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Basic Social Statistic for AL Geography

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

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Basic Social Statistic for AL Geography

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  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. 27oC, 28oC, 29oC,….. • 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: ArithmeticAverage

  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 Y X is independent variable, and Y is dependent variable

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

  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 : rs = spearman’s coefficient Di = difference between any pair of ranks N = sample size

  18. Spearman’s Rank

  19. Year October SOI Number of tropical cyclones 1970 +11 12 1971 +18 17 1972 -12 10 1973 +10 16 1974 +9 11 1975 +18 13 1976 +4 11 1977 -13 7 1978 -5 7 1979 -2 12 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. 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)

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

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

  23. Reilly’s Break-point i 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 x j

  24. Reilly’s Break-point

  25. Reilly’s Break-point

  26. Reilly’s Break-point

  27. Reilly’s Break-point

  28. Reilly’s Break-point

  29. Reilly’s Break-point Example

  30. Reilly’s Break-point

  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 predictsome variables by knowing others, or the extent to which some are associated with others.

  33. Linear Regression

  34. Linear Regression • 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. Linear Regression • Use the regression equation to represent population distribution, and • Knowing value X to predictvalue Y. • Correlation coefficient (r) is also use to indicate the relationship between X and Y.

  37. The End

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