Geo-Data Analysis (GIS)

Geo-Data Analysis (GIS)

1. Chapter 1

   • Data -> Information -> Knowledge -> Understanding -> Wisdom
     • there is 5 categories:
   • Theory -> hypothesis -> prediction
   • Measurement Theory -> importance of variability -> measurement scales
   • Measurement Scales:
   • Cartographic objects and measurement scales
   • Data problems
   • underlying population

2. Chapter 2

   • Advantages of data visualization and statistical graphs
   • Color coding of categorical, gradient and diverging map themes
   • Color blindness
   • Statistical graphs in relation to measurement scales
   • Construction of frequency distributions
   • Construction rules for histograms
   • Bar charts: ordering of columns
   • Shape of distributions: symmetry, skewness, modality, outliers
   • Construction of cumulative frequencies, concept of quartiles and median
   • Visual comparison of histograms versus empirical cumulative distribution functions
   • Quantiles and Percentiles: ordered data
   • Box-Plots with construction rules
   • Design guidelines for statistical graphs

3. Chapter03

   • Math review
   • Central Tendency
   • Variability

4. Chapter 4

   • Correlation
   • Bivariate regression
   • Multiple regression

5. Chapter 5

   • Sets and Probability
   • Univariate Distributions
   • Bivariate distributions

6. Chapter 6:

   • Concepts of representative, bias, and sampling error
   • Delineation of relevant population under investigation
   • Definitions: Target population and sampling frame
   • Component of sampling frame: non-response, sampled and ineligible
   • Sampling design guidelines
   • Properties of simple random sampling
   • Independence approximation in sampling without replacement
   • Definition of sample statistic as function of random variables
   • Distribution of a sample statistics form population properties
   • Definition: standard error
   • Spatial sampling designs:

7. Chapter 7

   • Impact of sampling variability
   • Difference between estimation and hypothesis testing
   • Point estimator with bias, efficiency, asymptotic properties, root-mean-square error
   • Tradeoff between bias and root-mean-square error
   • Interval Estimation: interval width, uncertainty, error probability, precision, interpretation of interval estimators
   • Properties of specific point estimators
   • Relationships: [a] error probability and interval width, [b] interval width and sample size
   • Intervals for non-normal populations, central limit theorem, t-distribution, binomial distribution
   • Calculation of sample sizes
   • Variance of binomial distribution and sample size

8. Chapter 8:

   • What are statistical hypothesis
   • One- and two-sided hypothesis
   • Relationship between[a] alpha error and critical value, and [b] value of sample test statistic and prob-value (significance level)
   • What errors can be committed in statistical hypothesis testing
   • Test for population expectation under varying assumptions
   • Exact and approximate test for population proportion
   • Relationship between tests and confidence intervals
   • Problems of hypothesis testing
   • Significance tests for correlation coefficients
   • Steps of classical hypothesis testing

9. Chapter 10

   • Difference between parametric and non-parametric tests
   • Assumptions of -test: Counts from a Poisson distribution, minimum size of expected frequencies
   • Goodness of fit test