Head measurements of football players

Data collected as part of a preliminary study examining the relation between football helmet design and neck injuries. There are 30 subjects in each of three groups: High school football players, college players and non-football players.

Format

A data frame with 90 observations on the following 7 variables.

group: a factor with levels High school College Non-football
width: a numeric vector: head width at widest dimension
circum: a numeric vector: head circumference
front.back: a numeric vector: front to back distance at eye level
eye.top: a numeric vector: eye to top of head
ear.top: a numeric vector:ear to top of head
jaw: a numeric vector: jaw width

Source

Rencher, A. C. (1995), Methods of Multivariate Analysis, New York: Wiley, Table 8.3.

Examples


data(FootHead)
str(FootHead)
#> 'data.frame':	90 obs. of  7 variables:
#>  $ group     : Factor w/ 3 levels "High school",..: 1 1 1 1 1 1 1 1 1 1 ...
#>  $ width     : num  13.5 15.5 14.5 15.5 14.5 14 15 15 15.5 15.5 ...
#>  $ circum    : num  57.1 58.4 55.9 58.4 58.4 ...
#>  $ front.back: num  19.5 21 19 20 20 21 19.5 21 20.5 20.5 ...
#>  $ eye.top   : num  12.5 12 10 13.5 13 12 13.5 13 13.5 13 ...
#>  $ ear.top   : num  14 16 13 15 15.5 14 15.5 14 14.5 15 ...
#>  $ jaw       : num  11 12 12 12 12 13 13 13 12.5 13 ...
require(car)

# use Helmert contrasts for group
contrasts(FootHead$group) <- contr.helmert
contrasts(FootHead$group)
#>              [,1] [,2]
#> High school    -1   -1
#> College         1   -1
#> Non-football    0    2

foot.mod <- lm(cbind(width, circum,front.back,eye.top,ear.top,jaw) ~ group, 
               data=FootHead)
Manova(foot.mod)
#> 
#> Type II MANOVA Tests: Pillai test statistic
#>       Df test stat approx F num Df den Df    Pr(>F)    
#> group  2   0.76116   8.4994     12    166 1.876e-12 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# show the HE plot for the first two variables
heplot(foot.mod, main="HE plot for width and circumference", fill=TRUE,
  col=c("red", "blue"))


# show it with tests of Helmert contrasts
heplot(foot.mod, hypotheses=list("group.1"="group1","group.2"="group2"),
  col=c("red", "blue", "green3", "green3" ),
  main="HE plot with orthogonal Helmert contrasts")


# show all pairwise HE plots
pairs(foot.mod)


# ... with tests of Helmert contrasts
pairs(foot.mod, hypotheses=list("group.1"="group1","group.2"="group2"),
  col=c("red", "blue", "green3", "green3"), hyp.labels=FALSE)


# see that the hypothesis for groups really is 2D
if(requireNamespace("rgl")){
heplot3d(foot.mod, variables=c(1,2,6),
  hypotheses=list("group.1"="group1","group.2"="group2"),
  col=c("red", "blue", "green3", "green3" ), wire=FALSE)
}