Description and Classification of Hawaiian Adzes

1 Project Tracking

1 Project Tracking

1.1 Complete Adzes

1.1.1 Adze Weight

1.1.1.1 Quantiles

r-weight-quantile-simple(x=whole-adzes)

z <- quantile(x$weight)
t(z)

Quantiles of whole adze weights in grams
0%	25%	50%	75%	100%
0	37	141	914	3466

1.1.1.2 Histogram

The weights of complete adze blades are plotted on a log scale to differentiate among the lighter blades

r-complete-weight-histogram-png(x=whole-adzes)

library(ggplot2) 
g <- ggplot(x, aes(x = weight)) 
g + geom_histogram(aes(y=..density..)) + geom_density(weight=2) + scale_x_log10()

r/adze_wt_log.png

Histogram of adze weights on a logarithmic scale

1.1.2 Adze Length

1.1.2.1 Quantiles

r-length-quantile-simple(x=whole-adzes)

z <- quantile(x$length_poll)
t(z)

Quantiles of adze lengths in millimeters
0%	25%	50%	75%	100%
25	61	103	205.75	351

1.1.2.2 Histogram

The lengths of the measured adze blades are plotted on a log scale to differentiate among the smaller blades

r-complete-length-histogram-log-png(x=whole-adzes)

library(ggplot2)
adze.len <- ggplot(x, aes(length_poll))
adze.len + geom_histogram(aes(y=..density..))  + geom_density(weight=2) + scale_x_log10()

r/adze_len_log.png

Histogram of adze lengths on a logarithmic scale

1.1.3 Edge Width

1.1.3.1 Quantiles

cutting-edge-summary(x=whole-adzes)

z <- quantile(x$width_edge)
t(z)

Quantiles of whole adze edge widths in millimeters
0%	25%	50%	75%	100%
1	26	36	53	119

1.1.3.2 Histograms

Logarithmic scale

r-cutting-edge-histogram-log-png(x=whole-adzes)

library(ggplot2)
adze.len <- ggplot(x, aes(width_edge))
adze.len + geom_histogram(aes(y=..density..)) + scale_x_log10() + geom_density(weight=2)

r/adze_cutting_edge_log.png

Histogram of cutting edge lengths on a logarithmic scale

Without the logarithmic scale

r-cutting-edge-histogram-png(x=whole-adzes)

library(ggplot2)
adze.len <- ggplot(x, aes(width_edge))
adze.len + geom_histogram(aes(y=..density..)) + geom_density(weight=2)

r/adze_cutting_edge.png

Histogram of cutting edge lengths

1.1.4 Edge Angle

1.1.4.1 Quantiles of directly measured edge angles

r-edge-angle-summary(x=whole-adzes)

z <- quantile(x$edge_angle)
t(z)

Quantiles of directly measured edge angles in degrees
0%	25%	50%	75%	100%
0	45	50	60	95

1.1.4.2 Histogram of directly measured edge angles

r-edge-angle-histogram(x=whole-adzes)

library(ggplot2)
adze.edge.angle <- ggplot(x, aes(edge_angle))
adze.edge.angle + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Measured cutting edge angle (degrees)")

r/adze_edge_angle.png

Histogram of directly measured cutting edge angles

1.1.4.3 Quantiles of calculated edge angles

r-cutting-edge-trig(x=whole-adzes)

z <- quantile(round((180/pi) * atan2(x$thickness_chin,x$length_chin),1))
t(z)

Quantiles of trigonometric cutting edge angle measure
0%	25%	50%	75%	100%
0	37.6	42.95	48.8	76

1.1.4.4 Histogram of calculated edge angles

r-adze-trig-edge-angle(x=whole-adzes)

library(ggplot2)
a <- (180/pi) * atan2(x$thickness_chin,x$length_chin)
p <- ggplot(as.data.frame(a), aes(a))
p + geom_histogram(aes(y=..density..)) + geom_density(weight=2) +
xlab("Calculated cutting edge angle (degrees)")

r/adze_trig_angle.png

Histogram of trigonometric measure of cutting edge angle

1.1.5 Adze Type

Secondary adzes have been fashioned using another tool as the raw material. They represent recycling of broken tools.

r-adze-type-summary(x=whole-adzes)

table(x$adze_type)

Distribution of primary and secondary adzes
Var1	Freq
primary	630
secondary	16

1.1.6 Bevel Shape

r-bevel-shape(x=whole-adzes)

table(x$bevel_shape)

Bevel shape
Var1	Freq
	3
concave	1
convex	615
flat	27

1.1.7 Edge Shape A

Viewed from the back of the blade

r-edge-shape-a(x=whole-adzes)

table(x$edge_shape_a)

Edge shape
Var1	Freq
angled	22
convex	216
straight	408

1.1.8 Edge Shape B

Viewed with the front superior

r-edge-shape-b(x=whole-adzes)

table(x$edge_shape_b)

Edge shape
Var1	Freq
convex	46
straight	600

1.1.9 Face Reduction

Reduction of the face near the poll to facilitate lashing the blade to the handle

r-adze-face-reduction(x=whole-adzes)

table(x$face_reduced)

Reduction of face
Var1	Freq
	1
false	95
true	550

1.2 Pairwise Comparison

Jenny comments "Were you thinking of running some stats too at the end – just to see in fact what attributes are most highly correlated with one another? This may allow us to define grouped functional variables."
This plot compares adze blade weight, length, edge width, shoulder width at front, shoulder width at back and shoulder thickness

pairs(x=whole-adzes)

whole.adze.metric <- x[,c(5,12,15,16,17,18)]
names(whole.adze.metric) <- c("wt","len","edge","front","back","thick")
pairs(whole.adze.metric)

r/adze_pairs.png

Pairwise comparison of six metric variables

1.3 Percussion

An attempt to measure percussive potential of blades

1.3.1 Scatterplot

Note that values above the smooth line have high percussive potential

percussion-basics(x=whole-adzes)

library(ggplot2)
p <- ggplot(x, aes(x=width_edge,y=weight))
p + geom_point() + geom_smooth()

r/percussion.png

Scatterplot of measures used to calculate percussive potential

1.3.2 Percussive Index

defined as weight / width_edge
percussive potential increases to the right on the histogram

percussion-index(x=whole-adzes)

library(ggplot2)
adze.pi <- ggplot(x, aes(weight/width_edge))
adze.pi + geom_histogram(aes(y=..density..))  + scale_x_log10() + geom_density(weight=2)

r/percussion-index.png

1.3.3 Blade Plan Index

The blade plan index relates the shoulder width to the edge width
The plan can flare to maximize edge width, or narrow to minimize edge width

blade-plan(x=whole-adzes)

library(ggplot2)
p <- ggplot(x, aes(x=width_edge/mapply(max,width_shoulder_front,width_shoulder_back)))
p + geom_histogram(aes(y=..density..)) + geom_density(weight=2) + xlab("Blade Plan Index")

r/blade-plan.png

Histogram of blade plan

1.4 Indices Remarquables

These are from Jose Garanger's paper, Herminettes lithiques oceaniennes: Elements de typologie

1.4.1 Shoulder index

indice de la section transversale principale = $ \dfrac{R-7 \times 100}{R-9} $, where
- R-7 = hauteur de la section transversale principale (thickness of the standard cross-section)
- R-9 = largeur de la section transversale principale (width of the standard cross-section)
This is due to Buck (1944)

1.4.1.1 Quantiles

buck-shoulder-index(x=whole-adzes)

b <- (x$thickness_shoulder * 100) / mapply(max, x$width_shoulder_front, x$width_shoulder_back)
z <- round(quantile(b),1)
t(z)

Buck's shoulder index
0%	25%	50%	75%	100%
20	50	66.7	87.9	157.8

1.4.1.2 Scatterplot

buck-basics(x=whole-adzes)

library(ggplot2)
b <- ggplot(x, aes(x=width_shoulder_front, y=thickness_shoulder))
b + geom_point() + geom_smooth() + xlab("R-9") + ylab("R-7")

r/buck-basics.png

Scatterplot of measures used to calculate Buck's shoulder index

1.4.1.3 Histogram

buck-shoulder-histogram(x=whole-adzes)

library(ggplot2)
b <- ggplot(x, aes(x=((thickness_shoulder * 100) / mapply(max, width_shoulder_front, width_shoulder_back))))
b + geom_histogram(aes(y=..density..))  + geom_density(weight=2) +
xlab("Buck Shoulder Index")

r/buck-shoulder-hist.png

Histogram of Buck's shoulder index

1.4.2 Blade size

indice de la largeur de la lame = $ \dfrac{R-2 \times 100}{R-9} $, where
- R-2 = longeur de la face frontale (blade length)
- R-9 = largeur de la section transversale principale (width of the standard cross-section)
This is due to Green and Green (1960)

1.4.2.1 Quantiles

green-blade-size(x=whole-adzes)

g <- (x$length_shoulder * 100) / mapply(max, x$width_shoulder_front, x$width_shoulder_back)
z <- round(quantile(g),1)
t(z)

Green and Green's blade size index
0%	25%	50%	75%	100%
0	147.7	194.9	264.9	510

1.4.2.2 Scatterplot

green-basics(x=whole-adzes)

library(ggplot2)
g <- ggplot(x, aes(x=length_shoulder, y=width_shoulder_front))
g + geom_point() + geom_smooth() + xlab("R-2") + ylab("R-9")

r/green-basics.png

Scatterplot of measures used to calculate Green and Green's blade size index

1.4.2.3 Histogram

blade-size-histogram(x=whole-adzes)

library(ggplot2)
b <- ggplot(x, aes(x=((length_shoulder * 100) / mapply(max, width_shoulder_front, width_shoulder_back))))
b + geom_histogram(aes(y=..density..))  + geom_density(weight=2) +
xlab("Blade Size Index")

r/blade-size-hist.png

1.4.3 Adze length

indice de la longeur de l'herminette = $ \dfrac{R-1 \times 100}{R-9} $
- R-1 = longeur maximum de l'herminette (length of the tool)
- R-9 = largeur de la section transversale principale (width of the standard cross-section)

1.4.3.1 Quantiles

adze-length-index(x=whole-adzes)

l <- (x$length_poll * 100) / mapply(max, x$width_shoulder_front, x$width_shoulder_back)
z <- round(quantile(l),1)
t(z)


0%	25%	50%	75%	100%
138.9	259.1	322.8	424.1	722.2

1.4.3.2 Scatterplot

len-index-basics(x=whole-adzes)

library(ggplot2)
l <- ggplot(x, aes(x=length_poll, y=width_shoulder_front))
l + geom_point() + geom_smooth() + xlab("R-1") + ylab("R-9")

r/len-index-basics.png

Scatterplot of measures used to calculate the adze length index

1.4.3.3 Histogram

adze-length-histogram(x=whole-adzes)

library(ggplot2)
b <- ggplot(x, aes(x=((length_poll * 100) / mapply(max, width_shoulder_front, width_shoulder_back))))
b + geom_histogram(aes(y=..density..))  + geom_density(weight=2) +
xlab("Adze Length Index")

r/adze-length-hist.png

1.4.4 Edge width

indice de longeur du tranchant = $ \dfrac{R-4 \times 100}{R-1} $, where
- R-1 = longeur maximum de l'herminette (length of the tool)
- R-4 = longeur du fil du tranchant (width of the edge)
This is due to Kellum (1966)

1.4.4.1 Quantiles

kellum(x=whole-adzes)

k <- (x$width_edge * 100) / x$length_poll
z <- round(quantile(k),1)
t(z)


0%	25%	50%	75%	100%
0.5	27.4	35.6	43.5	75.6

1.4.4.2 Scatterplot

kellum-basics(x=whole-adzes)

library(ggplot2)
k <- ggplot(x, aes(x=width_edge, y=length_poll))
k + geom_point() + geom_smooth() + xlab("R-4") + ylab("R-1")

r/kellum-basics.png

Scatterplot of measures used to calculate Kellum's edge width index

1.4.4.3 Histogram

edge-width-histogram(x=whole-adzes)

library(ggplot2)
b <- ggplot(x, aes(x=((width_edge * 100) / length_poll)))
b + geom_histogram(aes(y=..density..))  + geom_density(weight=2) +
xlab("Edge Width Index")

r/edge-width-hist.png

1.4.5 Butt length

indice de longeur du tranchant = $ \dfrac{R-1 \times 100}{R-3} $, where
- R-1 = longeur maximum de l'herminette (length of the tool)
- R-3 = longeur du talon (length of the butt)

1.4.5.1 Quantiles

Can't use this one without filtering for face_reduced

butt-length(y=whole-adzes)

x <- y[y$face_reduced=='true',]
b <- round((x$length_poll * 100) / (x$length_poll - x$length_shoulder),1)
z <- quantile(b)
t(z)

Quantiles of butt length index
0%	25%	50%	75%	100%
100	234	268.3	295.7	566.7

1.4.5.2 Scatterplot

butt-basics(y=whole-adzes)

library(ggplot2)
x <- y[y$face_reduced=='true',]
b <- ggplot(x, aes(x=length_poll, y=length_shoulder))
b + geom_point() + geom_smooth() + xlab("R-1") + ylab("R-3")

r/butt-basics.png

Scatterplot of measures used to calculate the butt length index

1.4.5.3 Histogram

butt-length-histogram(y=whole-adzes)

library(ggplot2)
x <- y[y$face_reduced=='true',]
b <- ggplot(x, aes(x=((length_poll * 100) / (length_poll - length_shoulder))))
b + geom_histogram(aes(y=..density..))  + geom_density(weight=2) +
xlab("Butt Length Index")

r/butt-length-hist.png

1.5 Exploratory Views

Adzes with chins thicker than shoulders prompted this series of graphs

1.5.1 Chin thickness index

Chin thickness / shoulder thickness

1.5.1.1 Quantiles

chin-thickness-index(x=whole-adzes)

b <- x$thickness_chin / x$thickness_shoulder
z <- round(quantile(b),1)
t(z)

Chin thickness index
0%	25%	50%	75%	100%
0	0.6	0.7	0.8	1.6

1.5.1.2 Scatterplot

chin-thick-scatter(x=whole-adzes)

library(ggplot2)
b <- ggplot(x, aes(x=thickness_chin, y=thickness_shoulder))
b + geom_point() + geom_smooth() + xlab("Chin thickness") +
ylab("Shoulder thickness")

r/chin-thick-scatter.png

Scatterplot of measures used to calculate chin thickness index

1.5.1.3 Histogram

chin-thickness-histogram(x=whole-adzes)

library(ggplot2)
b <- ggplot(x, aes(x=(thickness_chin/thickness_shoulder)))
b + geom_histogram(aes(y=..density..))  + geom_density(weight=2) +
xlab("Chin Thickness Index")

r/chin-thickness-hist.png

Histogram of the chin thickness index

1.6 Cross-section Classification

This is due to Emory, "East Polynesian Adze Relationships"
It is based on the relationship of front width (FW) at the shoulder to back width (BW) at the shoulder
Emory didn't partition exhaustively
The classification used here is:
- Triangular: $ FW \leq 0.15 \times BW $
- Subtriangular: $ 0.15 \times BW < FW \leq 0.3 \times BW $
- Trapezoidal: $ 0.3 \times BW < FW \leq 0.8 \times BW $
- Quadrangular: $ 0.8 \times BW < FW \leq 1.2 \times BW $
- Reversed Trapezoidal: $ 1.2 \times BW < FW \leq 1.7 \times BW $
- Reversed Subtriangular: $ 1.7 \times BW < FW \leq 1.85 \times BW $
- Reversed Triangular: $ FW > 1.85 \times BW $

1.6.1 Tabular View

whole-adze-table(x=whole-adzes)

x_section.breaks = c(0,0.15,0.3,0.8,1.2,1.7,1.85,1000000)
x_section.labels =
c("Triangular","Subtriangular","Trapezoidal","Quadrangular","Reversed_Trapezoidal", "Reversed_Subtriangular", "Reversed_Triangular")
x_section <- cut(x$width_shoulder_front / x$width_shoulder_back, x_section.breaks,
labels= x_section.labels)
table(x_section)

Classification by cross section
x_section	Freq
Triangular	1
Subtriangular	0
Trapezoidal	5
Quadrangular	557
Reversed_Trapezoidal	65
Reversed_Subtriangular	1
Reversed_Triangular	17

1.6.2 Dot chart

library(ggplot2)
e.breaks = c(0,0.15,0.3,0.8,1.2,1.7,1.85,1000000)
e.labels =
c("Triangular","Subtriangular","Trapezoidal","Quadrangular","Reversed_Trapezoidal", "Reversed_Subtriangular", "Reversed_Triangular")
e <- cut(x$width_shoulder_front / x$width_shoulder_back, e.breaks,
labels= e.labels)
e.d <- data.frame(table(e))
p <- ggplot(e.d, aes(Freq, e))
p + geom_point() + geom_segment(aes(x=0, xend=Freq, y=e, yend=e)) +
ylab("Class") + xlab("Frequency")

r/emory.png

Dot chart of cross-section classification

1.6.3 Diagnostic scatterplot

emory-diag(x=whole-adzes)

library(ggplot2)
e.breaks = c(0,0.15,0.3,0.8,1.2,1.7,1.85,1000000)
s = c(0.15,0.3,0.8,1.2,1.7,1.85)
i = rep.int(0,length(s))
ab <- data.frame(cbind(s,i))
n <- c("Triangular","Subtriangular","Trapezoidal","Quadrangular","Reversed_Trapezoidal", "Reversed_Subtriangular", "Reversed_Triangular")
e <- cut(x$width_shoulder_front / x$width_shoulder_back, e.breaks,
labels=n)
e.d <- data.frame(table(e))
p <- ggplot(x, aes(width_shoulder_back, width_shoulder_front))
p + geom_point() + geom_abline(aes(intercept = i, slope = s),
data=ab, linetype=3, color="grey50") + ylab("Front width (mm)") + xlab("Back width (mm)")

r/emory-diag.png

Diagnostic scatterplot of cross-section classification

1.6.4 Comments

Emory's system is designed to group the Hawaiian adzes in a way that sets them apart from adzes fashioned elsewhere in East Polynesia
Its object is the opposite of what we are trying to do
There is little variability in the relationship between shoulder width at front and back
Reversed triangular adzes tend to be small

1.6.4.1 Index of shoulder height

defined as thickness_shoulder / width_shoulder_front

shoulder-height-index(x=whole-adzes)

library(ggplot2)
adze.shi <- ggplot(x, aes(thickness_shoulder/(width_shoulder_front + width_shoulder_back)))
adze.shi + geom_histogram(aes(y=..density..)) + geom_density(weight=2) +  xlab("Shoulder Height Index")

r/shoulder-height-index.png

Histogram of the shoulder height index

1.6.4.2 Shoulder height by adze size

In the lab it seems that tall adzes are typically large
Here, "large" is captured by the length of the tool

shoulder-height-size(x=whole-adzes)

library(ggplot2)
b <- ggplot(x, aes(x=length_poll, y=thickness_shoulder/mapply(max, width_shoulder_front, width_shoulder_back)))
b + geom_point() + geom_smooth()  + xlab("Length") + ylab("Shoulder
Height Index")

r/shoulder-height-size.png

Scatterplot showing the relationship between adze blade length and shoulder height index

Here, "large" is captured by weight

shoulder-height-weight(x=whole-adzes)

library(ggplot2)
b <- ggplot(x, aes(x=weight,
y=thickness_shoulder/mapply(max,width_shoulder_front,width_shoulder_back)))
b + geom_point() + geom_smooth()  + xlab("Weight") + ylab("Shoulder
Height Index")

r/shoulder-height-weight.png

Scatterplot showing the relationship between adze blade weight and shoulder height index

1.7 Multivariate Views

1.7.1 Correspondence Analysis

A simple correspondence analysis on all metric variables

ca-1(x=whole-adzes)

v <- c(5,12,15:18)
y <- x[,v]
z <- round((180/pi) * atan2(x$thickness_chin,x$length_chin),1)
y <- cbind(y,z)
library(ca)
plot(ca(y),labels=c(0,2))

r/ca-1.png

1.8 EDXRF

Peter Mills and Steven Lundblad are characterizing the chemical composition of the BPBM adzes using a non-destructive technique
Their laboratory produces its most precise results for the mid-Z trace elements Rb, Sr, Y, Zr, and Nb

1.8.1 Elemental Review

1.8.1.1 Sodium

na2o-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(na2o_percent))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab(expression(paste(Na[2],O," (%)")))

r/edxrf-na2o.png

Histogram of Na₂O %

1.8.1.2 Magnesium

mgo-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(mgo_percent))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("MgO (%)")

r/edxrf-mgo.png

Histogram of MgO %

1.8.1.3 Aluminum

al2o3-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(al2o3_percent))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab(expression(paste(Al[2],O[3]," (%)")))

r/edxrf-al2o3.png

Histogram of Al₂O₃ %

1.8.1.4 Silicon

sio2-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(sio2_percent))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab(expression(paste(SiO[2]," (%)")))

r/edxrf-sio2.png

Histogram of Silicon dioxide %

1.8.1.5 Potassium

k20-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(k2o_percent))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab(expression(paste(K[2],O," (%)")))

r/edxrf-k2o.png

Histogram of K₂O %

1.8.1.6 Calcium

cao-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(cao_percent))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("CaO (%)")

r/edxrf-cao.png

Histogram of Calcium oxide %

1.8.1.7 Titanium

tio2-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(tio2_percent))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab(expression(paste(TiO[2]," (%)")))

r/edxrf-tio2.png

Histogram of Titanium dioxide %

1.8.1.8 Vanadium

v-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(v_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("V (ppm)")

r/edxrf-v.png

Histogram of Vanadium in parts per million

1.8.1.9 Manganese

mno-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(mno_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("MnO (ppm)")

r/edxrf-mno.png

Histogram of Manganese oxide in parts per million

1.8.1.10 Iron

fe-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(fe_percent))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Fe (%)")

r/edxrf-fe.png

Histogram of Iron %

1.8.1.11 Nickel

ni-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(ni_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Ni (ppm)")

r/edxrf-ni.png

Histogram of Nickel in parts per million

1.8.1.12 Copper

cu-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(cu_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Cu (ppm)")

r/edxrf-cu.png

Histogram of Copper in parts per million

1.8.1.13 Zinc

zn-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(zn_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Zn (ppm)")

r/edxrf-zn.png

Histogram of Zinc in parts per million

1.8.1.14 Rubidium

rb-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(rb_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Rb (ppm)")

r/edxrf-rb.png

Histogram of Rubidium in parts per million

1.8.1.15 Strontium

sr-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(sr_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Sr (ppm)")

r/edxrf-sr.png

Histogram of Strontium in parts per million

1.8.1.16 Yttrium

y-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(y_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Y (ppm)")

r/edxrf-y.png

Histogram of Yttrium in parts per million

1.8.1.17 Zirconium

zr-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(zr_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Zr (ppm)")

r/edxrf-zr.png

Histogram of Zirconium in parts per million

1.8.1.18 Niobium

nb-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(nb_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Nb (ppm)")

r/edxrf-nb.png

Histogram of Niobium in parts per million

1.8.1.19 Barium

ba-histogram(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
y <- ggplot(x, aes(ba_ppm))
y + geom_histogram(aes(y=..density..)) +
geom_density(weight=2) + xlab("Ba (ppm)")

r/edxrf-ba.png

Histogram of Barium in parts per million

1.8.2 Major Elements

SiO₂, Al₂O₃, Fe₂O₃, MgO, CaO, Na₂O, K₂O

1.8.2.1 Major Element Pairs

major-element-pairs(x=edxrf)

x <- x[x$type == 'adze',]
y <- x[,c(3,4,5,6,7,8,12)]
names(y) <- c("Na2O","MgO","Al2O3","SiO2","K2O","CaO","Fe")
pairs(y, labels=c(expression(paste(Na[2],O)),"MgO",expression(paste(Al[2],O[3])),expression(SiO[2]),expression(paste(K[2],O)),"CaO","Fe"))

r/edxrf-major-pairs.png

Pairs plot of major elements

1.8.2.2 Total Alkali Silica Diagram

Need to add classification

TAS(x=edxrf)

library(ggplot2)
x <- x[x$type == 'adze',]
b <- ggplot(x, aes(x=sio2_percent, y=(na2o_percent + k2o_percent)))
b + geom_point() + xlab(expression(SiO[2])) +
ylab(expression(paste(Na[2],O) + paste(K[2],O)))

r/edxrf-TAS.png

1.8.3 Minor Elements

1.8.3.1 Minor Element Pairs

minor-element-pairs(x=edxrf)

x <- x[x$type == 'adze',]
y <- x[,c(10,11,13,14,15,16,17,18,19,20,21)]
pairs(y, labels=c("V","MnO","Ni","Cu","Zn","Rb","Sr","Y","Zr","Nb","Ba"))

r/edxrf-minor-pairs.png

Pairs plot of minor elements

1.8.3.2 Mid-Z trace element pairs

mid-z-pairs(x=edxrf)

y <- x[x$lab == 'UH-Hilo',c(16,17,18,19,20)]
pairs(y, labels=c("Rb","Sr","Y","Zr","Nb"))

r/edxrf-mid-z-pairs.png

Pairs plot of mid-Z trace elements

1.8.4 Multiple ANOVA

Comparisons of UH and UH Hilo lab results for mid-Z trace elements and major elements both indicate inter-laboratory variability too great for direct comparability

1.8.4.1 Mid-Z trace elements

Multiple analysis of variance for mid-Z trace elements suggests that there are large differences between the UH and UH Hilo laboratories
The differences are especially pronounced for Niobium and Yttrium
Results suggest that analyses of mid-Z trace elements from these two labs are not directly comparable

mid-z-medians(x=edxrf)

y <- x[x$type=='quarry' & x$site=='Mauna Kea' & x$lab != 'UA',]
aggregate(y[,c("rb_ppm","sr_ppm","y_ppm","zr_ppm","nb_ppm")], list(lab=y$lab), median)


   Welcome to R!

      lab  rb_ppm   sr_ppm   y_ppm  zr_ppm  nb_ppm
1      UH 30.0000 538.0000 38.5000 313.500 43.5000
2 UH-Hilo 30.1035 576.7875 43.3335 323.575 36.4445

mid-z-manova(x=edxrf)

y <- x[x$type=='quarry' & x$site=='Mauna Kea' & x$lab != 'UA',]
y.manova <- manova(cbind(rb_ppm, sr_ppm, y_ppm, zr_ppm, nb_ppm) ~ lab, data=y)
summary.aov(y.manova)

   Welcome to R!

 Response rb_ppm :
             Df  Sum Sq Mean Sq F value Pr(>F)
lab           1     0.1     0.1  0.0055 0.9409
Residuals   820 13814.6    16.8               

 Response sr_ppm :
             Df  Sum Sq Mean Sq F value Pr(>F)
lab           1    3560    3560  2.6352 0.1049
Residuals   820 1107738    1351               

 Response y_ppm :
             Df  Sum Sq Mean Sq F value  Pr(>F)  
lab           1    48.9    48.9  3.3969 0.06568 .
Residuals   820 11806.1    14.4                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

 Response zr_ppm :
             Df Sum Sq Mean Sq F value Pr(>F)
lab           1    247     247  0.3623 0.5474
Residuals   820 558779     681               

 Response nb_ppm :
             Df  Sum Sq Mean Sq F value   Pr(>F)   
lab           1    91.3    91.3  7.3289 0.006927 **
Residuals   820 10218.6    12.5                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

major-medians(x=edxrf)

y <- x[x$type=='quarry' & x$site=='Mauna Kea' & x$lab != 'UA',]
aggregate(y[,c("na2o_percent","mgo_percent","al2o3_percent","sio2_percent","k2o_percent","cao_percent","tio2_percent")], list(lab=y$lab), median)

1.8.4.2 Major elements

There appears to be significant inter-laboratory differences for most major elements


   Welcome to R!

      lab na2o_percent mgo_percent al2o3_percent sio2_percent k2o_percent
1      UH       3.0900       5.020        13.490      48.2100       1.150
2 UH-Hilo       2.5705       3.196        12.897      45.1285       0.939
  cao_percent tio2_percent
1      9.3800        3.995
2      8.5075        3.631

y <- x[x$type=='quarry' & x$site=='Mauna Kea' & x$lab != 'UA',]
y.manova <- manova(cbind(na2o_percent,mgo_percent,al2o3_percent,sio2_percent,k2o_percent,cao_percent,tio2_percent) ~ lab, data=y)
summary.aov(y.manova)

   Welcome to R!

 Response na2o_percent :
             Df  Sum Sq Mean Sq F value  Pr(>F)  
lab           1   0.630   0.630  4.0835 0.04363 *
Residuals   820 126.544   0.154                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

 Response mgo_percent :
             Df Sum Sq Mean Sq F value   Pr(>F)   
lab           1   6.32    6.32  8.0757 0.004597 **
Residuals   820 641.92    0.78                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

 Response al2o3_percent :
             Df  Sum Sq Mean Sq F value Pr(>F)
lab           1    1.16    1.16  0.6568 0.4179
Residuals   820 1452.06    1.77               

 Response sio2_percent :
             Df  Sum Sq Mean Sq F value Pr(>F)
lab           1    18.0    18.0  1.2246 0.2688
Residuals   820 12074.2    14.7               

 Response k2o_percent :
             Df  Sum Sq Mean Sq F value    Pr(>F)    
lab           1 0.09200 0.09200  34.159 7.327e-09 ***
Residuals   820 2.20842 0.00269                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

 Response cao_percent :
             Df  Sum Sq Mean Sq F value  Pr(>F)  
lab           1   1.311   1.311  4.9519 0.02633 *
Residuals   820 217.128   0.265                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

 Response tio2_percent :
             Df  Sum Sq Mean Sq F value   Pr(>F)   
lab           1  0.2955  0.2955  10.452 0.001274 **
Residuals   820 23.1860  0.0283                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

1.8.5 Diagnostic Plots

The plots in this section currently show the adzes measured using EDXRF at Hilo against material from quarries contained in the spreadsheet QuarryData.xls
Bishop Museum adzes are indicated in the plots as 'unknown'
Quarry data reported by Sinton and Sinoto are not included because EDXRF data from Hilo are not directly comparable with them
Plots using the most reliably measured elements are followed by plots using elements measured with less precision
Note that issues of measurement reliability are unlikely to yield false positive results

1.8.5.1 Strontium Zirconium plot

This plot is a favorite of Mills and Lundblad, based on PCA of Mid-Z trace elements Rb, Sr, Y, Zr, and Nb

sr-zr-scatter(x=edxrf)

library(ggplot2)
y <- x[x$lab=='UH-Hilo',]
b <- ggplot(y, aes(x=zr_ppm, y=sr_ppm, colour=site))
b + geom_point() + xlab("Zr (ppm)") + ylab("Sr (ppm)") + scale_colour_brewer(pal="Set1")

r/sr-zr-scatter.png

Scatterplot of Strontium and Zirconium

1.8.5.2 Stontium Niobium plot

sr-nb-scatter(x=edxrf)

 library(ggplot2)
y <- x[x$lab=='UH-Hilo',]
 b <- ggplot(y, aes(x=nb_ppm, y=sr_ppm, colour=site))
 b + geom_point() + xlab("Nb (ppm)") + ylab("Sr (ppm)") + scale_colour_brewer(pal="Set1")

r/sr-nb-scatter.png

Scatterplot of Strontium and Niobium

1.8.5.3 Zirconium Niobium plot

nb-zr-scatter(x=edxrf)

library(ggplot2)
y <- x[x$lab=='UH-Hilo',]
b <- ggplot(y, aes(x=zr_ppm, y=nb_ppm, colour=site))
b + geom_point() + xlab("Zr (ppm)") + ylab("Nb (ppm)") + scale_colour_brewer(pal="Set1")

r/nb-zr-scatter.png

Scatterplot of Zirconium and Niobium

1.8.5.4 Weisler and Kirch

This plot was used by Weisler and Kirch to source Cook Island polished adze flakes analyzed by EDXRF (M.I. Weisler and P.V. Kirch, Interisland and interarchipelago transfer of stone tools in prehistoric Polynesia, PNAS 93:1381-5)

nb-zr-sr-scatter(x=edxrf)

library(ggplot2)
y <- x[x$lab=='UH-Hilo',]
b <- ggplot(y, aes(x=nb_ppm/sr_ppm, y=zr_ppm/sr_ppm, colour=site))
b + geom_point() + xlab("Nb/Sr") + ylab("Zr/Sr") + scale_colour_brewer(pal="Set1")

r/nb-zr-sr-scatter.png

Scatterplot of Niobium to Strontium and Zirconium to Strontium ratios

1.8.5.5 Fractionation Trends

This plot is after Melinda Allen and Kevin Johnston's work in the Cook Islands

fractionation(x=edxrf)

library(ggplot2)
y <- x[x$lab=='UH-Hilo',]
b <- ggplot(y, aes(x=mgo_percent/(mgo_percent + fe_percent), y=zr_ppm/nb_ppm, colour=site))
b + geom_point() + xlab("Mg/(Mg+Fe)") + ylab("Zr/Nb") + scale_colour_brewer(pal="Set1")

$r/fractionation.png$

Fractionation trends at quarries and among adzes

1.8.5.6 Titanium Iron plot

ti-fe-scatter(x=edxrf)

library(ggplot2)
y <- x[x$lab=='UH-Hilo',]
b <- ggplot(y, aes(x=tio2_percent, y=fe_percent, colour=site))
b + geom_point() + xlab(expression(paste(TiO[2]," (%)"))) + ylab("Fe (%)") + scale_colour_brewer(pal="Set1")

r/ti-fe-scatter.png

Scatterplot of Titanium and Iron

1.8.5.7 Titanium Zirconium plot

ti-zr-scatter(x=edxrf)

library(ggplot2)
y <- x[x$lab=='UH-Hilo',]
b <- ggplot(y, aes(x=zr_ppm, y=tio2_percent, colour=site))
b + geom_point() + xlab("Zr (ppm)") + ylab(expression(paste(TiO[2]," (%)"))) + scale_colour_brewer(pal="Set1")

r/ti-zr-scatter.png

Scatterplot of Titanium and Zirconium

1.8.5.8 Zirconium Nickel plot

Note that Nickel usefully discriminates most of the O`ahu quarry rock from Hawai`i Island

ni-zr-scatter(x=edxrf)

library(ggplot2)
y <- x[x$lab=='UH-Hilo',]
b <- ggplot(y, aes(x=zr_ppm, y=ni_ppm, colour=site))
b + geom_point() + xlab("Zr (ppm)") + ylab("Ni (ppm)") + scale_colour_brewer(pal="Set1")

r/ni-zr-scatter.png

Scatterplot of Zirconium and Nickel

1.8.6 Discriminant analysis

Linear discriminant analysis appears to work with the EDXRF quarry data, using the mid-z trace elements Rubidium, Strontium, Yttrium, Zirconium, and Niobium

lda-accuracy-total(x=edxrf)

library(MASS)
y <- x[x$lab=='UH-Hilo' & x$type=='quarry',]
fit <- lda(site ~  rb_ppm + sr_ppm + y_ppm + zr_ppm + nb_ppm,
           data=y, na.action="na.omit", CV=TRUE)
# total percent correct
ct <- table(y$site, fit$class)
round(sum(diag(prop.table(ct))),4)


   Welcome to R!

[1] 0.9985

Linear discriminant analysis using jacknifed predictions indicates that the mid-z elements discriminate among the six quarries with a high degree of accuracy

lda-accuracy-category(x=edxrf)

library(MASS)
y <- x[x$lab=='UH-Hilo' & x$type=='quarry',]
fit <- lda(site ~  rb_ppm + sr_ppm + y_ppm + zr_ppm + nb_ppm,
           data=y, na.action="na.omit", CV=TRUE)
# Assess the accuracy of the prediction
# percent correct for each category
ct <- table(y$site, fit$class)
diag(prop.table(ct, 1))


   Welcome to R!

Haleakala   Kilauea Mauna Kea      Nu`u    Pololu  Waiahole 
1.0000000 0.9846154 1.0000000 1.0000000 1.0000000 0.9935484

Here is how the linear discriminate analysis assigns adzes to quarries

lda-mid-z(x=edxrf)

library(MASS)
y <- x[x$lab=='UH-Hilo',]
fit <- lda(site ~  rb_ppm + sr_ppm + y_ppm + zr_ppm + nb_ppm,
           data=y, na.action="na.omit", CV=TRUE)
adzes <- y$site=='unknown'
cbind(BPBM=y$bpbm[adzes],round(fit$posterior[adzes,],2))


BPBM	Haleakala	Kilauea	Mauna Kea	Nu`u	Pololu	Waiahole	unknown
1985.134.01 adze	0	0.1	0	0	0	0.64	0.27
50-HA-1349-G-5 adze	0	0.85	0	0	0	0	0.14
50-HA-900-P24-1 microadze	0	0	1	0	0	0	0
50-M9-B8 38 #3 microadze	0	0.04	0.13	0	0	0.05	0.78
50-Ma-B8-41-TP4-8 microad	0	0.86	0	0	0	0	0.14
50-MA-B9-26-5 adze	1	0	0	0	0	0	0
H100 E10-2 microadze	0	0.61	0	0	0	0.25	0.14
H14 #3 adze	0	0.73	0	0	0	0.22	0.05
H14 237	0	0.75	0	0	0	0.04	0.2
H14 39	0	0	1	0	0	0	0
H14 40 adze	0	0.9	0	0	0	0	0.1
H14-266 adze	0	0.71	0	0	0	0.01	0.28
H14-267 adze	0	0	0	0	0	1	0
H1E15 4	0	0	1	0	0	0	0
H2-5 (H52-5 on adze)	0	0.34	0	0	0	0.03	0.63
H2ETI-38	0	0	0	1	0	0	0
H2WT4-21 adze	0	0.78	0	0	0	0.13	0.09
H-47 A 1-1 microadze	0	0.73	0	0	0	0	0.27
H50-5(Q3) adze	0	0.7	0	0	0	0.01	0.29
H8 F12-1	0	0.86	0	0	0	0	0.14
H8 Sur. 4 adze	0	0	1	0	0	0	0
H9826 16-6 small adze	0	0.7	0	0	0	0.05	0.25
HA B22 65 D-102 microadze	0	0.86	0	0	0	0	0.14
HA B22-22 TP3-2 microadze	0	0.88	0	0	0	0	0.11
HA B22-65 B-65 1 microadz	0	0.77	0	0	0	0.03	0.2
HA B22-B5-B-66 narrow mic	0	0.76	0	0	0	0.03	0.2
HA-B22-65-G31 microadze	0	0	0	0	0	0.99	0.01
HA-D4-27-1 microadze	0	0.83	0	0	0	0.02	0.15
HA-D4-48-6 microadze	0	0.58	0	0	0	0.09	0.33
Haw 131 adze	0	0	1	0	0	0	0
Haw 66 adze	0	0.93	0	0	0	0	0.07
HAW130 adze	0	1	0	0	0	0	0
HAW-167 adze	0	0.75	0	0	0	0.02	0.23
HAW-7 adze	0	0.82	0	0	0	0	0.18
HAW-88 adze	0	0	0	0	0	1	0
HAW-89 adze	0	0.86	0	0	0	0	0.13
Haw-90 adze	0	0.7	0	0	0	0.01	0.29
HBC 524 adze	0	0.86	0	0	0	0	0.14
HI E151 Frag 2 out of 2	0	0.95	0	0	0	0	0.05
HI G2-3 Frag 1 out of 2	0	0.57	0	0	0	0	0.42
HV-76 E9-7 microadze	0	0.78	0	0	0	0	0.21
K 16 1 2-1 adze	0	0.68	0	0	0	0	0.32
No Number 1 out of 2 adze	0	0.79	0	0	0	0.09	0.12
No Number 2 out of 2 adze	0	0	0	0	0	1	0
S 27-3 1-664 adze	0	0	0	0	1	0	0

1.9 Database Structure

names(x)

   Welcome to R!

 [1] "id"                   "identifier"           "storage_location"    
 [4] "site"                 "weight"               "adze_type"           
 [7] "bevel"                "edge_present"         "chin_present"        
[10] "shoulder_present"     "poll_present"         "length_poll"         
[13] "length_shoulder"      "length_chin"          "width_edge"          
[16] "width_shoulder_front" "width_shoulder_back"  "thickness_shoulder"  
[19] "thickness_chin"       "edge_angle"           "bevel_shape"         
[22] "edge_shape_a"         "edge_shape_b"         "face_reduced"        
[25] "butt_angle"           "color_value"          "complete"            
[28] "broken"               "reworked"             "polish"

database-structure(x=whole-adzes)

str(x)

   Welcome to R!

'data.frame':   646 obs. of  30 variables:
 $ id                  : int  1 2 3 4 6 7 13 14 17 18 ...
 $ identifier          : chr  "OA B1-30-29" "50-OA-B1-30-T8-1" "OA-B1-30-27" "50-OA-B1-30-T6-1" ...
 $ storage_location    : chr  "Tray 1" "Tray 1" "Tray 1" "Tray 1" ...
 $ site                : chr  "50-Oa-B1-30" "50-Oa-B1-30" "50-Oa-B1-30" "50-Oa-B1-30" ...
 $ weight              : int  111 32 35 54 45 24 31 29 40 245 ...
 $ adze_type           : chr  "primary" "secondary" "primary" "secondary" ...
 $ bevel               : chr  "single" "single" "single" "single" ...
 $ edge_present        : chr  "true" "true" "true" "true" ...
 $ chin_present        : chr  "true" "true" "true" "true" ...
 $ shoulder_present    : chr  "true" "true" "true" "true" ...
 $ poll_present        : chr  "true" "true" "true" "true" ...
 $ length_poll         : int  92 58 58 50 67 51 65 58 43 128 ...
 $ length_shoulder     : int  48 28 29 29 34 21 31 35 32 72 ...
 $ length_chin         : int  11 19 9 18 6 5 5 10 16 10 ...
 $ width_edge          : int  33 19 21 37 29 25 21 23 23 46 ...
 $ width_shoulder_front: int  29 18 21 36 27 22 17 20 21 45 ...
 $ width_shoulder_back : int  30 18 20 34 28 22 18 20 24 46 ...
 $ thickness_shoulder  : int  16 11 10 12 10 8 7 10 15 17 ...
 $ thickness_chin      : int  11 10 8 12 9 5 4 9 16 11 ...
 $ edge_angle          : int  36 35 36 35 36 34 34 34 35 38 ...
 $ bevel_shape         : chr  "convex" "convex" "convex" "convex" ...
 $ edge_shape_a        : chr  "straight" "straight" "straight" "straight" ...
 $ edge_shape_b        : chr  "straight" "straight" "straight" "straight" ...
 $ face_reduced        : chr  "true" "false" "true" "true" ...
 $ butt_angle          : int  10 0 10 0 0 0 14 0 0 8 ...
 $ color_value         : num  4 3 4 4 5 3 2.5 3 3 3 ...
 $ complete            : chr  "complete" "complete" "complete" "complete" ...
 $ broken              : chr  "" "" "" "edge and blade" ...
 $ reworked            : chr  "" "other" "" "other" ...
 $ polish              : chr  "present" "present" "present" "present" ...

1.10 Problems

1.10.1 Duplicate entries

Here is a list of duplicate entries and their storage locations
Need to delete duplicates


identifier	storage_location	n
10038	9511-10038	2
9511	9511-10038	2
9512	9511-10038	2
9812	9511-10038	2
Haw-131	Tray 4	2
Haw-89	Tray 4	2

1.10.2 Missing measures on whole adzes

Tool weight is missing

y = x[x$weight < 1,]
y[,c(2,3,5)]


identifier	storage_location	weight
C.1161	C.303-C.1179	0
C.6090	C.5501-C.6093	0
c.6034	C.5501-C.6093	0
C.8290	C.5501-C.6093	0
C.8297	C.8290-8352	0
C.4505	C.4504-C.4956	0
C.5488	C.5488	0

Tool length is missing

y = x[x$length_poll < 1,]
y[,c(2,3,12)]


identifier	storage_location	length_poll

Shoulder length is missing

y = x[x$length_shoulder < 1,]
y[,c(2,3,13)]


identifier	storage_location	length_shoulder
B1159	B.1096-B.1166	0
C.1772	C.1772-C.1838	0
C.1674	C.1671-C.1710	0

Chin length is missing

y = x[x$length_chin < 1,]
y[,c(2,3,14)]


identifier	storage_location	length_chin
C.5490	C.5488-5499	0

Edge width is missing

y = x[x$width_edge < 1,]
y[,c(2,3,15)]


identifier	storage_location	width_edge

Front shoulder width is missing

y = x[x$width_shoulder_front < 1,]
y[,c(2,3,16)]


identifier	storage_location	width_shoulder_front

Back shoulder width is missing

y = x[x$width_shoulder_back < 1,]
y[,c(2,3,17)]


identifier	storage_location	width_shoulder_back

Shoulder thickness is missing

y = x[x$thickness_shoulder < 1,]
y[,c(2,3,18)]


identifier	storage_location	thickness_shoulder

Chin thickness is missing

y = x[x$thickness_chin < 1,]
y[,c(2,3,19)]


identifier	storage_location	thickness_chin
C.5490	C.5488-5499	0

Edge angle is missing

y = x[x$edge_angle < 1,]
y[,c(2,3,20)]


identifier	storage_location	edge_angle
C.1772	C.1772-C.1838	0
C.1674	C.1671-C.1710	0
c.6034	C.5501-C.6093	0
C.5488	C.5488	0
C.9183	C.9180-84	0

Author: Thomas S. Dye

Date: 2010-12-24 06:19:05 HST

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