# Quant Methods

 Major Goals of Scientific Inquiry
 1) Description  We Will Write A Custom Essay Sample On ANY TOPIC SPECIFICALLYFOR YOU For Only \$13.90/page order now -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