Statistics for Archaeologists (eBook)

Preface to the Second Edition 6
Contents 12
Part I Numerical Exploration 17
1 Batches of Numbers 18
Stem-and-Leaf Plots 19
Back-to-Back Stem-and-Leaf Plots 24
Histograms 26
Multiple Bunches or Peaks 26
Practice 29
2 The Level or Center of a Batch 31
The Mean 31
The Median 33
Outliers and Resistance 34
Eliminating Outliers 34
The Trimmed Mean 35
Which Index to Use 37
Batches with Two Centers 37
Practice 39
3 The Spread or Dispersion of a Batch 41
The Range 41
The Midspread or Interquartile Range 42
The Variance and Standard Deviation 43
The Trimmed Standard Deviation 46
Which Index to Use 48
Practice 50
4 Comparing Batches 51
The Box-and-Dot Plot 51
Removing the Level 56
Removing the Spread 56
Unusualness 59
Standardizing Based on the Mean and Standard Deviation 62
Practice 63
5 The Shape or Distribution of a Batch 64
Symmetry 64
Transformations 66
Correcting Asymmetry 69
The Normal Distribution 72
Practice 74
6 Categories 75
Column and Row Proportions 81
Proportions and Densities 82
Bar Graphs 83
Categories and Sub-batches 85
Practice 87
Part II Sampling 89
7 Samples and Populations 90
What Is Sampling? 91
Why Sample? 91
How Do We Sample? 93
Representativeness 96
Different Kinds of Sampling and Bias 96
Use of Nonrandom Samples 99
The Target Population 104
Practice 107
8 Different Samples from the Same Population 108
All Possible Samples of a Given Size 108
All Possible Samples of a Larger Given Size 111
The ``Special Batch'' 114
The Standard Error 115
9 Confidence and Population Means 118
Getting Started with a Random Sample 119
What Populations Might the Sample Have Come From? 120
Confidence versus Precision 126
Putting a Finer Point on Probabilities – Student's T 129
Error Ranges for Specific Confidence Levels 132
Finite Populations 134
A Complete Example 135
How Large a Sample Do We Need? 137
Assumptions and Robust Methods 139
Practice 141
10 Medians and Resampling 144
The Bootstrap 147
Practice 149
11 Categories and Population Proportions 150
How Large a Sample Do We Need? 153
Practice 154
Part III Relationships between Two Variables 156
12 Comparing Two Sample Means 157
Confidence, Significance, and Strength 161
Comparison by t Test 163
The One-Sample t Test 166
The Null Hypothesis 167
Statistical Results and Interpretations 170
Assumptions and Robust Methods 171
Practice 173
13 Comparing Means of More than Two Samples 175
Comparison with Estimated Means and Error Ranges 176
Comparison by Analysis of Variance 178
Strength of Differences 184
Differences between Populations versus Relationshipsbetween Variables 186
Assumptions and Robust Methods 188
Practice 189
14 Comparing Proportions of Different Samples 191
Comparison with Estimated Proportions and Error Ranges 191
Comparison with Chi-Square 192
Measures of Strength 198
The Effect of Sample Size 199
Differences between Populations versus Relationships between Variables 201
Assumptions and Robust Methods 201
Postscript: Comparing Proportions to a Theoretical Expectation 203
Practice 206
15 Relating a Measurement Variable to Another Measurement Variable 208
Looking at the Broad Picture 209
Linear Relationships 210
The Best-Fit Straight Line 213
Prediction 216
How Good Is the Best Fit? 218
Significance and Confidence 220
Analysis of Residuals 222
Assumptions and Robust Methods 226
Practice 229
16 Relating Ranks 232
Calculating Spearman's Rank Correlation 233
Significance 235
Assumptions and Robust Methods 237
Practice 237
Part IV Special Topics in Sampling 239
17 Sampling a Population with Subgroups 240
Pooling Estimates 241
The Benefits of Stratified Sampling 243
18 Sampling a Site or Region with Spatial Units 245
Spatial Sampling Units: Points, Transects, and Quadrats 246
Estimating Population Proportions 249
Estimating Population Means 253
Densities 255
19 Sampling without Finding Anything 256
20 Sampling and Reality 260
Part V Multivariate Analysis 266
21 Multivariate Approaches and Variables 267
A Sample Dataset 268
Kinds of Variables, Missing Data, and Statpacks 271
22 Similarities between Cases 274
Euclidean Distance 275
Euclidean Distance with Standardized Variables 277
When to Use Euclidean Distance 279
Presence/Absence Variables: Simple Matching and Jaccard's Coefficients 280
Mixed Variable Sets: Gower's and Anderberg's Coefficients 283
Similarities between Ixcaquixtla Household Units 284
23 Multidimensional Scaling 287
Configurations in Different Numbers of Dimensions 288
Interpreting the Configuration 291
24 Principal Components Analysis 300
Correlations and Variables 301
Extracting Components 303
Carrying Out the Analysis 304
25 Cluster Analysis 309
Single Linkage Clustering 310
Complete Linkage Clustering 312
Average Linkage Clustering 313
Which Linkage Criterion to Choose 315
How Many Clusters to Define 316
Clustering by Variables 316
Clustering the Ixcaquixtla Household Data 318
Index 326
Suggested Reading 321
General Statistics Books 321
Introductions To Statistics For (And Often By) Archaeologists 322
Archaeologists Consider Statistics In Our Discipline 323
Multivariate Analysis 324
Index 326