Quant Methods

Geography
Major Goals of Scientific Inquiry 

1) Description 

-Data Collection, Classification 

2) Prediction 

-Based on Inference from existing patterns

3) Explanation

-Prediction of values

4) Control

-Ultimately to change or manipulate physical or social process  

Basic vs. Applied Research 

-Example: GIScience 

-Basic Research (Making better GIS techniques and software)

-Applied(Doing environmental studies with GIS) 

Empirical Concepts 

-Case: The objects studied 

Measurements: How we determine attributes or properties of cases 

1) Literacy

-Concepts, writing papers and reports 

2) Numeracy 

-Measurements, statistical understanding and quantitative analysis 

3) Graphicacy 

-Interpreting graphs, diagrams, maps and photographs 

 

Ways of Knowing 

1) Realism enables empiricism 

2) Causality moves in a forward direction 

-Cause and effect are measurable 

3) Simplicity 

-Principle of parsimony ‘elegant’ solutions to problems

4) Skepticism 

-Falsification by evidence 

5) Quantitative Thinking 

-Instruments, mathematical modeling and computation 

Geography Methods 

-Methods are a major source of historical and modern contention in geography 

+Quantitative Vs. Qualitative 

+Physical Vs. Human Geography 

+Quantitative Human Geography 

Quantitative and Qualitative 

1) Data Collection 

-Numeric Data 

2) Structure 

-Formal, structured research approach 

3) Analysis 

-Formal analytical methods 

 

Primary and secondary 

-Primary Sources 

+First hand data collection 

-Secondary 

+Census 

Nominal 

-Classification of data

-Qualitative 

-Numeric Values refer to classes 

 

Ordinal 

-Numeric values describing rank or relative order 

-Top rankings

-Rating Scales 

+Preferences 

Interval 

-Relative Quantitative values without a true zero

+Express relative values 

-Mathematical relations don’t hold true;

+Temp.

-Examples

+Temp

+Time

+Lat/Long

Ratio

-Typical attribute data;

-Mathematical relations hold true;

;

Cumulative Frequency Tables;

-Cumulative frequency: Sum per category;

-Relative frequency: Proportion (%)

-Cumulative Relative frequency: Cumulative summation of relative frequency;

Cumulative Frequency Diagram

-Ogive

+Sums up relative proportions;

Kinds of Data Collection;

1) Physical Measurements

-GPS; Weather Stations;

2) Observation of behavior;

-Subjects are not explicitly aware of being studied;

3) Archival sources

-Older data and photograph;

4) Explicit Reports;

-People being studied are aware of data collection;

-Requires ‘self-reporting’

+Surveys

+Open-ended questions

5) Computational Models

;

Hierarchy of Scales

-Smaller scale processes ‘nested’ in larger scale processors;

+Nested Scales

+Ex: Local to Global economics, global climate change;

+Ex: Remote Sensing Anderson’s land cover classification 

 

Discrete and Continuous 

-Discrete data have defined limits 

+Population 

-Continuous data can be estimated 

+Snowfall interpolation 

-Discrete data 

+Nominal, Interval 

-Continuous 

+NOIR

Measurements 

-Discrete vs. continuous 

+50 cm or 50.212cm

-Accuracy: Correctness of measurement 

+How close measure to the actual value 

-Precision: Sharpness or resolution of measurement 

+How repeatable?

-Spurious Precision:

+5.125345634566 inches 

+Better to use one decimal place more than the original data 

Descriptive Stats 

-Visual Methods 

+Histograms, Boxplots 

-Measures of Central Tendency

+Mean, Median, Mode 

+Absolute Frequency, Relative Frequency 

-Variability 

+Inter-Quatile range 

+Variance and standard deviation 

-Descriptive Spatial 

-Mean Center 

-Distance, Standard distance 

Measures of Dispersion: Range 

-Min and Max

-Symmetric and Skewed Distributions 

Skewness 

-Is a measure of the asymmetry of a histogram 

-A perfectly symmetric histogram has a skewness value of zero 

-Positive Skew: More observations below the mean than above 

Kurtosis 

-Is a measure of distribution (Histogram) asymmetry and peaksharpness 

-Letokurtic (Thin)

-Mesokurtic (Middle) 

-Platykurtic (Flat)

-Index measure of flatness or peakedness in distributions 

-High peakedness, Kurtosis > 3.0 (Letokurtic)

-Low peakedness, Kurtosis

Additional Measure

-Coefficient of Variation (Relative Variability)- s/x(100)

+Ratio of Standard Deviation to the Mean

+Divide standard deviation by mean to give a standardized value for comparisons 

Standard Scores 

-Standardizing observations from different distributions and different means 

+Z-Score: Subtract a value from the mean and then divide by the standard deviation

+Z-Score gives the number of standard deviations from the mean

Normal Distribution 

-Use standard scores (Normal deviate) or z-scores

+Can be positive or negative 

Measures of Variability 

-Sample variance s2

+Average squared deviation of observations from the mean 

 

Methods: Processing spatial data 

-Multiple ways to address the same issue 

-Points 

-Counts 

+Discrete Distribution-Point data within discrete areas, choropleth mapping 

-Surfaces 

+Continuous Distribution Statistical surfaces ‘Smoothed’ Surfaces 

 

Modifiable areal unit problem 
How you divide space affects the density of the values, alters stats 
Classification Methods 

-Equal Interval: Divides data into a number of classes of equal width 

-Quantile: Data divided so that an equal number of observations falls within each class 

-Natural Breaks- Divides data into classes divided from natural breaks in a data histogram 

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