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| Preface | |
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| Introduction | |
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| Why Statistics and Sampling? | |
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| What is so Special about Spatial Data? | |
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| MAUP- The Modifiable Areal Unit Problems | |
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| Spatial Autocorrelation | |
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| Spatial Data and the Needs For Spatial Analysis/Statistics | |
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| Fundamentals in Spatial Analysis and Statistics | |
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| Scales of Measurement | |
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| Mathematical Notations | |
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| Scale, Extent, and Projection | |
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| ArcView Notes - Data Model and Examples | |
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| Data Model Used In Arcview GIS | |
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| Random Sampling - The Generic Way | |
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| Random and Systematic Point Sampling - An Extended Function | |
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| References Cited | |
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| Exercises | |
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| Classical Statistics | |
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| Distribution Descriptors: One Variable (Univariate) | |
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| Measures of Central Tendency | |
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| Mode | |
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| Median | |
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| Mean | |
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| Grouped or Weighted Mean | |
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| Measures of Dispersion | |
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| Range, Minimum, Maximum and Percentiles | |
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| Mean Deviation | |
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| Variance and Standard Deviation | |
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| Weighted Variance and Weighted Standard Deviation | |
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| Coefficient of Variation | |
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| ArcView Examples | |
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| Descriptive Statistics | |
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| Higher Moments Statistics | |
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| Skewness and Kurtosis | |
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| ArcView Examples | |
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| Statistical Charts | |
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| Additional Statistics | |
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| Application Example | |
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| Summary | |
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| References Cited | |
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| Exercises | |
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| Relationship Descriptors: Two Variables (Bivariate) | |
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| Correlation Analysis | |
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| Correlation: Nominal Scale | |
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| Nominal Scale and Binary: Phi Coefficient | |
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| Nominal Scale and Polychotomous: Chi-Square Statistic | |
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| Correlation: Ordinal Scale | |
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| Correlation: Interval / Ratio Scale | |
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| Trend Analysis | |
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| Simple Linear Regression Models | |
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| Coefficient of Determination | |
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| Empirical Examples | |
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| ArcView Notes | |
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| Application Examples | |
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| Reference Cited | |
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| Exercises.Hypothesis Testers | |
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| Probability Concepts | |
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| Probability Functions | |
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| The Binomial Distribution | |
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| Poisson Distribution | |
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| The Normal Distribution | |
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| ArcView Notes | |
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| Central Limit Theorem and Confidence Intervals | |
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| Hypothesis Testing | |
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| ArcView Notes | |
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| Types of Error | |
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| Parametric Test Statistics | |
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| Difference in Variances | |
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| ArcView Note | |
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| Difference in Means | |
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| Small Sample Size | |
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| Large Sample Size | |
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| ArcView Note | |
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| Difference between a mean and a fixed value | |
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| ArcView Note | |
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| Significance of Pearson''s correlation coefficient | |
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| ArcView Note | |
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| Significance of Regression Parameters | |
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| ArcView Note | |
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| Testing Non-Parametric Statistics: Chi-Square Statistics, C | |
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| ArcView Note | |
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| Spearman''s Rank Coefficient | |
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| ArcView Notes | |
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| Kolmogorov-Smirnov Test | |
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| ArcView Note | |
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| Summary | |
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| Reference used in this chapter | |
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| Exercises | |
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| Spatial Statistics | |
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| Point Pattern Descriptors | |
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| The Nature of Point Features | |
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| Central Tendency of Point Distributions | |
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| Mean Center | |
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| Weighted Mean Center | |
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| Median Center | |
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| Dispersion and Orientation of Point Distributions | |
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| Standard Distance | |
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| Standard Deviational Ellipses | |
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| ArcView Notes | |
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| Application Examples | |
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| References Cited | |
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| Exercises | |
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| Point Pattern Analyzers | |
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| Scale and Extent | |
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| Quadrat Analysis | |
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| General Concepts in Quadrat Analysis | |
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| Comparing the Observed with the Expected Distributions using K-S test | |
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| Comparing the observed with the expected using variance-mean ratio | |
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| ArcView Example: Quadrat Analysis of Northeast Ohio Cities | |
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| Ordered Neighbor Analysis | |
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| Nearest Neighbor Statistic | |
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| Testing for pattern using Nearest Neighbor Statistic | |
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| Higher Ordered Neighbor Statistics | |
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| Boundary Adjustments of the Nearest Neighbor Statistics | |
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| ArcView Example: Nearest neighbor analysis of Northeast Ohio Cities | |
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| K-Function | |
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| ArcView Example: K-Function Analysis of Northeast Ohio Cities | |
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| Spatial Autocorrelation of Points | |
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| Measures for Spatial Autocorrelation | |
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| Significance Testing of Spatial Autocorrelation Measures | |
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| ArcView Example: Spatial Autocorrelation Analysis of Northeast Ohio Cities | |
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| Application Examples | |
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| References Cited | |
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| Exercises | |
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| Line Pattern Analyzers | |
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| The Nature of Linear Features: Vectors and Networks | |
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| Characteristics and Attributes of Linear Features | |
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| Geometric Characteristics of Linear Features | |
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| Spatial Attributes of Linear Features: Length | |
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| Spatial Attributes of Linear Features: Orientation and Direction | |
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| ArcView Example: Linear Attributes | |
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| Directional Statistics | |
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| Exploring Statistics for Liner Features | |
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| Directional Mean | |
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| Circular Variance | |
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| ArcView Example: Directional Statistics | |
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| Network Analysis | |
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| Spatial Attribute of Network Features: Connectivity or Topology | |
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| Assessing Connectivity Level | |
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| Evaluating Accessibility | |
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| ArcView Example: Network Analysis | |
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| Application Examples | |
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| Length Attribute Analysis of Linear Features | |
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| Application Example for Directional Statistics | |
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| Application Example for Network Analysis | |
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| References Cited | |
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| Exercises | |
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| Polygon Pattern Analyzers | |
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| Introduction | |
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| Spatial Relationships | |
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| Spatial Dependency | |
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| Spatial Weights Matrices | |
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| Neighborhood Definitions | |
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| Binary Connectivity Matrix | |
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| Stochastic or Row Standardized Weights Matrix | |
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| Centroid Distances | |
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| Nearest Distances | |
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| ArcView Eaxmple | |
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| Spatial Weights Matrices | |
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| Spatial Autocorrelation Statistics and Notations | |
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| Joint Count Statistics | |
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| Free Sampling | |
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| Randomization Sampling | |
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| ArcView Examples | |
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| Joint Count Statistics.(** modify the sections in the original manuscript **) | |
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| Global Statistics | |
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| Moran''s I | |
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| Geary''s Ratio | |
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| General G Statistic | |
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| ArcView Example | |
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| Global Statistics for Spatial Autocorrelation | |
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| Local Spatial Autocorrelation Statistics | |
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| Local Indicators of Spatial Association (LISA) | |
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| Local G-Statistics | |
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| Moran Scatterplot | |
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| ArcView Example | |
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| Local Spatial Autocorrelation Statistics and Moran Scatterplot | |
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| Bivariate Spatial Autocorrelation | |
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| Application Examples | |
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| Summary | |
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| References Cited | |
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| Exercises | |