1. Exploratory Spatial Data Analysis (ESDA) Analysis through Visualization

2. Data Normalization Values (attributes) by themselves are sometimes misleading. Normalization refers to the division of multiple sets of data by a common variable in order to negate that variable's effect on the data. Normalization can help to compare samples. Example: The number of people in a county does not tell us about the relative density of the people. What we may want is the # of people per area. Density = (# of people in county / county area)

3. Data Normalizatoin Approaches Density – divide count by area Divide an area –based count variable by another area based count variable X = Area on wheat / Total area in crops X = higher ratio indicates that wheat is more important Compute ratio of two count variables X = $ of Wheat Sold / $ of all Crops Sold X = higher ratio indicates that wheat contributed more income to area Compute summary numerical measures for each unit (sum, mean, SD, etc.)

4. Data Normalization Raw - # of Hispanics per Tract Normalized - #Hispanic/Total#

5. Mapping Common ESDA Methods Quantile - Each class contains an equal number of features. Percentile - Sort values in numerical order, compute % of total observations. Note that the Median = 50% quartile Standard Deviation – good for normal distribution Box Map – Shows outliers as the function of quartiles. IQR = Q75 – Q25 Lower Outlier = Q25 – Hinge * IQR Upper Outlier = Q75 + Hinge * IQR

6. Mapping (%Hispanic)

7. Exploration of Data Histogram - examine distribution Scatter Plot - examine correlation between variables Box Plot - compare distribution between variables Parallel Coordinate Plot - examine relation between variables

8. Box Plots and Quantile

10. Spatial Autocorrelation First law of geography: “everything is related to everything else, but near things are more related than distant things” – Waldo Tobler Spatial Autocorrelation – correlation of a variable with itself through space. – If there is any systematic pattern in the spatial distribution of a variable, it is said to be spatially autocorrelated. – If nearby or neighboring areas are more alike, this is positive spatial autocorrelation. – Negative autocorrelation describes patterns in which neighboring areas are unlike. – Random patterns exhibit no spatial autocorrelation.

11. Why spatial autocorrelation is important Most statistics are based on the assumption that the values of observations in each sample are independent of one another Positive spatial autocorrelation may violate this, if the samples were taken from nearby areas Goals of spatial autocorrelation – Measure the strength of spatial autocorrelation in a map – test the assumption of independence or randomness

12. Moran’s I One of the oldest indicators of spatial autocorrelation (Moran, 1950). Still a defacto standard for determining spatial autocorrelation. Applied to zones or points with continuous variables associated with them. Compares the value of the variable at any one location with the value at all other locations.

13. Moran’s I Where N is the number of cases X i is the variable value at a particular location X j is the variable value at another location X-bar is the mean of the variable W ij is a weight applied to the comparison between location i and location j. Weights are based either on distance or adjacency.