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Course Overview

Geospatial statistical tools are the most basic ones. It helps in analysis of exploratory data and geographical data, probability distributions and their applications, single and multivariate analysis and hypothesis testing, and spatial smoothing and interpolation. The R statistical language will be used to solve problems in geographical contexts. Students may get course credit through testing.

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Course Objectives

The goal of this course is to provide students with a foundational grasp of statistical techniques as they are applied to a variety of spatial methodologies and technologies. The course programme includes detailed objectives for each week.

Students will learn the following:

  • How to graphically explore a dataset
  • Compute summary statistics
  • Investigate the nature of discrete and continuous distributions
  • Create a model to perform analysis of variance and regression with one or more dependent continuous or categorical variables using the open-source R statistical computing language.

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Course Evaluation and Requirements

The following criteria will be used to evaluate undergraduate students:

  • Weekly graded work is due every Sunday (35 percent)
  • Two mid-course examinations (35 percent - 17.5 percent each)
  • The final test (30 percent)

The following criteria will be used to evaluate graduates:

  • Weekly graded work is due every Sunday (25 percent)
  • Two mid-course examinations (25 percent - 12.5 percent each)
  • Completed Project (15 percent)
  • The final test (20 percent)

Blackboard Hosting Datasets and Digital Documents Used in Weekly Graded Assignments And/or Examinations

Week Topic and Objectives Readings
1

Statistics and Geospatial Data

By the end of this module, students will...

  • be able to outline the scientific method including hypotheses, models, and exploratory and confirmatory methods.
  • be able to explain what kind of problems geospatial technologists encounter that require an understanding of statistics.
  • be familiar with R as a statistical or data mining “calculator” in the geospatial context.
  • understand different types of data and how to simply describe them.

Rogerson, Chapter 1
Quick-R:

http://www.statmethods.net
/index.html

http://www.statmethods.net
/interface/index.html

http://www.statmethods.net
/interface/help.html

http://www.statmethods.net
/interface/workspace.html

http://www.statmethods.net
/interface/io.htm

2

Descriptive Statistics

At the end of this module, students will...

  • be able to categorize data as nominal, ordinal, interval or ratio.
  • be able to explain a variety of techniques to visualize and describe data including several forms of central tendency, spread, and distribution.
  • know how to import a variety of data types into R and organize them into useful data objects.
  • use R to visualize numerical and categorical data.
  • use R to compute descriptive statistics for spatial data.
  • use R to compute descriptive statistics for angular data.
Rogerson, Chapter 2
3

Discrete Probability Distributions

By the end of this module, students should be able to...

  • explain what a discrete probability distribution is and how it is related to a histogram.
  • describe the characteristics of a discrete probability distribution.
  • model a problem using one of the four discrete probability distributions (binomial, Poisson, geometric, hypergeometric).
  • calculate the probability of an event occurring (under the proper distribution) using R.
Rogerson, Chapter 3
4

Continuous Probability Distributions

By the end of this module, students should be able to...

  • explain what a continuous probability distribution is and how it is related to a histogram.
  • describe the characteristics of a continuous probability distribution.
  • model a problem using one of the three continuous
  • probability distributions (normal, exponential,  Poisson).
  • calculate the probability of an event occurring (under the proper distribution) using R.
Rogerson, Chapter 4
5

Inferential Statistics: Confidence Intervals, Hypothesis Testing, and Sampling

By the end of this module, students should be able to...

  • explain the reasoning behind, and the limitations of, inferential statistics.
  • use R to construct confidence intervals around means and proportions.
  • use R to test hypotheses about means and proportions
  • summarize the effects of spatial dependence on statistical tests.
  • test hypotheses about spatial centrality and spatial
    variability.
Rogerson, Chapter 5
6 & 7

Analysis of Variance

By the end of this module, students should be able to...

  • explain how to compare means of three or more samples and determine the likelihood of them being drawn from the same population.
  • use R to perform an analysis of variance on geospatial datasets.
Rogerson, Chapter 6
8 & 9

Correlation

By the end of this module, students should be able to...

  • explain the nature of the relationship between two
  • variables and contrast correlations and causality.
  • explain the effects of sample size on tests of significance.
  • use R to analyze the relationship between two variables and test for significance.
Rogerson, Chapter 7
10 & 11

Introduction to Regression

By the end of this module, students should be able to...

  • model one variable as a linear function of another.
  • fit a straight line through a set of points plotted in two dimensions.
  • explain the relationship of regression to analysis of
  • variance.
  • state the assumptions on which linear regression depends.
  • test the significance of the regression slope.
  • use R to compute and analyze the first five objectives.
Rogerson, Chapter 8
12 & 13

More on Regression III

By the end of this module, students should be able to...

  • model one variable as a function of two or more other variables.
  • interpret multiple regression coefficients.
  • choose explanatory variables from a set of observations.
  • regress against categorical dependent variables (i.e. use logistic regression).
Rogerson, Chapter 9
14 & 15

Spatial Patterns

By the end of this module, students should be able to...

  • model a geospatial problem as a point pattern or
  • areal/lattice analysis.
  • apply various local statistics to areal data using R.
Rogerson, Chapter 10

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Following are the type of warnings:

Tornado Warning: Severe weather (Tornado Warning):

  • Obey the instructor's or emergency personnel's instructions.
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  • Protect yourself by using chairs, desks, mobile phones, or anything is nearby to distract and/or defend yourself and others from an assault.

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