Spatial Statistics Study Guide Week 1

Week 1 Study Guide

• Mean and Median Centers

  • Mean Center: The geographic center of the data. If data points cluster in a specific area, the mean center is located there.
  • Median Center: The middle data point (numerically) when the data is ordered. It may not be exactly at the geographic center, and is useful for identifying outliers.
  • Mean Center Location: Situated at the geographic center of a dataset, particularly useful for clustering (e.g. wells). Outlier location is noted when compared to the median center.

• Spatial Statistics

  • Definition: Analyzing data across space to understand relationships and patterns.
  • Importance: Helps with choosing appropriate analysis tools and avoids incorrect conclusions.
  • Patterns and Relationships: Analysis focuses on finding consistent patterns in spatial data.

• Data Exploration Steps

  • Determine data clustering, dispersion, orientation, and central tendency.
  • Compare mean and median centers to find skewness and outliers.
  • Analyze data distribution using ellipses to understand data spread and orientation.
  • Cluster Identification: Data clustering and dispersion is explored.

• Normal Distribution

  • Characteristics: Bell-shaped, symmetrical, mean and median are similar.
  • Skewness: Asymmetry in the data. Positive skew (long tail to the right), negative skew (long tail to the left), bimodal (two peaks).

• Frequency and Histograms

  • Frequency: The number of times a value occurs.
  • Histograms: Graphical representation of data using bars. They show the distribution of data and help identify skewness.
    • Data Distribution: Histograms visually represent the distribution of data, including skewness.

• QQ Plot

  • Purpose: Compares data distribution to a normal distribution using a reference line. Deviations from the line indicate a non-normal distribution.
    • Normal Distribution Comparison: Data distribution is compared to a typical normal Gaussian distribution using a reference line.

• Semivariogram and Spatial Autocorrelation

  • Semivariogram: Graphical tool for determining spatial autocorrelation.
  • Spatial Autocorrelation: The similarity of data values based on distance. Close points tend to have more similar values; this is measured by distance and direction.
  • Anisotropic: Spatial autocorrelation differs depending on distance and direction.
  • Isotropic: Spatial autocorrelation depends only on distance, independent of direction.
    • Spatial relationship and patterns: Spatial autocorrelation explains the spatial relationships between the data points.

• Data Variation and Stationarity

  • Stationarity: Consistent data variation across a study location.
  • Example: Weather data collected at monitoring stations should have consistent temperature readings unless influenced by external factors.
    • Consistent data variation :Data variation is consistent across a study location; good examples include weather data.

• Tessellations and Voronoi Maps

  • Tessellations: Polygons that cover a surface completely without overlapping.
  • Voronoi Maps: Tessellations used to identify spatial variation. Each polygon represents the area closest to a specific data point.
    • Spatial Analysis: Voronoi maps are used to explore the spatial variation of data patterns.

• Data Outliers

  • Identification: Outliers significantly affect data analyses. Methods like Voronoi maps, histograms, and QQ plots identify them.
  • Causes: Mistakes, unusual events, or shifts in data patterns.
    • Data Integrity: Data outliers can disrupt the analyses and are hence important to understand and correct, particularly via visualizations like Voronoi maps.