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. 27 o C, 28 o C, 29 o C, ….. Ratio Scale Eg. $20, $30, $40, …..

Normal distribution Where = 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. X  YX  Y X is independent variable, and Y is dependent variable

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

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 : r s = 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 YearOctober SOINumber of tropical cyclones 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) YearOct OSINo. of TC OSI Rank No. TC Rank DiDi 

Spearman’s Rank (Examples) Calculation r s 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.

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

Example

Reilly’s Break-point CentrePopulationRoad distance from Bridgewater (km) Break-point distance from Bridgewater (km) Bridgewater Weston X Frome Y Yeovil Minehead

Reilly’s Break-point

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

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

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