Dogfood Preferences

Description

A tiny hypothetical dataset to illustrate one-way MANOVA.

A dogfood manufacturer wanted to study preference for different dogfood formulas, two of their own ("Old", "New") and two from other manufacturers ("Major", "Alps"). In a between-dog design, 4 dogs were presented with a bowl of one formula and the time to start eating and amount eaten were recorded.

Usage

data("dogfood")

Format

A data frame with 16 observations on the following 3 variables.

formula

factor, a factor with levels Old, New, Major, Alps

start

numeric, time to start eating

amount

numeric, amount eaten

Details

In addition to testing the overall effects of formula, three useful (and orthogonal) contrasts can specified for this 3-df factor:

• Ours vs. Theirs, with weights c(1, 1, -1, -1)

• Major vs. Alps, with weights c(0, 0, 1, -1)

• Old vs. New, with weights c(1, -1, 0, 0)

Because these are orthogonal contrasts, they fully decompose the main effect of formula, in that their sum of squares add to the overall sum of squares.

Source

Used in my Psych 6140 lecture notes, http://friendly.apps01.yorku.ca/psy6140/

Examples

data(dogfood)
library(car)
library(candisc)

# make some boxplots
op <- par(mfrow = c(1,2))
boxplot(start ~ formula, data = dogfood)
points(start ~ formula, data = dogfood, pch=16, cex = 1.2)

boxplot(amount ~ formula, data = dogfood)
points(amount ~ formula, data = dogfood, pch=16, cex = 1.2)
par(op)

# setup contrasts to test interesting comparisons
C <- matrix(
       c( 1,  1, -1, -1,         #Ours vs. Theirs
          0,  0,  1, -1,           #Major vs. Alps
          1, -1,  0,  0),             #New vs. Old
       nrow=4, ncol=3)
# assign these to the formula factor
contrasts(dogfood$formula) <- C
# re-fit the model
dogfood.mod <- lm(cbind(start, amount) ~ formula, data=dogfood)

dogfood.mod <- lm(cbind(start, amount) ~ formula, data=dogfood)
Anova(dogfood.mod)

# data ellipses
covEllipses(cbind(start, amount) ~ formula, data=dogfood,
  fill = TRUE, fill.alpha = 0.1)

# test these contrasts with multivariate tests 
linearHypothesis(dogfood.mod, "formula1", title="Ours vs. Theirs")
linearHypothesis(dogfood.mod, "formula2", title="Old vs. New")
linearHypothesis(dogfood.mod, "formula3", title="Alps vs. Major")

heplot(dogfood.mod, fill = TRUE, fill.alpha = 0.1)

# display contrasts in the heplot 
hyp <- list("Ours/Theirs" = "formula1",
            "Old/New" = "formula2")
heplot(dogfood.mod, hypotheses = hyp,
       fill = TRUE, fill.alpha = 0.1)

dogfood.can <- candisc(dogfood.mod, data=dogfood)
heplot(dogfood.can, 
       fill = TRUE, fill.alpha = 0.1, 
       lwd = 2, var.lwd = 2, var.cex = 2)