Skulls: Egyptian Skulls

In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

Egyptian Skulls

Description

Measurements made on Egyptian skulls from five epochs.

Format

A data frame with 150 observations on the following 5 variables.

epoch

the epoch the skull as assigned to, an ordered factor with levels c4000BC c3300BC, c1850BC, c200BC, and cAD150, where the years are only given approximately, of course.

mb

maximal breadth of the skull.

bh

basibregmatic height of the skull.

bl

basialiveolar length of the skull.

nh

nasal height of the skull.

Details

The epochs correspond to the following periods of Egyptian history:

1. the early predynastic period (circa 4000 BC);

2. the late predynastic period (circa 3300 BC);

3. the 12th and 13th dynasties (circa 1850 BC);

4. the Ptolemiac period (circa 200 BC);

5. the Roman period (circa 150 AD).

The question is whether the measurements change over time. Non-constant measurements of the skulls over time would indicate interbreeding with immigrant populations.

Note that using polynomial contrasts for epoch essentially treats the time points as equally spaced.

Source

D. J. Hand, F. Daly, A. D. Lunn, K. J. McConway and E. Ostrowski (1994). A Handbook of Small Datasets, Chapman and Hall/CRC, London.

References

Thomson, A. and Randall-Maciver, R. (1905) Ancient Races of the Thebaid, Oxford: Oxford University Press.

Hand, D. J., F. Daly, A. D. Lunn, K. J. McConway and E. Ostrowski (1994). A Handbook of Small Datasets, Chapman and Hall/CRC, London.

Examples

data(Skulls)
library(car)    # for Anova

# make shorter labels for epochs
Skulls$epoch <- factor(Skulls$epoch, labels=sub("c","",levels(Skulls$epoch)))

# longer variable labels
vlab <- c("maxBreadth", "basibHeight", "basialLength", "nasalHeight")

# fit manova model
sk.mod <- lm(cbind(mb, bh, bl, nh) ~ epoch, data=Skulls)

Anova(sk.mod)
summary(Anova(sk.mod))

# test trends over epochs
print(linearHypothesis(sk.mod, "epoch.L"), SSP=FALSE) # linear component
print(linearHypothesis(sk.mod, "epoch.Q"), SSP=FALSE) # quadratic component

# typical scatterplots are not very informative
scatterplot(mb ~ bh|epoch, data=Skulls, 
            ellipse = list(levels=0.68), 
            smooth=FALSE, 
            legend = list(coords="topright"),
            xlab=vlab[2], ylab=vlab[1])

scatterplot(mb ~ bl|epoch, data=Skulls, 
            ellipse = list(levels=0.68), 
            smooth=FALSE, 
            legend = list(coords="topright"),
            xlab=vlab[3], ylab=vlab[1])

# HE plots

heplot(sk.mod, 
       hypotheses=list(Lin="epoch.L", Quad="epoch.Q"), 
       xlab=vlab[1], ylab=vlab[2])

pairs(sk.mod, 
      hypotheses=list(Lin="epoch.L", Quad="epoch.Q"), 
      var.labels=vlab)

# 3D plot shows that nearly all of hypothesis variation is linear!
## Not run: 
heplot3d(sk.mod, hypotheses=list(Lin="epoch.L", Quad="epoch.Q"), col=c("pink", "blue"))

# view in canonical space
if (require(candisc)) {
	sk.can <- candisc(sk.mod)
	sk.can
	heplot(sk.can)
	heplot3d(sk.can)
}

## End(Not run)

heplots documentation built on Sept. 8, 2023, 5:32 p.m.