Chapter 9 - Montello and Sutton
An Introduction to Scientific
Research Methods in Geography

 Statistical data analysis
 Statistical description
 Statistical inference
 Geospatial Analysis

 Set of display and mathematical techniques
 Logical and conceptual considerations
 Allows us to:
 Extract meaning from systematically collected measurements
 Communicate that meaning to others

 Geographers view data as statistical
(complex and imperfect) rather than deterministic
 Three reasons:
 Imperfect sample of larger population
 Measurement involves error
 Phenomena are expressions of complex sets of many interacting variables

 Goal: summarize potentially important properties of our data using
 Parameters - summary indices to describe the population
 Properties:
 Central tendency
 Variability / dispersion
 Form / shape of distribution
 Relationships

 Average or representative value
 Three most common:
 Mode - most frequent
 Median - middle value
 Mean (“average”)

 Tells how data points differ from the central tendency
 How representative the central tendency is
 Greater when variability is low
 Three common:
 Range - distance between high and low
 Variance - average of deviations from the mean
 Standard deviation - square root of the variance

 Shape of entire data set
 Modality - number of local modes
 Skewness - distribution uneven
 Positive - mostly low and medium scores
 Negative - mostly medium and high scores
 Symmetry - mirror around central tendency
 Bimodal
 Unimodal normal or “bell-shaped” curve

 Derived scores
 Describe the value of individual scores relative to the rest of the data set
 Three common:
 Rank - 1, 2, 3, etc.
 Percentile rank - percentage of the data that is less than the score in question
 z-score - standard deviation units above or below the mean of the data set

 Systematic (consistent) patterns of high or low values across pairs of variables
 Linear relationship - two variables form a straight line when graphed
 Positive (or direct) - high value A has high value B; low value A has low value B
 Negative (or indirect) - high value A has low value B; low value A has high value B

 Relationship strength - degree that patterns hold across all cases
 Correlation coefficient - square of correlation measure of relationship strength
 Regression analysis - expresses relationship as an equation that predicts the values of Y (criterion variable) as a function of X (predictor variable)
 Monotonic relationship - goes up or down; not necessarily in a straight line

 Goal: Draw informed guesses about likely patterns in population, based on sample data evidence
 Assign probabilities to guesses
 Sampling distribution - distribution of a sample statistic based on all possible samples of a given size, from a given population

 Assumptions:
 Distribution is normal and variances are equal
 Data values are independent
 Model specification (such as linearity, inclusive of relevant predictor constructs)

 Two approaches:
 Estimation
 Point estimate - guess about specific parameter value
 Confidence interval - range of values distributed around the point estimate, expressed as probability
 Hypothesis Testing
 Null hypothesis ( H
0 parameter
) is about exact point of
 Alternative hypothesis ( H
A
) is that the exact point of the parameter is not the null

 Four possible outcomes, based on:
 Two possible truths ( H
0 is true, H
A
 Two possible decisions (reject H accept H
A
; reject both H
0 and H
A
0
) is false) and
 Two types of errors:
 Type I - reject H
0 when H
0
 Type II - fail to reject H
0 is true when H
0 is false

 Geography data are different :
 They are spatially distributed
 Have location, extent or size, shape, pattern, connectivity, etc.
 They represent natural and human earthsurface features and processes
 Spatiality is the focus or is central to the analysis

 Influences the accuracy of inferential statistical analyses of nonspatial variables
 Spatial autocorrelation exists when there are patterns of spatial dependence – places are “like” other places
 Distance decay – near things are “more like” each other than things further away

 Which areal units to use?
 Problems:
 Using data from continuous source, but treat with discrete spatial analysis techniques
 Politicization of unit determination (like gerrymandering )
 Modifiable Areal Unit Problem (MAUP) – effect that theoretically arbitrary areal geometries have on geographic analysis

 Why is data analysis in geography usually conceptualized in statistical (probabilistic) terms?
 What is meant by strength and form of statistical relationships?
 What is the purpose of statistical inference? Why are statistical inferences necessarily and ultimately uncertain?
 What are two types of correct decisions and two types of errors possible when hypothesis testing?
 What is spatial autocorrelation, what forms can it take, and why is it so important to geographic data analysis?