Upload
philip-ross
View
221
Download
0
Embed Size (px)
Citation preview
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