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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 | |