4 Course Competencies

4.1 Tier 1: Foundations of Quantitative Methods

4.1.1 Assessment Structure:

Competency: Completes Lab 1-3 with Meets Expectations
Mastery: Completes Case Study #1 with Meets Expectations

4.1.2 Concept 1: The Quantitative Revolution

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

4.1.3 Concept 2: Data and Descriptive Statistics

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

4.1.4 Concept 3: Spatial Description

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

4.2 Tier 2: Classical Statistical Inference

4.2.1 Assessment Structure:

Competency: Completes Lab 4-6 with Meets Expectations
Mastery: Completes Case Study #2 with Meets Expectations

4.2.2 Concept 4: Probability

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

Explain the characteristics of stochastic processes and justify the use of probability theory in modeling systems with uncertainty
Explain how empirical probability is used to interpret likelihood based on observations
Explain how theoretical probability is used to interpret likelihood based on models of possible outcomes and their underlying assumptions
Describe the assumptions of the binomial and normal distributions and interpret situations in which each model is applicable
Compute and interpret simple event (empirical) probabilities using historical data
Compute and interpret probabilities for discrete and continuous data using the binomial and normal distribution

4.2.3 Concept 5: Inferential Statistics

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

Describe the key assumptions underlying classical statistical inference (e.g., independence, randomness in sampling)
Explain the Central Limit Theorem and why it allows us to generalize from samples to populations
Explain how sampling variability leads to differences between sample statistics and true population parameters
Explain the role of the standard normal (z) and t distributions in statistical inference
Describe the main spatial and non-spatial sampling designs (simple, systematic, stratified, cluster) and select an appropriate sampling strategy for a given research context
Estimate and interpret population parameters (means and proportions) from samples (calculate point estimates and confidence intervals)

4.2.4 Concept 6: Hypothesis Testing

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

Describe the issues with using classical hypothesis testing for spatial data
Describe the idea of “natural samples” in geography
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, two sample, and paired 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

4.3 Tier 3: Spatial Statistics

4.3.1 Assessment Structure:

Competency: Completes Lab 7-10 with Meets Expectations
Mastery: Completes Case Study #3 with Meets Expectations

4.3.2 Concept 7: Patterns in Events

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

Define spatial point pattern data and identify datasets that qualify as point data
Distinguish between first-order (intensity) and second-order (interaction) spatial processes
Explain the null hypothesis of Complete Spatial Randomness (CSR) and its representation using a homogeneous Poisson process
Compute and interpret quadrat test statistics to assess first-order spatial randomness and statistical significance
Determine when an inhomogeneous Poisson process is required to account for spatial heterogeneity in intensity prior to conducting second-order analyses
Calculate and interpret nearest neighbor statistics (e.g., ANN, L-function) to evaluate second-order spatial patterns and departures from CSR.
Explain why Monte Carlo simulations are used to generate empirical probability distributions for assessing statistical significance in spatial point pattern analysis

4.3.3 Concept 8: Patterns in Values

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

Define and justify alternative spatial neighborhood structures (k-nearest neighbors, contiguity such as Queen’s case, and distance-based thresholds) for different data types and hypothesized spatial processes
Compute and interpret global spatial autocorrelation statistics (e.g., Moran’s I), including statistical significance under appropriate null hypotheses of spatial randomness
Decompose and evaluate local spatial autocorrelation (LISA) results to identify and classify spatial regimes (hot spots, cold spots, spatial outliers), and critically interpret their statistical reliability and spatial meaning
Diagnose and explain how first-order and second-order spatial processes generate observed autocorrelation patterns

4.3.4 Concept 9: Bivariate Spatial Relationships

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

Visualize and diagnose bivariate relationships using maps and scatterplots, and formulate directional, theory-informed hypotheses about underlying spatial processes
Estimate and interpret simple OLS models, including coefficients, residuals, and model fit, in relation to geographic processes
Diagnose violations of OLS assumptions by testing for spatial autocorrelation in residuals and interpreting implications for inference
Differentiate and apply spatial regression models (e.g., spatial lag vs. spatial error) based on hypothesized spatial processes (diffusion vs. unobserved spatial structure).
Compare and justify model selection between non-spatial and spatial regression approaches using both statistical evidence and theoretical expectations

4.3.5 Concept 10: Spatially Continuous Surfaces

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

Explain and apply inverse distance weighting (IDW) to estimate values at unsampled locations, and interpret how distance-based weighting influences predicted surfaces
Evaluate and justify IDW parameter choices (e.g., inverse distance power) using cross-validation metrics (e.g., RMSE), and assess how parameter changes alter spatial smoothness vs. locality
Interpret semivariograms by identifying nugget, range, and sill, and explain what these features indicate about spatial autocorrelation and scale of influence
Select and justify an appropriate semivariogram model (e.g., spherical, exponential) based on empirical patterns and theoretical considerations
Explain the conceptual differences between deterministic interpolation (IDW) and probabilistic approaches (kriging), including assumptions about spatial processes and treatment of uncertainty.
Estimate and interpret kriging models as realizations of an underlying spatial process and assess how prediction reliability varies across space