Nearest-neighbor analysis and the distribution of sinkholes: an introduction to spatial statistics

Rick Ford
Weber State University
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This is an exercise I use in an upper-division geomorphology course to introduce students to nearest-neighbor analysis, a basic technic in spatial statistics. This technique provides an objective method for categorizing various point distributions (clustered, random, regular). In this specific exercise students will use topographic maps to analysis the spatial distribution of sinkholes on the Mitchell karst plain of southern Indiana.

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undergraduate course in geomorphology

Skills and concepts that students must have mastered

1. using map scale to measure distances on a topographic map
2. basic population statistics, including hypothesis testing (helpful, but not required)

How the activity is situated in the course

stand-alone exercise


Content/concepts goals for this activity

Students gain experience in recognizing karst features, specifically sinkholes, on topographic maps. More importantly, they collect nearest-neighbor distance data, calculate a population statistic (nearest-neighbor index),and use that statistic in formal hypothesis testing.

Higher order thinking skills goals for this activity

This activity require student to collect their own data and to consider the potential for measurement error. They then use their data and nearest-neighbor analysis to formally test hypotheses related to the spatial distribution of sinkholes within their selected study area. For some students, this may be their first introduction to the use of statistics in a geoscience context.

Other skills goals for this activity

The students are also required to summarize their findings in a short written report, using a format similar to a scientific journal article.

Description of the activity/assignment

This is an exercise I use in an upper-division geomorphology course to introduce students to nearest-neighbor analysis, a basic technique in spatial statistics. Nearest-neighbor analysis is a method of comparing the observed average distance between points and their nearest neighbor to the expected average nearest-neighbor distance in a random pattern of points. The pattern of points on a map or 2-D graph can be classified into three categories: CLUSTERED, RANDOM, REGULAR. Nearest-neighbor analysis provides an objective method for distinguishing among these possible spatial distributions. The technique also produces a population statistic, the nearest-neighbor index, which can be compared from area to area. In general, nearest-neighbor analysis can be applied to any geoscience phenomenon or feature whose spatial distribution can be categorized as a point pattern. The basic distance data can come from topographic maps, aerial photographs, or field measurements. The exercise presented here applies this technique to the study of karst landforms on topographic maps, specifically the spatial distribution of sinkholes. The advantages of introducing nearest-neighbor analysis in an undergraduate lab is that: (1) it reinforces important concepts related to data collection (e.g significant figures), map use (e.g. scale and the UTM grid), and basic statistics (e.g. hypothesis testing); (2) the necessary calculations are easily handled by most students; and (3) once learned, the technique can be widely applied in geoscience problem-solving.
Designed for a geomorphology course
Addresses student fear of quantitative aspect and/or inadequate quantitative skills

Determining whether students have met the goals

I check the student's final reports, including their basic calculations, and use a rubric to assign grades.

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