class: center, middle, inverse, title-slide # Bases du modèle linéaire ## Chapitre V - ANOVA à deux facteurs BIE ### Antoine Bichat - Émilie Lebarbier<br>AgroParisTech --- # Chargement des données ```r champagnes <- read.table('champagnes.txt', header = T) str(champagnes) ``` ``` 'data.frame': 42 obs. of 3 variables: $ Juge : int 1 1 1 2 2 2 3 3 3 4 ... $ Champagne: Factor w/ 7 levels "A","B","C","D",..: 3 4 7 1 4 5 2 4 6 1 ... $ Note : int 36 16 19 22 25 29 24 19 26 27 ... ``` -- # Transformation en facteur ```r champagnes$Juge <- as.factor(champagnes$Juge) str(champagnes) ``` ``` 'data.frame': 42 obs. of 3 variables: $ Juge : Factor w/ 14 levels "1","2","3","4",..: 1 1 1 2 2 2 3 3 3 4 ... $ Champagne: Factor w/ 7 levels "A","B","C","D",..: 3 4 7 1 4 5 2 4 6 1 ... $ Note : int 36 16 19 22 25 29 24 19 26 27 ... ``` --- # Tables ```r table(champagnes$Juge) ``` ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ``` ```r table(champagnes$Champagne) ``` ``` A B C D E F G 6 6 6 6 6 6 6 ``` ```r table(champagnes$Juge, champagnes$Champagne) ``` ``` A B C D E F G 1 0 0 1 1 0 0 1 2 1 0 0 1 1 0 0 3 0 1 0 1 0 1 0 4 1 0 0 1 1 0 0 5 0 1 0 0 1 0 1 6 1 1 1 0 0 0 0 7 1 0 0 0 0 1 1 8 0 1 0 1 0 1 0 9 0 0 1 1 0 0 1 10 1 0 0 0 0 1 1 11 0 1 0 0 1 0 1 12 0 0 1 0 1 1 0 13 1 1 1 0 0 0 0 14 0 0 1 0 1 1 0 ``` --- # Note par champagne ```r by(champagnes$Note, champagnes$Champagne, mean) ``` ``` champagnes$Champagne: A [1] 29.66667 -------------------------------------------------------- champagnes$Champagne: B [1] 28.66667 -------------------------------------------------------- champagnes$Champagne: C [1] 32.83333 -------------------------------------------------------- champagnes$Champagne: D [1] 19.83333 -------------------------------------------------------- champagnes$Champagne: E [1] 26.16667 -------------------------------------------------------- champagnes$Champagne: F [1] 30.83333 -------------------------------------------------------- champagnes$Champagne: G [1] 25.5 ``` --- # Avec le tidyverse ```r library(tidyverse) champagnes %>% group_by(Champagne) %>% summarise(Moyenne = mean(Note), Min = min(Note), Median = median(Note), Max = max(Note)) %>% arrange(desc(Moyenne)) ``` ``` # A tibble: 7 x 5 Champagne Moyenne Min Median Max <fct> <dbl> <int> <dbl> <int> 1 C 32.8 26 35 36 2 F 30.8 25 31.5 38 3 A 29.7 22 29.5 37 4 B 28.7 24 28.5 34 5 E 26.2 19 24.5 37 6 G 25.5 19 26.5 33 7 D 19.8 16 20 25 ``` --- # Note par juge ```r ggplot(champagnes) + aes(x = Juge, y = Note, color = Juge) + geom_label(aes(label = Champagne), size = 5) + theme_minimal() + theme(legend.position = "none") ``` <img src="chap5_files/figure-html/unnamed-chunk-5-1.png" width="648" style="display: block; margin: auto;" /> --- # Modèle d'ANOVA à deux facteurs sans intercation ```r modele <- lm(Note ~ Champagne + Juge, data = champagnes) modele ``` ``` Call: lm(formula = Note ~ Champagne + Juge, data = champagnes) Coefficients: (Intercept) ChampagneB ChampagneC ChampagneD ChampagneE 26.69048 -2.64286 3.85714 -7.92857 -4.07143 ChampagneF ChampagneG Juge2 Juge3 Juge4 2.28571 -5.00000 2.64286 -0.92857 -0.02381 Juge5 Juge6 Juge7 Juge8 Juge9 6.54762 5.57143 6.54762 3.40476 1.33333 Juge10 Juge11 Juge12 Juge13 Juge14 -0.78571 9.21429 3.61905 3.90476 -0.71429 ``` --- # Graphes de diagnostic ```r par(mfrow = c(2, 2)) plot(modele) ``` <img src="chap5_files/figure-html/diag-1.png" width="504" style="display: block; margin: auto;" /> --- # Test du modèle ```r modele_0 <- lm(Note ~ 1, data = champagnes) anova(modele_0, modele) ``` ``` Analysis of Variance Table Model 1: Note ~ 1 Model 2: Note ~ Champagne + Juge Res.Df RSS Df Sum of Sq F Pr(>F) 1 41 1585.64 2 22 571.05 19 1014.6 2.0573 0.05296 . --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ``` --- # Test des facteurs ```r anova(modele) ``` ``` Analysis of Variance Table Response: Note Df Sum Sq Mean Sq F value Pr(>F) Champagne 6 660.14 110.024 4.2387 0.005529 ** Juge 13 354.45 27.266 1.0504 0.443958 Residuals 22 571.05 25.957 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ``` -- ```r car::Anova(modele) ``` ``` Anova Table (Type II tests) Response: Note Sum Sq Df F value Pr(>F) Champagne 492.29 6 3.1609 0.02169 * Juge 354.45 13 1.0504 0.44396 Residuals 571.05 22 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ``` --- # Coefficients ```r summary(modele) ``` ``` Call: lm(formula = Note ~ Champagne + Juge, data = champagnes) Residuals: Min 1Q Median 3Q Max -7.3333 -2.7440 -0.5357 3.1310 9.9762 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 26.69048 4.00855 6.658 1.08e-06 *** ChampagneB -2.64286 3.33531 -0.792 0.4366 ChampagneC 3.85714 3.33531 1.156 0.2599 ChampagneD -7.92857 3.33531 -2.377 0.0266 * ChampagneE -4.07143 3.33531 -1.221 0.2351 ChampagneF 2.28571 3.33531 0.685 0.5003 ChampagneG -5.00000 3.33531 -1.499 0.1481 Juge2 2.64286 4.44708 0.594 0.5584 Juge3 -0.92857 4.44708 -0.209 0.8365 Juge4 -0.02381 4.44708 -0.005 0.9958 Juge5 6.54762 4.44708 1.472 0.1551 Juge6 5.57143 4.44708 1.253 0.2234 Juge7 6.54762 4.44708 1.472 0.1551 Juge8 3.40476 4.44708 0.766 0.4520 Juge9 1.33333 4.15986 0.321 0.7516 Juge10 -0.78571 4.44708 -0.177 0.8614 Juge11 9.21429 4.44708 2.072 0.0502 . Juge12 3.61905 4.44708 0.814 0.4245 Juge13 3.90476 4.44708 0.878 0.3894 Juge14 -0.71429 4.44708 -0.161 0.8739 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 5.095 on 22 degrees of freedom Multiple R-squared: 0.6399, Adjusted R-squared: 0.3288 F-statistic: 2.057 on 19 and 22 DF, p-value: 0.05296 ``` --- # Moyennes ajustées des champagnes ```r lsmeans <- lsmeans::lsmeans(modele, pairwise ~ Champagne, adjust = "bonferroni") lsmeans$lsmeans ``` ``` Champagne lsmean SE df lower.CL upper.CL A 29.6 2.32 22 24.8 34.4 B 26.9 2.32 22 22.1 31.7 C 33.4 2.32 22 28.6 38.2 D 21.6 2.32 22 16.8 26.5 E 25.5 2.32 22 20.7 30.3 F 31.9 2.32 22 27.0 36.7 G 24.6 2.32 22 19.8 29.4 Results are averaged over the levels of: Juge Confidence level used: 0.95 ``` --- # Comparaison des champagnes ```r lsmeans$contrasts ``` ``` contrast estimate SE df t.ratio p.value A - B 2.643 3.34 22 0.792 1.0000 A - C -3.857 3.34 22 -1.156 1.0000 A - D 7.929 3.34 22 2.377 0.5579 A - E 4.071 3.34 22 1.221 1.0000 A - F -2.286 3.34 22 -0.685 1.0000 A - G 5.000 3.34 22 1.499 1.0000 B - C -6.500 3.34 22 -1.949 1.0000 B - D 5.286 3.34 22 1.585 1.0000 B - E 1.429 3.34 22 0.428 1.0000 B - F -4.929 3.34 22 -1.478 1.0000 B - G 2.357 3.34 22 0.707 1.0000 C - D 11.786 3.34 22 3.534 0.0392 C - E 7.929 3.34 22 2.377 0.5579 C - F 1.571 3.34 22 0.471 1.0000 C - G 8.857 3.34 22 2.656 0.3034 D - E -3.857 3.34 22 -1.156 1.0000 D - F -10.214 3.34 22 -3.062 0.1198 D - G -2.929 3.34 22 -0.878 1.0000 E - F -6.357 3.34 22 -1.906 1.0000 E - G 0.929 3.34 22 0.278 1.0000 F - G 7.286 3.34 22 2.184 0.8374 Results are averaged over the levels of: Juge P value adjustment: bonferroni method for 21 tests ``` --- # Avec {broom} ```r library(broom) lsmeans$lsmeans %>% tidy() %>% arrange(desc(estimate)) ``` ``` # A tibble: 7 x 6 Champagne estimate std.error df conf.low conf.high <fct> <dbl> <dbl> <dbl> <dbl> <dbl> 1 C 33.4 2.32 22 28.6 38.2 2 F 31.9 2.32 22 27.0 36.7 3 A 29.6 2.32 22 24.8 34.4 4 B 26.9 2.32 22 22.1 31.7 5 E 25.5 2.32 22 20.7 30.3 6 G 24.6 2.32 22 19.8 29.4 7 D 21.6 2.32 22 16.8 26.5 ``` -- ```r lsmeans$contrasts %>% tidy() %>% filter(p.value < 0.05) ``` ``` # A tibble: 1 x 7 level1 level2 estimate std.error df statistic p.value <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> 1 C D 11.8 3.34 22 3.53 0.0392 ``` --- class: center, middle, inverse # Des questions ? .footnote[Slides créées avec le package <b><a href="https://github.com/yihui/xaringan" target="_blank">xaringan</a></b>.]