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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 Regions, ("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.

See also

Pottery for the related (subset) data set; RBPottery for a newer version with more variables.

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)
}
}