MANOVA etc

References

Load packages

library(ggplot2)
library(rrcov)
library(reshape2)
library(lme4)

Create bivariate data

## Create
dat <- read.table(header = TRUE, text = "
group   x       y
o      -2       1
o       0       4
o       1       1
o       2       2
o       3      -5
o       3       2
o       3       4
o       4       2
o       5       3
o       6       2
c      -5      -2
c      -4       0
c      -4       0
c      -1      -2
c      -1       0
c      -1      -2
c      -1       0
c       0      -1
c       0       0
c       0       2
")

## Graph
ggplot(data = dat,
       mapping = aes(x = x, y = y, color = group)) +
    layer(geom = "point", size = 5) +
    theme_bw() +
    theme(legend.key = element_blank())

plot of chunk unnamed-chunk-3

MANOVA

## Using manova
resManova <- manova(cbind(x,y) ~ group, data = dat)
summary(resManova)
##           Df Pillai approx F num Df den Df  Pr(>F)    
## group      1  0.562     10.9      2     17 0.00089 ***
## Residuals 18                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## One-way MANOVA (Bartlett Chi2) (same as manova())
Wilks.test(group ~ x + y, data = dat, method = "c")
## 
##  One-way MANOVA (Bartlett Chi2)
## 
## data:  x
## Wilks' Lambda = 0.4378, Chi2-Value = 14.04, DF = 2.00, p-value = 0.0008933
## sample estimates:
##      x    y
## c -1.7 -0.5
## o  2.5  1.6

## Robust One-way MANOVA (Bartlett Chi2)
Wilks.test(group ~ x + y, data = dat, method = "mcd")
## 
##  Robust One-way MANOVA (Bartlett Chi2)
## 
## data:  x
## Wilks' Lambda = 0.324, Chi2-Value = 4.754, DF = 1.143, p-value = 0.03609
## sample estimates:
##        x      y
## c -1.700 -0.500
## o  2.444  2.333

## One-way MANOVA (Bartlett Chi2) rank based?
Wilks.test(group ~ x + y, data = dat, method = "rank")
## 
##  One-way MANOVA (Bartlett Chi2)
## 
## data:  x
## Wilks' Lambda = 0.3976, Chi2-Value = 15.68, DF = 2.00, p-value = 0.0003936
## sample estimates:
##       x    y
## c  6.35  6.9
## o 14.65 14.1