Basic Social Statistic for AL Geography

HO Pui-sing

ContentLevel of Measurement (Data Types)Normal DistributionMeasures of central tendencyDependent and independent variablesCorrelation coefficientSpearman’s RankReilly’s Break-point / Reilly’s LawLinear 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 ScaleEg. $20, $30, $40,…..

Normal distribution

Where = mean, s = standard deviationx

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 Y

X is independent variable, and Y is dependent variable

Scattergram

X – independent variable

Y –

dep

ende

n t v

aria

b le

(7,8) where x=7, y=8

(3,8) where x=3, y=8

Where x = incomey = 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 +1Perfect positive correlation: +1Perfect negative correlation: -1No 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 +1Perfect positive correlation: +1Perfect negative correlation: -1No 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

TCOSI

RankNo. TC Rank

Di Di2

1970 +11 121971 +18 171972 -12 101973 +10 161974 +9 111975 +18 131976 +4 111977 -13 7

1978 -5 7

1979 -2 12---- ---- ---- ---- ----

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.

Where j = trading centre ji = trading centre ix = break-point = distance between i and j Pi = population size of iPj = population size of j = break-point distance from j to x

Reilly’s Break-pointi

j

x

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-pointCentre Population Road distance

from Bridgewater (km)

Break-point distance from Bridgewater (km)

Bridgewater 26598 0 0

Weston 50794 24 X

Frome 13384 46 Y

Yeovil 25492 32 16.2

Minehead 8063 34 21.9

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, andKnowing value X to predict value Y.Correlation coefficient (r) is also use to indicate the relationship between X and Y.

The End