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Chapter 4 Statistical Data Analysis

Chapter 4 Statistical Data Analysis. An Introduction to Scientific Research Methods in Geography GEOG 4020. Learning Objectives. How do the graphical and mathematical techniques of data analysis help to achieve the 4 scientific goals? What are descriptive statistics?

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Chapter 4 Statistical Data Analysis

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  1. Chapter 4Statistical Data Analysis An Introduction to Scientific Research Methods in Geography GEOG 4020

  2. Learning Objectives • How do the graphical and mathematical techniques of data analysis help to achieve the 4 scientific goals? • What are descriptive statistics? • What is the statistical relationship? • What are inferential statistics? • What are the properties of geospatial data?

  3. Introduction • Data Analysis • Extracting meaning from systematically collected measurements • Helping to achieve 4 scientific goals • Efficiently identifying and describing patterns in large amounts of data • 3 reasons geographers treat data as statistical • Data are incomplete sample of larger population • Imperfect measurement • Phenomena of interest are complex

  4. Statistical Description • Displaying data in graphs, tables, maps, etc. • Properties • Central tendency • Mode • Median • Mean • Arithmetic mean • Variation • Range • Variance • Standard Deviation • Modality

  5. Statistical Description cont’d… • Distribution • Bell-shaped/normal • Skewness • Positive & negative • Derived scores • Percentile rank • Z-score

  6. Statistical Description cont’d… • Relationship • Linear • Positive & negative • Correlation coefficient • Form • Regression analysis • Criterion & predictor variables • Error of prediction • Monotonic • Non-linear

  7. Statistical Inference • Informed guess about likely patterns of data in a population on the basis of evidence from samples drawn from that population. • Conceptually difficult • Sampling error • “Sampling variability” • Not a mistake that can be avoided • Assigning probabilities to guesses

  8. Statistical Inference cont’d… • Sampling distribution • Assumptions • Distributional assumptions • Parametric & nonparametric • Independence of scores • Correct specification of models

  9. Statistical Inference cont’d… • Estimation and hypothesis testing

  10. Statistical Inference cont’d… • Modus tollens • Testing the hypothesis you don’t believe is true • “Antecedent” and “consequent” propositions • Fallacy of affirming the consequent • Statistical significance and the p level

  11. Statistical Inference cont’d… • Power • Probability of correctly rejecting the null • 1 – β • Determined by α

  12. Data in Space and Place: Introduction to Geospatial Analysis • Geographic features have location, extent, shape, pattern, connectivity, etc. • Spatial autocorrelation • Positive & negative • Distance decay • Variogram • Areal units • Treating continuous data discretely • Gerrymandering • Modifiable Areal Unit Problem • Challenges with aggregation • General rule of thumb

  13. Discussion • Can you think of an example of negative spatial autocorrelation? • What is the modus tollens? Why is it important in hypothesis testing? • What are some assumptions that have to be made in sampling distributions? • What are some of the unique challenges in geospatial analysis?

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