1. Basic Social Statistic for AL Geography HO Pui-sing

2. Content Level of Measurement (Data Types) Normal Distribution Measures of central tendency Dependent and independent variables Correlation coefficient Spearman ’ s Rank Reilly ’ s Break-point / Reilly ’ s Law Linear Regression

3. Level of Measurement Nominal Scale: Eg. China, USA, HK, ……. Ordinal Scale: Eg. Low, Medium, High, Very High, …. Interval Scale: Eg. 27 o C, 28 o C, 29 o C, ….. Ratio Scale Eg. $20, $30, $40, …..

4. Normal distribution Where = mean, s = standard deviation

5. Measures of central tendency Use a value to represent a central tendency of a group of data. Mode: Most Frequent Median: Middle Mean: Arithmetic Average

6. Mode: Most Frequent

7. Median: Middle

8. Mean: Arithmetic Average

9. Dependent and Independent variables Dependent variables: value changes according to another variables changes. Independent variables: Value changes independently. X  YX  Y X is independent variable, and Y is dependent variable

10. Scattergram X – independent variable Y – dependent variable (7,8) where x=7, y=8 (3,8) where x=3, y=8 Where x = income y = beautiful

11. Correlation Coefficient The correlation coefficient (r) indicates the extent to which the pairs of numbers for these two variables lie on a straight line. (linear relationship) Range of (r): -1 to +1 Perfect positive correlation: +1 Perfect negative correlation: -1 No correlation: 0.0

12. Correlation Coefficient Strong positive correlation (relationship)

13. Correlation Coefficient Strong negative correlation (relationship)

14. Correlation Coefficient No correlation (relationship)

15. Correlation Coefficient

16. Spearman’s Rank 史皮爾曼等級 相關係數 Compare the rankings on the two sets of scores. It may also be a better indicator that a relationship exists between two variables when the relationship is non-linear. Range of (r): -1 to +1 Perfect positive correlation: +1 Perfect negative correlation: -1 No correlation: 0.0

17. Spearman’s Rank where : r s = spearman ’ s coefficient Di = difference between any pair of ranks N = sample size

18. Spearman’s Rank

19. Spearman’s Rank (Examples) The following table shows the SOI in the month of October and the number of tropical cyclones in the Australian region from 1970 to 1979. YearOctober SOINumber of tropical cyclones 1970+1112 1971+1817 1972-1210 1973+1016 1974+911 1975+1813 1976+411 1977-137 1978-57 1979-212 Using the Spearman’s rank correlation method, calculate the coefficient of correlation between October SOI and the number of tropical cyclones and comment the result

20. Spearman’s Rank (Examples) YearOct OSINo. of TC OSI Rank No. TC Rank DiDi 2 1970+1112 1971+1817 1972-1210 1973+1016 1974+911 1975+1813 1976+411 1977-137 1978-57 1979-212 ---- 

21. Spearman’s Rank (Examples) Calculation r s Comments:

22. Reilly’s Break-point 雷利裂點公 式 Reilly proposed that a formula could be used to calculate the point at which customers will be drawn to one or another of two competing centers.

23. Where j = trading centre j i = trading centre i x = break-point = distance between i and j Pi = population size of i Pj = population size of j = break-point distance from j to x Reilly’s Break-point i j x

29. Example

30. Reilly’s Break-point CentrePopulationRoad distance from Bridgewater (km) Break-point distance from Bridgewater (km) Bridgewater 2659800 Weston 5079424X Frome 1338446Y Yeovil 254923216.2 Minehead 80633421.9

31. Reilly’s Break-point

32. Linear Regression It indicates the nature of the relationship between two (or more) variables. In particular, it indicates the extent to which you can predict some variables by knowing others, or the extent to which some are associated with others.

33. Linear Regression

34. A linear regression equation is usually written Y = a + bX where Y is the dependent variable a is the Y intercept b is the slope or regression coefficient (r) X is the independent variable (or covariate)

35. Linear Regression

36. Use the regression equation to represent population distribution, and Knowing value X to predict value Y. Correlation coefficient (r) is also use to indicate the relationship between X and Y.

37. The End