spatstat_stats_overview - Spatial Statistics Concepts(O&U...

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Briggs UT-Dallas GISC 6382 Spring 2007 1 Spatial Statistics Concepts (O&U Ch. 3) Centrographic Statistics (O&U Ch. 4 p. 77-81) single, summary measures of a spatial distribution Point Pattern Analysis (O&U Ch 4 p. 81-114) -- pattern analysis; points have no magnitude (“no variable”) Quadrat Analysis Nearest Neighbor Analysis Spatial Autocorrelation (O&U Ch 7 pp. 180-205 One variable The Weights Matrix Join Count Statistic Moran’s I (O&U pp 196-201) Geary’s C Ratio (O&U pp 201) General G LISA Correlation and Regression Two variables Standard Spatial
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Briggs UT-Dallas GISC 6382 Spring 2007 2 Description versus Inference Description and descriptive statistics Concerned with obtaining summary measures to describe a set of data Inference and inferential statistics Concerned with making inferences from samples about populations Concerned with making legitimate inferences about underlying processes from observed patterns We will be looking at both!
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Briggs UT-Dallas GISC 6382 Spring 2007 3 Classic Descriptive Statistics: Univariate Measures of Central Tendency and Dispersion Central Tendency: single summary measure for one variable: mean (average) median (middle value) mode (most frequently occurring) Dispersion: measure of spread or variability Variance Standard deviation (square root of variance) Formulae for variance 2 ) ( 1 2 = - N X X n i i ] / ) [( 1 2 = = - N N X X n i i Formulae for mean These may be obtained in ArcGIS by: --opening a table, right clicking on column heading, and selecting Statistics --going to ArcToolbox>Analysis>Statistics>Summary Statistics
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Briggs UT-Dallas GISC 6382 Spring 2007 4 A counting of the frequency with which values occur on a variable Most easily understood for a categorical variable (e.g. ethnicity) For a continuous variable, frequency can be: calculated by dividing the variable into categories or “bins” (e.g income groups) represented by the proportion of the area under a frequency curve Classic Descriptive Statistics: Univariate Frequency distributions 0 -1.96 2.5% 1.96 2.5% In ArcGIS, you may obtain frequency counts on a categorical variable via: --ArcToolbox>Analysis>Statistics>Frequency
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Briggs UT-Dallas GISC 6382 Spring 2007 5 Classic Descriptive Statistics: Bivariate Pearson Product Moment Correlation Coefficient (r) Measures the degree of association or strength of the relationship between two continuous variables Varies on a scale from –1 thru 0 to +1 -1 implies perfect negative association As values on one variable rise, those on the other fall (price and quantity purchased) 0 implies no association +1 implies perfect positive association As values rise on one they also rise on the other (house price and income of occupants) X Where Sx and Sy are the standard deviations of X and Y, and X and Y are the means.
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