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# Statistics for Anthropology

**by**Lorena Madrigal

2nd

### 9780521147088

0521147085

Paperback

4/9/2012

Cambridge University Press

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## Summary

Anthropology as a discipline is rapidly becoming more quantitative, and anthropology students are now required to develop sophisticated statistical skills. This book provides students of anthropology with a clear, step-by-step guide to univariate statistical methods, demystifying the aspects that are often seen as difficult or impenetrable. Explaining the central role of statistical methods in anthropology and using only anthropological examples, the book provides a solid footing in statistical techniques. Beginning with basic descriptive statistics, this new edition also covers more advanced methods such as analyses of frequencies and variance, simple and multiple regression analysis with dummy and continuous variables. It addresses commonly encountered problems such as small samples and non-normality. Each statistical technique is accompanied by clearly worked examples and the chapters end with practice problem sets. Many of the datasets are available for download at www.cambridge.org/9780521147088.

## Author Biography

Lorena Madrigal is Professor of Anthropology at the University of South Florida, Tampa. A biological anthropologist, she is particularly interested in the evolution of Afro and Indo Costa Rican populations residing in the Atlantic coast of Costa Rica. She is currently President of the American Association of Physical Anthropologists.

## Table of Contents

List of partial statistical tables | p. xi |

Preface | p. xiii |

Introduction to statistics and simple descriptive statistics | p. 1 |

Statistics and scientific enquiry | p. 1 |

Basic definitions | p. 3 |

Variables and constants | p. 3 |

Scales of measurement | p. 4 |

Accuracy and precision | p. 6 |

Independent and dependent variables | p. 6 |

Control and experimental groups | p. 7 |

Samples and statistics, populations and parameters. Descriptive and inferential statistics. A few words about sampling | p. 8 |

Statistical notation | p. 9 |

Chapter 1 key concepts | p. 12 |

Chapter 1 exercises | p. 12 |

The first step in data analysis: summarizing and displaying data. Computing descriptive statistics | p. 13 |

Frequency distributions | p. 13 |

Frequency distributions of discontinuous numeric and qualitative variables | p. 13 |

Frequency distributions of continuous numeric variables | p. 15 |

Stem-and-leaf displays of data | p. 17 |

Graphing data | p. 18 |

Bar graphs and pie charts | p. 19 |

Histograms | p. 21 |

Polygons | p. 21 |

Box plots | p. 21 |

Descriptive statistics. Measures of central tendency and dispersion | p. 25 |

Measures of central tendency | p. 26 |

Measures of variation | p. 29 |

Chapter 2 key concepts | p. 39 |

Computer resources | p. 40 |

Chapter 2 exercises | p. 40 |

Probability and statistics | p. 42 |

Random sampling and probability distributions | p. 43 |

The probability distribution of qualitative and discontinuous numeric variables | p. 44 |

The binomial distribution | p. 46 |

The Poisson distribution | p. 48 |

Bayes' theorem | p. 53 |

The probability distribution of continuous variables | p. 57 |

z scores and the standard normal distribution (SND) | p. 63 |

Percentile ranks and percentiles | p. 71 |

The probability distribution of sample means | p. 73 |

Is my bell shape normal? | p. 77 |

Chapter 3 key concepts | p. 78 |

Computer resources | p. 79 |

Chapter 3 exercises | p. 80 |

Hypothesis testing and estimation | p. 83 |

Different approaches to hypothesis testing and estimation | p. 83 |

The classical significance testing approach | p. 83 |

The maximum likelihood approach | p. 84 |

The Bayesian approach | p. 84 |

Estimation | p. 84 |

Confidence limits and confidence interval | p. 85 |

Point estimation | p. 89 |

Hypothesis testing | p. 90 |

The principles of hypothesis testing | p. 90 |

Errors and power in hypothesis testing | p. 93 |

Hypothesis tests using z scores | p. 98 |

One-and two-tailed hypothesis tests | p. 100 |

Assumptions of statistical tests | p. 101 |

Hypothesis testing with the t distribution | p. 103 |

Hypothesis tests using t scores | p. 104 |

Reporting hypothesis tests | p. 105 |

The classical significance testing approach. A conclusion | p. 106 |

Chapter 4 key concepts | p. 106 |

Chapter 4 exercises | p. 107 |

The difference between two means | p. 108 |

The un-paired t test | p. 108 |

Assumptions of the un-paired t test | p. 112 |

The comparison of a single observation with the mean of a sample | p. 116 |

The paired t test | p. 117 |

Assumptions of the paired t test | p. 119 |

Chapter 5 key concepts | p. 120 |

Computer resources | p. 120 |

Chapter 5 exercises | p. 121 |

The analysis of variance (ANOVA) | p. 122 |

Model I and model II ANOVA | p. 122 |

Model I, one-way ANOVA. Introduction and nomenclature | p. 123 |

ANOVA assumptions | p. 131 |

Post-hoc tests | p. 132 |

The Scheffé test | p. 133 |

Model I, two-way ANOVA | p. 135 |

Other ANOVA designs | p. 143 |

Chapter 6 key concepts | p. 144 |

Computer resources | p. 145 |

Chapter 6 exercises | p. 145 |

Non-parametric tests for the comparison of samples | p. 146 |

Ranking data | p. 147 |

The Mann-Whitney U test for a two-sample un-matched design | p. 148 |

The Kruskal-Wallis for a one-way, model I ANOVA design | p. 153 |

The Wilcoxon signed-ranks test for a two-sample paired design | p. 159 |

Chapter 7 key concepts | p. 164 |

Computer resources | p. 164 |

Chapter 7 exercises | p. 164 |

The analysis of frequencies | p. 166 |

The X^{2} test for goodness-of-fit | p. 166 |

The Kolmogorov-Smirnov one sample test | p. 170 |

The X^{2} test for independence of variables | p. 172 |

Yates' correction for continuity | p. 175 |

The likelihood ratio test (the G test) | p. 176 |

Fisher's exact test | p. 178 |

The McNemar test for a matched design | p. 183 |

Tests of goodness-of-fit and independence of variables. Conclusion | p. 184 |

The odds ratio (OR): measuring the degree of the association between two discrete variables | p. 185 |

The relative risk (RR): measuring the degree of the association between two discrete variables | p. 188 |

Chapter 8 key concepts | p. 190 |

Computer resources | p. 190 |

Chapter 8 exercises | p. 191 |

Correlation analysis | p. 193 |

The Pearson product-moment correlation | p. 193 |

Non-parametric tests of correlation | p. 199 |

The Spearman correlation coefficient r_{s} | p. 199 |

Kendall's coefficient of rank correlation-tau (¿) | p. 202 |

Chapter 9 key concepts | p. 208 |

Chapter 9 exercises | p. 208 |

Simple linear regression | p. 209 |

An overview of regression analysis | p. 210 |

Regression analysis step-by-step | p. 214 |

The data are plotted and inspected to detect violations of the linearity and homoscedasticity assumptions | p. 214 |

The relation between the X and the Y is described mathematically with an equation | p. 215 |

The regression analysis is expressed as an analysis of the variance of Y | p. 215 |

The null hypothesis that the parametric value of the slope is not statistically different from 0 is tested | p. 217 |

The regression equation is used to predict values of Y | p. 217 |

Lack of fit is assessed | p. 219 |

The residuals are analyzed | p. 221 |

Transformations in regression analysis | p. 225 |

Chapter 10 key concepts | p. 232 |

Computer resources | p. 232 |

Chapter 10 exercises | p. 232 |

Advanced topics in regression analysis | p. 234 |

The multiple regression model | p. 234 |

The problem of multicollinearity/collinearity | p. 235 |

The algebraic computation of the multiple regression equation | p. 236 |

An overview of multiple-regression-model building | p. 240 |

Dummy independent variables | p. 247 |

An overview of logistic regression | p. 251 |

Writing up your results | p. 255 |

Chapter 11 key concepts | p. 255 |

Computer resources | p. 256 |

Chapter 11 exercises | p. 256 |

References | p. 257 |

Index | p. 260 |

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