#### Transcript Basic Social Statistic

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 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,….. Normal distribution Where x = mean, s = standard deviation 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 Mode: Most Frequent Median: Middle Mean: Arithmetic Average Dependent and Independent variables Dependent variables: value changes according to another variables changes. Independent variables: Value changes independently. XY X is independent variable, and Y is dependent variable Scattergram (3,8) where x=3, y=8 (7,8) where x=7, y=8 Where x = income y = beautiful X – independent variable 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 Correlation Coefficient Strong positive correlation (relationship) Correlation Coefficient Strong negative correlation (relationship) Correlation Coefficient No correlation (relationship) Correlation Coefficient 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 Spearman’s Rank where : rs = spearman’s coefficient Di = difference between any pair of ranks N = sample size Spearman’s Rank 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. 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 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 Spearman’s Rank (Examples) Year Oct OSI No. of TC 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 ---- ---- ---- OSI Rank No. TC Rank ---- ---- Di Di2 Spearman’s Rank (Examples) Calculation rs Comments: 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. 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 Reilly’s Break-point Reilly’s Break-point Reilly’s Break-point Reilly’s Break-point Reilly’s Break-point Reilly’s Break-point Example Reilly’s Break-point Centre Population Road distance from Break-point Bridgewater (km) distance from Bridgewater (km) Bridgewater 26598 0 0 Weston 50794 24 X Frome 13384 46 Y Yeovil 25492 32 16.2 8063 34 21.9 Minehead Reilly’s Break-point X Y 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. Linear Regression 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) Linear Regression Linear Regression 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. The End