1. Zakaria A. Khamis GE 2110 GEOGRAPHICAL STATISTICS GE 2110

2. Spatial analysis and Spatial pattern comparison – Introduction to spatial analysis – Judging spatial association visually – The concept of Clustering and Cluster analysis – Spatial Cross-Correlation – Pearson, Spearman – Multivariate spatial association measures

3. Traditional vs. Spatial Statistics (1) Traditional Statistics : It is inherently non-spatial as it seeks to represent a data set by its typical response regardless of spatial patterns. – The mean, standard deviation and other statistics are computed to describe the central tendency of the data in abstract numerical space without regard to the relative positioning of the data in real world geographic space.

4. Traditional vs. Spatial Statistics (2) Spatial Statistics, on the other hand, extends traditional statistics on two fronts. – First, it seeks to map the variation in a data set to show where unusual responses occur, instead of focusing on a single typical response. – Secondly, it can uncover “numerical spatial relationships” within and among mapped data layers, such as generating a prediction map identifying where likely customers are within a city based on existing sales and demographic information.

5. Traditional vs. Spatial Statistics (3) Spatial analysis, extends the basic set of discrete map features of points, lines and polygons to surfaces that represent continuous geographic space as a set of contiguous grid cells. It provides a mathematical/statistical framework by numerically representing geographic space.

6. Zakaria A. Khamis GE 2110 GEOGRAPHICAL STATISTICS GE 2110

7. Inferential statistic tests Inferential statistic tests are performed to test for the HYPOTHESIS formulated to answer the RESEARCH QUESTIONS What is HYPOTHESIS? At the end of the study, HYPOTHESIS need to be tested so as to conclude the answers to the questions Hypothesis testing constitute a fundamental way in which inferences about a population are made from a sample

8. Hypothesis are of 2 types  Null and Alternative Null Hypothesis (H 0 ) implies the inference that the mean statistic of the sample is equal to the mean parameter of the population Alternative Hypothesis (H A ) implies the inference that the mean statistic of the sample is not equal to the mean parameter of the population Inferential statistic tests

9. The above alternative hypothesis is two-sides hypothesis. And if we assume that the mean statistic of the sample is greater (same as less) than mean parameter of the population, the hypothesis is one- side The inferential statistic tests are used to test for the hypothesis  hypothesis testing Through the hypothesis testing, the researcher may either accept or reject the Null Hypothesis Accepting the null hypothesis means the mean parameter of the population is not different from the hypothesized mean Inferential statistic tests

10. Rejecting the null hypothesis occur when we find evidence for a significant difference between the population mean and the hypothesized mean The statistical tests provide the analyst with the significant levels from which s/he should choose so as to accept or reject the hypothesis Amongst the inferential statistic tests are  z-score test, t-test ( one or two tail tests), Chi-square test Inferential statistic tests

11. This test is mostly used for categorical data It is the testing of expected parameter set by Null Hypothesis to the observed parameter Null Hypothesis  there is no significant difference between the expected and observed result It provide the basis for the significance of accepting or rejecting the Null Hypothesis The probability value of greater than 0.05 lead to the rejection of Null hypothesis and less than 0.05 lead to the acceptance of Null Hypothesis Chi-Square test

12. What is the First Law of Geography? Tobler’s Law  “Everything is related to everything else, but near things are more related than distant things” We call this “spatial dependence” Spatial analysis transforms “Tobler’s law” into quantifiable assessments SPATIAL ANALYSIS

15. Formal quantitative study of phenomena that manifest themselves in space (Anselin) Spatial analysis includes the transformations, manipulations, and methods that can be applied to geographic data to add value to them, to support decisions, and to reveal patterns and anomalies that are not immediately obvious The human eye and brain are also very sophisticated processors of geographic data and excellent detectors of patterns and anomalies in maps and images

16. So the approach taken here is to regard spatial analysis as spread out along a continuum of sophistication, ranging from the simplest types that occur very quickly and intuitively when the eye and brain look at a map To the types that require complex software and sophisticated mathematical understanding. Spatial analysis is a set of methods whose results change when the locations of the objects being analyzed, or the frame used to analyze them, changes SPATIAL ANALYSIS

17. The study of methods for the description and or the quantitative study of phenomena located in space explanation of a process operating in space based on a sample of observations of the process Modifications, extensions, and additions to statistical techniques that explicitly consider the importance of locations or spatial arrangement Data are spatially located and explicit consideration is given to the possible importance of their spatial arrangement in the analysis SPATIAL ANALYSIS

18. Spatial analysis can be: Inductive, to examine empirical evidence in the search for patterns that might support new theories or general principles, in this case with regard to disease causation. Deductive, focusing on the testing of known theories or principles against data Normative, using spatial analysis to develop or prescribe new or better designs SPATIAL ANALYSIS

19. Spatial Analysis provides Analytical capacity to:- – Understand the spatial distribution of values (identify trends and clusters) – Develop possible explanations (models) for the observed patterns – Use the models to indicate what can happen in other occasions SPATIAL ANALYSIS

20. Spatial pattern is the way in which features are organized spatially There are several ways to analyze quantitatively the spatial patterns – To divide the landscape into a number of data collection unit, then make counts of the number of features within each unit  this can be normalized by area to get Density – Another approach is spatial arrangement of features across the landscape  random, regular or cluster The arrangements may be easy for one to observe them; however, there are also mathematical measures which can be used to describe them SPATIAL PATTERN ANALYSIS

21. Amongst the measures employed for spatial analysis include – Spatial Autocorrelation  the association/correlation of features in themselves – Connectivity  measure the degree to which line features are interconnected – Fragmentation and Diversity  measure the degree at which the area features belong to each category are aggregated (clumped) with respect to each other SPATIAL PATTERN ANALYSIS

22. Amongst the measures employed for spatial analysis include – Spatial Autocorrelation  the association/correlation of features in themselves – Connectivity  measure the degree to which line features are interconnected – Fragmentation and Diversity  measure the degree at which the area features belong to each category are aggregated (clumped) with respect to each other SPATIAL PATTERN ANALYSIS

23. Counting the number of features within small data collection units on the earth is the beginning point for spatial analysis  data collection units such as Shehia, Districts, Regions etc Point Counts Point counts give you information about the abundance of point features in each data collection unit The spatial analysis of the pattern for the point features may involve the analysis of relative abundance  this is calculated by comparing the abundance of each unit from the average abundance Feature Counts

24. Line Counts Linear features are counted within data collection units in the same way as point features Counting the linear feature posses a bit problem when the feature crosses more than one data collection unit  in that case, one may decide to count the feature in each unit or only in one unit in which most of the feature lies Area Counts This is done by first determining the total surface area of the features in the data collection units Feature Counts