1. 4.2.2 Inductive Statistics 1 UPA Package 4, Module 2 INDUCTIVE STATISTICS

2. 4.2.2 Inductive Statistics 2 Inductive Statistics Statistics and the Geographic Research Process Normal Distribution Inductive Statistics Correlations and Relationships Introduction exercise 4.2.2

3. 4.2.2 Inductive Statistics 3 Statistics and the Geographic Research Process

4. 4.2.2 Inductive Statistics 4 Frequency Distributions

5. 4.2.2 Inductive Statistics 5 Normal Distribution Normal curve Bell-shape curves described by its mean (center of the distribution) and standard deviation (shape of the curve)

6. 4.2.2 Inductive Statistics 6 Normal Distribution Areas under the normal curve The 68 – 95 - 99.7% rule Z or standard scores Standard score =

7. 4.2.2 Inductive Statistics 7 Normal Distribution Symmetrical distributions Positive and negatively skewed distributions Mean not equal to median Impact of extreme cases e.g. very high incomes on mean

8. 4.2.2 Inductive Statistics 8 Inductive Statistics Hypotheses Null and Research Hypothesis Assumptions Level of significance Two and one tailed test Degree of Freedom Tests Parametric and non-parametric tests Cross tables

9. 4.2.2 Inductive Statistics 9 Inductive Statistics scattergram (house value / income)

10. 4.2.2 Inductive Statistics 10 Inductive Statistics Tests Level of significance Cross tables

11. 4.2.2 Inductive Statistics 11 Inductive Statistics Procedure for testing statistical hypotheses: Assumptions Sampling procedure Sign. Level, critical region Testing Decision/conclusions

12. 4.2.2 Inductive Statistics 12 Correlations and Relationships

13. 4.2.2 Inductive Statistics 13 Introduction Exercise 4.2.2 Create Histograms visual check on normality Calculate z-scores and ‘areas under the normal curve’ Create a scattergram Calculate correlation coefficient

14. 4.2.2 Inductive Statistics 14 Introduction Exercise 4.2.2 Histogram / Bar chart

15. 4.2.2 Inductive Statistics 15 Introduction to Exercise 4.2.2 Population density vs. Income Data refer to mean values per municipality in the Netherlands Higher Income – higher population densities?