Results of chemical analyses of 48 specimens of Romano-British pottery
published by Tubb et al. (1980). The numbers are the percentage of various
metal oxides found in each sample for elements of concentrations greater
than 0.01%. This is the original data set from Tubb et al. (1980), in
contrast to Pottery
.
Format
A data frame with 48 observations on the following 12 variables.
Region
a factor with levels
Gl
NF
Wales
Site
a factor with levels
AshleyRails
Caldicot
Gloucester
IsleThorns
Llanedryn
Kiln
a factor with levels
1
2
3
4
5
Al
amount of aluminum oxide, \(Al_2O_3\)
Fe
amount of iron oxide, \(Fe_2O_3\)
Mg
amount of magnesium oxide, MgO
Ca
amount of calcium oxide, CaO
Na
amount of sodium oxide, \(Na_2O\)
K
amount of potassium oxide, \(K_2O\)
Ti
amount of titanium oxide, \(TiO_2\)
Mn
amount of manganese oxide, MnO
Ba
amount of BaO
Source
Originally slightly modified from files by David Carlson, now at
RBPottery
.
Details
The specimens are identified by their rownames
in the data frame.
Kiln
indicates at which kiln site the pottery was found; Site
gives the location names of those sites. The kiln sites come from three
Region
s, ("Gl"=1, "Wales"=(2, 3), "NF"=(4, 5))
, where the full
names are "Gloucester", "Wales", and "New Forrest".
The variable Kiln
comes pre-supplied with contrasts to test
interesting hypotheses related to Site
and Region
.
References
Baxter, M. J. 2003. Statistics in Archaeology. Arnold, London.
Carlson, David L. 2017. Quantitative Methods in Archaeology Using R. Cambridge University Press, pp 247-255, 335-342.
Tubb, A., A. J. Parker, and G. Nickless. 1980. The Analysis of Romano-British Pottery by Atomic Absorption Spectrophotometry. Archaeometry, 22, 153-171.
Examples
library(car)
data(Pottery2)
# contrasts for Kiln correspond to between Region [,1:2] and within Region [,3:4]
contrasts(Pottery2$Kiln)
#> G.WN W.N W2.W3 NF4.NF5
#> 1 4 0 0 0
#> 2 -1 1 1 0
#> 3 -1 1 -1 0
#> 4 -1 -1 0 1
#> 5 -1 -1 0 -1
pmod <-lm(cbind(Al,Fe,Mg,Ca,Na,K,Ti,Mn,Ba)~Kiln, data=Pottery2)
car::Anova(pmod)
#>
#> Type II MANOVA Tests: Pillai test statistic
#> Df test stat approx F num Df den Df Pr(>F)
#> Kiln 4 2.2268 5.3025 36 152 1.391e-13 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# extract coefficient names for linearHypotheses
coefs <- rownames(coef(pmod))[-1]
# test differences among regions
linearHypothesis(pmod, coefs[1:2])
#>
#> Sum of squares and products for the hypothesis:
#> Al Fe Mg Ca Na K
#> Al 151.65057276 -40.53893273 -90.32962804 6.93651249 1.398166750 -49.20000025
#> Fe -40.53893273 233.23920836 52.50699833 35.47123205 11.719323014 45.78071096
#> Mg -90.32962804 52.50699833 57.42066307 0.62797642 0.709273843 33.46637847
#> Ca 6.93651249 35.47123205 0.62797642 6.58156100 2.093516673 3.22560998
#> Na 1.39816675 11.71932301 0.70927384 2.09351667 0.670448844 1.32056847
#> K -49.20000025 45.78071096 33.46637847 3.22560998 1.320568467 20.74890960
#> Ti 9.24314119 -5.42115551 -5.88182924 -0.07236204 -0.075203080 -3.43159076
#> Mn -2.43619545 2.85554855 1.73219182 0.25851436 0.097397909 1.11376927
#> Ba 0.03092721 0.04339183 -0.01183411 0.01008451 0.003094097 -0.00245479
#> Ti Mn Ba
#> Al 9.243141192 -2.436195e+00 3.092721e-02
#> Fe -5.421155511 2.855549e+00 4.339183e-02
#> Mg -5.881829237 1.732192e+00 -1.183411e-02
#> Ca -0.072362038 2.585144e-01 1.008451e-02
#> Na -0.075203080 9.739791e-02 3.094097e-03
#> K -3.431590759 1.113769e+00 -2.454790e-03
#> Ti 0.602509224 -1.777282e-01 1.199732e-03
#> Mn -0.177728182 6.098404e-02 1.518182e-05
#> Ba 0.001199732 1.518182e-05 1.830653e-05
#>
#> Sum of squares and products for error:
#> Al Fe Mg Ca Na K
#> Al 96.20132468 21.11225325 5.506287013 -2.096574026 0.569593506 10.55401948
#> Fe 21.11225325 19.88942753 2.157729870 -0.685039740 0.918994935 4.50978519
#> Mg 5.50628701 2.15772987 16.303520519 0.274558961 0.090970260 5.88807922
#> Ca -2.09657403 -0.68503974 0.274558961 1.760672078 -0.025830519 0.24870156
#> Na 0.56959351 0.91899494 0.090970260 -0.025830519 0.735820130 0.56027961
#> K 10.55401948 4.50978519 5.888079221 0.248701558 0.560279610 14.63247117
#> Ti 0.96768701 1.99152987 0.041040519 -0.120881039 0.062710260 0.32167922
#> Mn 0.37119545 0.26490145 -0.131911818 0.009635636 0.059562091 0.10489073
#> Ba 0.07495727 0.02567727 -0.007025091 0.004785182 0.004963455 0.01005364
#> Ti Mn Ba
#> Al 0.967687013 0.371195455 0.0749572727
#> Fe 1.991529870 0.264901455 0.0256772727
#> Mg 0.041040519 -0.131911818 -0.0070250909
#> Ca -0.120881039 0.009635636 0.0047851818
#> Na 0.062710260 0.059562091 0.0049634545
#> K 0.321679221 0.104890727 0.0100536364
#> Ti 1.368520519 0.015238182 0.0037669091
#> Mn 0.015238182 0.089093964 0.0030718182
#> Ba 0.003766909 0.003071818 0.0004249909
#>
#> Multivariate Tests:
#> Df test stat approx F num Df den Df Pr(>F)
#> Pillai 2 1.86181 53.88966 18 72 < 2.22e-16 ***
#> Wilks 2 0.00383 58.97836 18 70 < 2.22e-16 ***
#> Hotelling-Lawley 2 34.11493 64.43932 18 68 < 2.22e-16 ***
#> Roy 2 25.10339 100.41357 9 36 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# test differences within regions B, C
linearHypothesis(pmod, coefs[3:4])
#>
#> Sum of squares and products for the hypothesis:
#> Al Fe Mg Ca Na K
#> Al 3.1562321 1.8776786 1.6154857 -0.19634643 0.31648036 -0.74230357
#> Fe 1.8776786 1.7032143 1.6611429 -0.16853571 0.33919643 -1.02896429
#> Mg 1.6154857 1.6611429 1.6629886 -0.16227714 0.34223429 -1.08144286
#> Ca -0.1963464 -0.1685357 -0.1622771 0.01677929 -0.03300607 0.09801071
#> Na 0.3164804 0.3391964 0.3422343 -0.03300607 0.07059089 -0.22565893
#> K -0.7423036 -1.0289643 -1.0814429 0.09801071 -0.22565893 0.76313929
#> Ti 0.3105857 0.2461429 0.2322686 -0.02473714 0.04694429 -0.13454286
#> Mn 0.0667875 0.0777250 0.0795600 -0.00750750 0.01647875 -0.05377750
#> Ba 0.0062575 0.0054250 0.0052360 -0.00053950 0.00106575 -0.00317750
#> Ti Mn Ba
#> Al 0.31058571 0.06678750 0.00625750
#> Fe 0.24614286 0.07772500 0.00542500
#> Mg 0.23226857 0.07956000 0.00523600
#> Ca -0.02473714 -0.00750750 -0.00053950
#> Na 0.04694429 0.01647875 0.00106575
#> K -0.13454286 -0.05377750 -0.00317750
#> Ti 0.03698857 0.01055000 0.00079400
#> Mn 0.01055000 0.00387575 0.00024275
#> Ba 0.00079400 0.00024275 0.00001735
#>
#> Sum of squares and products for error:
#> Al Fe Mg Ca Na K
#> Al 96.20132468 21.11225325 5.506287013 -2.096574026 0.569593506 10.55401948
#> Fe 21.11225325 19.88942753 2.157729870 -0.685039740 0.918994935 4.50978519
#> Mg 5.50628701 2.15772987 16.303520519 0.274558961 0.090970260 5.88807922
#> Ca -2.09657403 -0.68503974 0.274558961 1.760672078 -0.025830519 0.24870156
#> Na 0.56959351 0.91899494 0.090970260 -0.025830519 0.735820130 0.56027961
#> K 10.55401948 4.50978519 5.888079221 0.248701558 0.560279610 14.63247117
#> Ti 0.96768701 1.99152987 0.041040519 -0.120881039 0.062710260 0.32167922
#> Mn 0.37119545 0.26490145 -0.131911818 0.009635636 0.059562091 0.10489073
#> Ba 0.07495727 0.02567727 -0.007025091 0.004785182 0.004963455 0.01005364
#> Ti Mn Ba
#> Al 0.967687013 0.371195455 0.0749572727
#> Fe 1.991529870 0.264901455 0.0256772727
#> Mg 0.041040519 -0.131911818 -0.0070250909
#> Ca -0.120881039 0.009635636 0.0047851818
#> Na 0.062710260 0.059562091 0.0049634545
#> K 0.321679221 0.104890727 0.0100536364
#> Ti 1.368520519 0.015238182 0.0037669091
#> Mn 0.015238182 0.089093964 0.0030718182
#> Ba 0.003766909 0.003071818 0.0004249909
#>
#> Multivariate Tests:
#> Df test stat approx F num Df den Df Pr(>F)
#> Pillai 2 0.3584150 0.8733388 18 72 0.610701
#> Wilks 2 0.6493732 0.9370114 18 70 0.538962
#> Hotelling-Lawley 2 0.5279530 0.9972445 18 68 0.473824
#> Roy 2 0.5041642 2.0166569 9 36 0.065976 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
heplot(pmod, fill=c(TRUE,FALSE), hypotheses=list("Region" =coefs[1:2], "WithinBC"=coefs[3:4]))
# all pairwise views; note that Ba shows no effect
pairs(pmod, fill=c(TRUE,FALSE))
# canonical view, via candisc::heplot
if (require(candisc)) {
# canonical analysis: how many dimensions?
(pcan <- candisc(pmod))
heplot(pcan, scale=18, fill=c(TRUE,FALSE), var.col="darkgreen", var.lwd=2, var.cex=1.5)
if (FALSE) {
heplot3d(pcan, scale=8)
}
}