4 Course Competencies

4.1 Tier 1: Foundations of Quantitative Methods

Guiding Question: Why did geography become a quantitative discipline, and how did it change how we study space?

Describe the origins of the Quantitative Revolution in geography and how political and academic pressures pushed geography towards a “spatial science”
Identify assumptions built into quantitative reasoning (measurability, objectivity, universality)
Reflect on critiques and limits of the Quantitative Revolution from human and critical geographers
Interpret early spatial models
Explain how MAUP, spatial dependence, spatial heterogeneity, and distance decay influence the structure and interpretation of spatial data
Connect the “spatial problem” to violations of independence in classical inference

Guiding Question: How do we summarize and describe variation in data?

Classify different types of geographic data and variables (e.g., primary vs. secondary, individual vs. aggregated, qualitative vs. quantitative, level of measurement), and explain how these distinctions influence analysis
Explain the major sources and key dimensions of geographic (coverage, resolution, scale, temporality, completeness, positional accuracy, and bias) and how these dimensions influence analysis.
Describe basic geographic data structures (vector/raster)
Explain and evaluate measurement quality in geographic data, including precision, accuracy, validity, and reliability.
Summarize and interpret attribute data using descriptive statistics (central tendency, dispersion, shape) and data visualizations

Guiding Question: How do we summarize and describe variation in geographic data?

Use maps to visually analyze spatial patterns and understand the role of classification schemes for grouping spatial data values
Compute and interpret spatial descriptive statistics (mean center, standard distance, standard deviational ellipse) and explain how they extend non-spatial descriptive measures

Guiding Question: How can we use probability to quantify uncertainty and understand patterns in events?

Compute and interpret simple event (empirical) probabilities
Compute and interpret probabilities for discrete and continuous data using theoretical probability distributions
Visualize probability across space

Guiding Question: How can we use sample data to understand and estimate characteristics of a population?

Explain the Central Limit Theorem and why it allows us to generalize from samples to populations.
Identify how sampling design affects representativeness and uncertainty (simple, systematic, stratified, cluster, spatial hybrid).
Estimate and interpret population parameters (means and proportions) from samples (calculate point estimates and confidence intervals)

Guiding Question: How can we generate and test hypotheses about a population using sample data?

Distinguish between the null (H₀) and alternative (H₁) hypotheses
Identify the two types of error in hypothesis testing (Type I and Type II)
Formulate testable hypotheses and identify an appropriate statistical test based on the characteristics of the data
Run and interpret one sample and two sample t-tests to compare means between one or two groups
Run and interpret Chi-Square tests to assess relationships between categorical variables
Differentiate statistical significance from substantive importance

Guiding Question: How can we assess the distribution/pattern of individual events in space?

Distinguish random, clustered, and regular event patterns
Compute and interpret quadrat tests to assess spatial randomness (CSR) and determine statistical significance
Compute and interpret nearest neighbor statistics to assess spatial randomness and determine statistical significance
Visualize event patterns using point maps and density surfaces (kernel density estimation)
Evaluate the effects of scale and edge boundaries on event pattern analysis

Guiding Question: How can we detect patterns in attribute values across points or areas?

Define spatial influence (neighborhoods) for point and aerial data using KNN, Queens Case, and distance-based measures
Compute and interpret measures of global autocorrelation (Moran’s I)
Compute and interpret measures of local autocorrelation (LISA) and use mapping to identify and analyze spatial patterns (hot-spots, cold-spots)
Discuss how scale, zoning, and MAUP influence patterns

Guiding Question: How can we examine and model relationships between two variables across space?

Visualize and interpret bivariate relationships using maps and scatterplots
Explain how linear regression extends hypothesis testing to relationships between two variables
Estimate and interpret simple bivariate regression models in a geographic context
Diagnose spatial dependence in regression residuals using spatial autocorrelation measures
Estimate and interpret spatial regression models
Compare non-spatial regression results with spatial regression results to pick an appropriate model

Guiding Question: How can we estimate values at unsampled locations and understand spatial clustering and uncertainty across continuous surfaces?

Compute point estimates at unsampled locations using Thiessen polygons, IDW, and k-point means.
Define and interpret the semivariogram to understand spatial clustering, correlation, and range of influence.
Approximate uncertainty for predictions using sample variance or semivariogram-based approaches and interpret the implications.