Data
1. Scatterplot among contracts and sales
2. Pearson correlation between sales and contracts
3. Contingency frequency table
4. Contingency frequency table (2nd option)
5. MANOVA
6. Homogeneity of dependent variables between levels of factors
7. Homogeneity of covariance of dependent variables among all levels of the interaction of the factors
8. Stepdown analysis
Remark: Mahalanobis distance
The above example is contained in the paragraph 5.6 of the book "Στατιστική ανάλυση με τη γλώσσα R" (in Greek, ISBN: 978-960-93-9445-1) published in Thessaloniki, 2017.
perform.A = c(63.3, 68.3, 86.7, 52.8, 75, 58, 69.5, 32.7, 60.9, 58.2)
contracts.A = c(24, 30, 33, 19, 30, 22, 28, 13, 17, 18)
A.gender = c(1, 1, 1, 0, 0, 0, 1, 0, 0, 0)
perform.B = c(72.8, 88.2, 80.8, 71.3, 81.5, 47.6, 81, 81.4, 83, 76, 74.5)
contracts.B = c(25, 26, 29, 22, 41, 15, 40, 37, 39, 29, 26)
B.gender = c(1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1)
perform.C = c(82.3, 89.7, 81, 85.1, 74.1, 75.9, 74.7, 81.1, 76.4, 81.8)
contracts.C = c(38, 42, 48, 42, 40, 45, 33, 31, 47, 38)
C.gender = c(0, 0, 1, 0, 1, 1, 1, 1, 1, 0)
sales = c(perform.A, perform.B, perform.C)
contracts = c(contracts.A , contracts.B , contracts.C)
gender = c(A.gender, B.gender, C.gender)
group = c(rep(1, 10), rep(2, 11), rep(3, 10))
gender =factor(gender, levels = c(0,1), labels=c("Woman", "Man"))
group = factor(group, levels = c(1,2,3), labels = c("Α", "Β", "Γ"))
manova.df = data.frame(group, gender, sales, contracts)
1. Scatterplot among contracts and sales
plot(contracts, sales, xlab = "Πωλήσεις", ylab = "Contracts",
main = "Correlation between sales and contracts",
cex = 1.3, cex.main = 1.3, cex.axis = 1.3, cex.lab = 1.3)
2. Pearson correlation between sales and contracts
cor.test(contracts, sales)
3. Contingency frequency table
table(group, gender)
4. Contingency frequency table (2nd option)
library(expss)
manova.df = apply_labels(manova.df,
gender = "Gender",
group = "Group",
sales = "Sales",
contracts = "Contracts")
cro_cases(manova.df$group, manova.df$gender, total_label = "Total")
5. MANOVA
library(car)
lm.manova = lm(cbind(sales,contracts) ~ group + gender + group*gender, manova.df, contrasts=list(group=contr.sum, gender=contr.sum))
man.res = Manova(lm.manova, type="III", test ="Pillai")
summary(man.res, multivariate=TRUE)
6. Homogeneity of dependent variables between levels of factors
leveneTest(sales ~ group * gender, manova.df, center = mean)
leveneTest(contracts ~ group * gender, manova.df, center = mean)
7. Homogeneity of covariance of dependent variables among all levels of the interaction of the factors
library(magrittr)
group1 = unclass(manova.df$group) %>% as.numeric
gender1 = unclass(manova.df$gender) %>% as.numeric
manova.df$interaction = factor(group1 * 10 + gender1)
BoxMTest(manova.df[, c(3,4)], manova.df[, 5])
Remark: Function BoxMTest is available here8. Stepdown analysis
lm.anova.sales = lm(sales ~ group + gender + group*gender, manova.df, contrasts=list(group=contr.sum, gender=contr.sum))
Anova(lm.anova.sales, type="III")
lm.anova.contracts = lm(contracts ~ group + gender + group*gender, manova.df, contrasts=list(group=contr.sum, gender=contr.sum))
Anova(lm.anova.contracts, type="III")
lm.post.hoc.ancova = lm(contracts ~ group + gender + group * gender + sales, manova.df, contrasts=list(group=contr.sum, gender=contr.sum))
Anova(lm.post.hoc.ancova, type="III")
Remark: Mahalanobis distance
mahal.manova.df = as.numeric(as.matrix(manova.df[, -c(1, 2)]))
mahal.manova.df = matrix(mahal.manova.df,nrow = 31,ncol = 3)
mahal_dist = mahalanobis(mahal.manova.df,colMeans(mahal.manova.df), cov(mahal.manova.df))
manova.df$MD = round(mahal_dist, 1)
hist(manova.df$MD, main = "Mahalanobis distance",
col = c("grey45"), xlab = "Mahalanobis distance",
ylab = "Συχνότητα", ylim = c(0,25))
# critical value: Any observation with Mahalanobis distance greater than qchisq(0.999, 2, lower.tail=TRUE) is considered to be a multivariate outlier.
manova.df$outlier = "No"
manova.df$outlier[manova.df$MD > qchisq(0.999, 2, lower.tail=TRUE)] = "Yes"
The above example is contained in the paragraph 5.6 of the book "Στατιστική ανάλυση με τη γλώσσα R" (in Greek, ISBN: 978-960-93-9445-1) published in Thessaloniki, 2017.
Comments
Post a Comment