Drennan R.D. Statistics for Archaeologists: A Common Sense Approach
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Index
Adjacent values, 40
Anderberg’s coefficient, 280–281
Archaeology
artifact typology, 309
multivariate analysis, 264
quadrats
random sample, 240, 241
selection of, 242
two-dimensional spatial unit, 240
radiocarbon dating, 258
statistics, 322–324
transects, random sample, 241–243
Archaic subperiods weights,
comparison of, 167
Artifact status index, floor area, 229
Average linkage clustering
similarities, matrix of, 313
similarity coefficients, 313–315
similarity scores, 315
Back-to-back stem-and-leaf plots,
9–11
box-and-dot plot and, 133
of Early and Late Classic period site areas,
133–135
Formative and Classic period house floor
areas, 147
of post hole diameters from Black and
Smith sites, 10–11, 40–41
of weights of flakes recovered from
bell-shaped pits, 18–19
Bar graphs
of proportions of ceramic types in
assemblages, 72
of proportions of incised and unincised
sherds, 71–72
pseudo three-dimensional, 73
stacked, 74
three-dimensional effect of, 73
Batch
comparison, 42
examples of, 3
Formative and Classic period house floor
areas, 147–148
indexes of center of
mean, 17–19
median, 19–20
skewed distribution, 52–53
trimmed mean, 21–23
index of spread of
midspread, 28–29
range, 27–28
selection of, 34–35
trimmed standard deviation, 32–34
variance and standard deviation, 29–32
multiple peaks in, 12–13
normality in distributions of, 59–61
removal of level from, 42
removal of spread from
mathematical method, 42
post hole diameters, 42–43
unusualness, 45–48
shape of, 51
effect of transformations on
(see Transformations)
symmetry, 51–53
standardization based on mean and
standard deviation, 48
stem-and-leaf plot of (see Stem-and-leaf
plot)
with two centers, 23–25
Best-fit straight line, 204–207, 209
devastating effect of, 219
downward curvilinear pattern, 220
oval clouds, effect of, 219
for points, 208
residuals, sum of squares, 209
scatter plot, 209
327
328 Index
site area, 214
variance, 210
Bias, sampling, 92–93
Black-Smith sites
floor areas of structures at, 23–24
post hole diameters, removal of level
and spread from, 48
Bootstrap
assessment of error ranges with, 138
error ranges for median and, 137
histogram, 136
Bowl sherds, average proportion of, 183
Box-and-dot plot
Early and Late Classic period site areas,
135
Formative and Classic period house floor
areas, 147
graphical approach, 38
with level and spread removed, 44–46
post hole diameters at Black–Smith sites,
40–41
of post hole diameters from Smith site,
38–40
stem-and-leaf plot and, 37
Bronze Age, 256
Burials, 266, 268, 269, 290
Categorical variables, 211
Categories (See also Batch)
data recorded in terms of, 63
definition of, 63
pottery decoration, 68
pottery sherds, 63
sherds, unincised and incised, 65–68
and sub-batches, 73–75
Central limit theorem, 106, 128
Ceramic assemblage
cord-marked sherds,
proportion of, 244
standard error, 246
Ceramic typology, 264
Chi-square
average, 183
comparison, 182–188
distribution, 185
statistics
degrees of freedom, 186
error ranges, 188
tests, 183, 186, 187, 191
area survey, 194
Cramer’s V, 199
data, 192
expected numbers of sites, 195
principal concern, 191
two-by-two table, 192
Classical statistical theory, 133
Cluster analysis, 309
Column proportions, 69
Commonsense representation, 272
Complete linkage clustering
sequence of, 312
similarity scores, 313
Computational method, 207
Computer programs, 178
Computer statpacks, 192, 246
Confidence
intervals (see Error ranges)
vs. precision, 115–118
statistical notion of, 257
in statistics, 151–152
Cord-marked sherds, proportions
estimation, 249
Cottonwood River valley
Archaic period animals, hunting of, 165
Archaic projectile points, 165
weight and period data, 166
early/middle/late archaic projectile points
of, 167–171
Cramer’s V, 199
Cross tabulations, 192
Cube transformation, 56
Data analysis, 193
Data-recording error, 217
Debitage, 267
Densities and proportions, 70–71
Dissimilarity coefficients, 271
Dummy quadrats, 242
Eigenvalue, 303
Error ranges, 126
assessment of, 138
calibration, 122
at 95% confidence level, 120, 130, 143
estimated proportions, comparison,
181–182
at fixed level of confidence, 122
graphical representation of, 149
level of confidence associated with, 119,
120, 126, 137
means of populations, 118
in notched box plots, 162
for specific confidence levels, 121–122
1 standard error range, 121–122, 140
t test and, 155
Index 329
Estimation proportion, 182
Euclidean distances, 272–274, 280
calculation of, 277
projectile points
measurement of, 273
standardized variables, 276
tabular presentation, 274
Pythagorean theorem, 272
standard deviations, 275
standardized variables, 274–276
standardization of measurements, 276
two-dimensional scaling configuration,
289
variables, 276
Excavations, 265
Expected values, 184
Fauna/sherd ratio, 266, 290, 305
Finite population corrector, 123, 124, 141
Fisher’s exact test, 193
Fisher’s method, 192
Formative Mesoamerican site, 265
Gower’s coefficient, 280, 283
Grab sampling, 86
Grid squares, 239
Gut feelings, 260
Haphazard sampling, 86
Haphazard surface collection, 89–91
Heterogeneous batch, 140
Hierarchical cluster analysis, 309
agglomerative, 310
clustering by variables, 316–318
clustering criteria, 310
Histograms, 11, 14, 136
Household units, 281–283
Ixcaquixtla household dataset, 286, 287
clustering of, 318
single-linkage clustering, 318
variables, 319
clusters and gradients, 297
component loadings analysis, 304
component loadings, analysis of, 306
decline of stress values, graph of, 287
detectable cluster, 293
gradient identification, 293
household units, multidimensional scaling
of, 288
multidimensional scaling, 294, 295
domain of, 296
orthogonally rotated component loadings,
306
presence/absence variables, 303
principal components extracted,
eigenvalues, 304
similarity, matrix of, 286
spurious patterns, substantial risk of, 296
three-dimensional configuration, 289
three-dimensional scaling, plots of,
290–295
Ixcaquixtla household units, similarities,
281–283
Ixcaquixtla, multivariate dataset, 265
Jaccard’s coefficients, 278
presence/absence variables, 277–279
similarity between sherds, 279
simple matching coefficient, 277, 279
Jackknife, 138
Jar sherds
comparison of bowl and, 182
proportions of bowl and, 181
Judgmental sampling, 86, 87
Kiln wasters and obsidian, relationship,
306
Kiskiminetas river valley
areas of sites in, 12
histogram of areas of sites in, 13
Konsankoro plain, 224, 226
Least-squares regression, 206
Linear regression, 210, 211
logic of, 218, 223
statistical technique, 205
Linear relationships
algebraic expressions, 202
comparison of, 203
geometric expressions, 202
straight-line relationships, 201, 202, 204
Linkage criterion
dendrograms, comparison of, 315
hierarchical clustering, 316
Lithic debitage, proportion of, 319
Log transformation, 57
Mace heads, 266, 267
Marine shell, 266
330 Index
Mean, 169, 171
calculation of, 17, 18
median and trimmed mean, 23
outliers and, 20–21
standardization based on, 70
trimmed (see Trimmed mean)
weights of flakes from pits, 18, 28
Mean projectile point length, standard
deviations, 275
Mean weights, 169
differences, strength of, 174–175
estimation, 177, 178
probability, 177
Measurement variable, 199, 201
categorical variable, relationship, 199
logic of, 210
percentages, 199
product-moment correlation coefficient,
210
real measurements, 268
relationship, 199
scatter plot, 200, 201
Median
estimation, 178
mean and trimmed mean, 23
weights of flakes recovered from
bell-shaped pits, 18, 28
Midspread
method for calculation, 28–29
of weights of flakes recovered from pits, 29
Missing data
code, 269
notion of, 268
Multidimensional scaling, 285, 305, 317
algorithms, 286
interpretation of, 289
one-dimensional configuration, 286
similarity/dissimilarity, matrix of, 285
simplicity of, 285
Multiple regression, 263
Multiple-sample case, 183
Multivariate analysis, 263–269, 324–325
artifact typologies, 264
dataset, 271
missing data, 268
missing data codes, 269
Multivariate approaches and variables,
263–264
Multivariate datasets, 264, 267, 269
Negative reciprocal transformation, 56
Neolithic sites, 256, 257
Nonrandom sampling procedures, 88–89
Normal distribution, 59–61
Notched box-and-dot plot, Early and Late
Classic site areas, 161, 162
Null hypothesis
postulates, 157
rejection/acceptation, 157, 158, 160
significance tests and, 157–159
Obsidian artifacts, sample of, 91, 92
Obsidian lithics records, 267
Obsidian projectile points, 251, 252
One-sample t test, 156–157
Outliers
definition, 4
elimination, 20–21
low/high, 40
Pearson’s r, 210, 223, 225
Physical measurements, 271
Pie charts, 73
Point distributions, linear regression, 217
Pooling estimates, 234–236
Population proportion estimation
cluster sampling, standard error, 243
confidence levels and, 253, 254
large sample, 142–143
obsidian projectile points
error range, 139–141
standard deviation of proportion,
140
standard error estimation, 141
random sampling, 243
small sample, 142
Populations
confidence vs. precision, 115–117
estimation, 239
samples, means, 182
finite, 123–124
infinite, 109, 123
mean
largest possible error in estimation,
98–99
and mean of special batch, 104–105
procedure of estimation, 124–125
post holes, 97–98
proportion (see Population proportion
estimation)
and sample mean, 110
special batching of means of samples from,
110–111
standard deviation, 110
Index 331
within 1 standard error of sample mean,
115
trimmed mean of, 128–130
Presence/absence variables, 267
coded, 278
correlation coefficients, 317
scatter plot, relationship, 301
square symmetric matrix, 317
Principal components analysis
category variables, 301
correlation coefficients, 301
multidimensional scaling, 299–300, 317
multivariate analysis, 307
regression analysis, 307
variables, set of, 300
Principal components, extraction
component loadings, 303
dataset, scatter plot, 302
procedure for, 302
Probability, 175
Product-moment correlation coefficient, 210
Projectile point weights
early/middle/late archaic subsample,
169–171
period, comparison of, 168
stem-and-leaf plots for, 169, 171
shape differences, 170
Proportions and densities, 70–71
Pseudo three-dimensional bar graphs, 73
Purposive obsidian sample, 91–92
Purposive sampling, 86–88
Radiocarbon age, 258
Random number table, 82–84
Random sample
assumptions, 128
means of selection, 82
of projectile points, 108–109
sherds, ten excavation units, 244
from single population, 97
target population and, 94
Range
definition, 27
statistical properties, 35
of weights of flakes recovered from pits,
27–28
Rank order correlation coefficient, 222
Rank order relationship, magnitude of, 222
Regression analysis, 207, 211
mathematical complexity of, 206
measurement, 214
prediction, 208
Regression relationships, 212
Regular/trimmed standard deviation squared,
178
Representativeness, 85
Resampling technique
bootstrap (see Bootstrap)
jackknife, 138
Residuals
hoes and soil productivity, 215
scatter plot of, 216
number of hoes, 216
positive/negative, 215
predictions, 214
regression analysis, 213
soil productivity, 215
R´ıo Seco valley
hoes, Oasis phase sites, 214
number of hoes, 200
Oasis phase sites, 212
Row proportions, 69–70
Samples (See also Sampling)
comparison
on basis of error bars, 150
Formative and Classic period house
floor areas and size, 149–150
by one-sample t test, 156–157
in terms of level and spread, 148
by two-sample t test, 153–156
two-way, 150–151
dataset, 265–268
estimation of population means, 247–248
of given size, all possible, 97–99
of larger given size, all possible, 100–103
projectile points, lengths of, 247
sample mean, calculation of, 248
selection
biased, 92
effects of known or possible bias in, 89
large, 125–129
nonrandom ways of, 86
size and sampling fraction, 127
size, effect of, 189–190
standard error, 247
Sampling (See also Samples)
bias, 92–93
calculation check, 246
carbon atoms, 258
cluster sampling, 239
computerized solution, 246
definition of, 80
densities, 249
distribution of mean, 106
elements, 239
332 Index
estimation of population, 239
fraction, 127
heavy weight, 246
mean site size, 233
pooled estimate, 236
problem of, 259
purpose of, 80–82
random sample selection, 259
random sampling, 82–94, 249
and reality, 255–260
with replacement, 84–85
river bottom sites, 235
site areas (ha), 234
statistics, 251
stem-and-leaf plots
areas of sites, 235
symmetrical shape, 233
stratified random, 86
stratum pooling, 235
subgroups, population, 233–234
technical problems, impact, 243
weighted deviations calculation, 245
Scrapers
length, width, thickness, and weight of, 3
much too dense a stem-and-leaf plot of
weights of, 8
stem-and-leaf plot at an appropriate scale
of weights of, 7
too dense a stem-and-leaf plot of weights
of, 8
too sparse stem-and-leaf plot of
weights of, 6
Shell/sherd ratio, 266
Significance probability, 151–152
Significance, statistical concept of, 151
Significance tests, 157–159
Significant rank-order correlation, 226–230
Similarity and dissimilarity coefficients,
271–272
Simple random sampling, 85
Single linkage clustering, 310–312
dendrogram, 311
similarity coefficients, matrix of, 310
Skewed distribution, 52–53
Software solution, 283
Soil productivity ratings, 224
Spatial sampling, 240–243
Spearman’s rank correlation coefficient, 223,
224
calculation of, 223, 224
normal distributions, 228
probability values for, 228
rank order correlations, 228
rank ordering determination, 225
soil productivity, 225
Special batch, 103–104
characteristics of, 106
means of samples selected from population,
111–115
spread of, 111
standard deviation of (see Standard error)
Square transformation, 56
Standard deviation
equation for, 31
of flakeweights from pit 1, 31–32
of flakeweights from pit 2, 30
of proportion, 140
of special batch (see Standard error)
standardization of based on, 52trimmed
(see Trimmed standard deviation)
Standard error
definition of, 105
equation for, 105
error range of, 126
assessment of, 138
calibration, 122
at 95% confidence level, 123–129, 143
at fixed level of confidence, 122
graphical representation of, 149
level of confidence associated with,
119, 121, 126, 137
means of populations, 118
in notched box plots, 162
1 standard error range, 121–122, 140
t test and, 155
finite population corrector in equation for,
123–124
of mean, 137
pooled, 150–151
of sample, 105, 121
Standardized number scale, 47
Statistical reasoning, 257
Statistical tools, 259–260
Statistic analogous, 211
Statpack, 14
Stem-and-leaf plot
back-to-back (see Back-to-back
stem-and-leaf plots)
bunching of numbers in, 11, 12
of diameters of post holes at black site, 4
much too dense, 8
scale for
approaches to spreading out or
compressing, 8–9
appropriate, 4, 7
symmetry of batch with, 51–52
too dense, 7–8
Index 333
too sparse, 6
of weights of scrapers from black
site, 5–7
Straight-line equations
linear equation, 206
principles of, 204
Straight-line relationships
algebraically, 205
mathematical relationship, 204
scatter plot, 204
Stratified random sampling, 86
Stratified sampling
benefits of, 236–240
error range, 237
Strength, measures of, 188–189
Student’s t distribution, 118, 119
Sum of squares, 30
Target population
inferences about, 94
and population, discrepancies between, 95
random sampling procedures, 94
Transformations
for asymmetry correction
normal ruler, 59
upward skewness, 56–57
cube, 56
effect on shape of batch, 54–56
negative reciprocal, 56
selection,
square, 56
Trimmed mean, 21–22, 178
mean and median, 23
of population, 128–130
Trimmed standard deviation, 32
calculation of, 33
equation for, 33
for flake weights from Pit 1, 34
t test, 178, 194
assumptions, 161
one-sample, 156–157
two-sample, 153–156, 199
Two-peaked batch, 25
Two-sample t test
assumptions, 161
for Formative and Classic period house
floor area samples, 153–154
pooled standard error from, 154, 156
Variables, 200, 267
Variance
analysis, 168–173
archaeology, 175
calculation, 174
computer output for, 174
computer programs, 178
dependent/independent, 176
grouping/independent, 174
between groups, 171, 173
within groups, 172
populations vs. relationship, 176–178
regression analysis, 211
relationships vs. populations, 191
samples, 169
subsamples, 172
basic concept of, 29
equation for, 31
Vessel, sherds of, 183
expected number of, 184
row proportions of, 183
sample of, 189
Volume measurements, 221
Weight dependent variable, 174
Weighting factor, 245, 248
Weights comparison samples, 170
Winsorized batch, 33
Winsorized variance, 33
Wood-plank-with-mud-brick, 267