 2024 :", nrow(alg24))Effectifs 2022 : 88
Effectifs 2023 : 72
Effectifs 2024 : 48note22 = alg22$note22
sexe22 = alg22$Sexe
cat("Moyenne globale :", mean(note22, na.rm = TRUE))
cat("\nMoyenne F :", mean(note22[sexe22 == "F"], na.rm = TRUE))
cat("\nMoyenne M :", mean(note22[sexe22 == "M"], na.rm = TRUE))Moyenne globale : 10.85227
Moyenne F : 11.13333
Moyenne M : 10.7069boxplot(note22 ~ sexe22,
main = "Notes d'algèbre 2022 par sexe",
col = c("pink", "lightblue"),
ylab = "Note", xlab = "Sexe")
tapply(note22, sexe22, shapiro.test)$F
Shapiro-Wilk normality test
data: X[[i]]
W = 0.96625, p-value = 0.4424
$M
Shapiro-Wilk normality test
data: X[[i]]
W = 0.96015, p-value = 0.05433
anova(lm(note22 ~ sexe22))| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| <int> | <dbl> | <dbl> | <dbl> | <dbl> | |
| sexe22 | 1 | 3.595637 | 3.595637 | 0.2038419 | 0.652774 |
| Residuals | 86 | 1516.983908 | 17.639348 | NA | NA |
wilcox.test(note22 ~ sexe22)
Wilcoxon rank sum test with continuity correction
data: note22 by sexe22
W = 905.5, p-value = 0.7577
alternative hypothesis: true location shift is not equal to 0note23 = alg23$note23
sexe23 = alg23$Sexe
cat("Moyenne F :", mean(note23[sexe23 == "F"], na.rm = TRUE))
cat("\nMoyenne M :", mean(note23[sexe23 == "M"], na.rm = TRUE))Moyenne F : 11.46774
Moyenne M : 11.59756boxplot(note23 ~ sexe23,
main = "Notes d'algèbre 2023 par sexe",
col = c("pink", "lightblue"),
ylab = "Note", xlab = "Sexe")
tapply(note23, sexe23, shapiro.test)$F
Shapiro-Wilk normality test
data: X[[i]]
W = 0.9805, p-value = 0.8266
$M
Shapiro-Wilk normality test
data: X[[i]]
W = 0.96268, p-value = 0.195
anova(lm(note23 ~ sexe23))
wilcox.test(note23 ~ sexe23)| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| <int> | <dbl> | <dbl> | <dbl> | <dbl> | |
| sexe23 | 1 | 0.297502 | 0.297502 | 0.01587188 | 0.900106 |
| Residuals | 70 | 1312.077498 | 18.743964 | NA | NA |
Wilcoxon rank sum test with continuity correction
data: note23 by sexe23
W = 636.5, p-value = 0.9955
alternative hypothesis: true location shift is not equal to 0note24 = alg24$note24
sexe24 = alg24$Sexe
cat("Moyenne F :", mean(note24[sexe24 == "F"], na.rm = TRUE))
cat("\nMoyenne M :", mean(note24[sexe24 == "M"], na.rm = TRUE))Moyenne F : 12.8
Moyenne M : 12.95652boxplot(note24 ~ sexe24,
main = "Notes d'algèbre 2024 par sexe",
col = c("pink", "lightblue"),
ylab = "Note", xlab = "Sexe")
tapply(note24, sexe24, shapiro.test)$F
Shapiro-Wilk normality test
data: X[[i]]
W = 0.87419, p-value = 0.005257
$M
Shapiro-Wilk normality test
data: X[[i]]
W = 0.86408, p-value = 0.004951
anova(lm(note24 ~ sexe24))
wilcox.test(note24 ~ sexe24)| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| <int> | <dbl> | <dbl> | <dbl> | <dbl> | |
| sexe24 | 1 | 0.2934783 | 0.2934783 | 0.01881647 | 0.8914926 |
| Residuals | 46 | 717.4565217 | 15.5968809 | NA | NA |
Wilcoxon rank sum test with continuity correction
data: note24 by sexe24
W = 240, p-value = 0.3309
alternative hypothesis: true location shift is not equal to 0notes_all = c(note22, note23, note24)
sexe_all = c(as.character(sexe22), as.character(sexe23), as.character(sexe24))
annee_all = c(rep("2022", length(note22)), rep("2023", length(note23)), rep("2024", length(note24)))
sexe_all = factor(sexe_all)
annee_all = factor(annee_all)boxplot(notes_all ~ sexe_all,
main = "Notes d'algèbre (toutes années) par sexe",
col = c("pink", "lightblue"),
ylab = "Note", xlab = "Sexe")
On peut tester l’effet du sexe, de l’année, et de leur interaction :
anova(lm(notes_all ~ sexe_all * annee_all))| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| <int> | <dbl> | <dbl> | <dbl> | <dbl> | |
| sexe_all | 1 | 4.786533 | 4.786533 | 0.2726279 | 0.60214648 |
| annee_all | 2 | 122.684828 | 61.342414 | 3.4938968 | 0.03223111 |
| sexe_all:annee_all | 2 | 3.818403 | 1.909202 | 0.1087429 | 0.89701345 |
| Residuals | 202 | 3546.517928 | 17.557019 | NA | NA |
# Sans interaction
anova(lm(notes_all ~ sexe_all + annee_all))| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| <int> | <dbl> | <dbl> | <dbl> | <dbl> | |
| sexe_all | 1 | 4.786533 | 4.786533 | 0.2750311 | 0.6005461 |
| annee_all | 2 | 122.684828 | 61.342414 | 3.5246949 | 0.0312679 |
| Residuals | 204 | 3550.336331 | 17.403609 | NA | NA |
interaction.plot(annee_all, sexe_all, notes_all,
main = "Interaction Année × Sexe",
col = c("pink", "lightblue"), lwd = 2,
xlab = "Année", ylab = "Moyenne des notes")
kruskal.test(notes_all ~ sexe_all)
Kruskal-Wallis rank sum test
data: notes_all by sexe_all
Kruskal-Wallis chi-squared = 0.021761, df = 1, p-value = 0.8827| Année | Méthode | Conclusion |
|---|---|---|
| 2022 | ANOVA + Wilcoxon | À interpréter selon les p-values |
| 2023 | ANOVA + Wilcoxon | À interpréter selon les p-values |
| 2024 | ANOVA + Wilcoxon | À interpréter selon les p-values |
| Toutes | ANOVA 2 facteurs + Kruskal-Wallis | Effet global |
Points clés :