Spearman's Rank 史皮尔曼等级相关系数
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Centre Population Road distance from Break-point Bridgewater (km) distance from Bridgewater (km) Bridgewater Weston Frome Yeovil Minehead
26598 50794 13384 25492 8063
0 24 46 32 34
0 X Y 16.2 21.9
Reilly’s Break-point
24 24 = = 10.08 X= 50794 2.38 1+ 1+ 26598
46 46 Y= = = 26.9 13384 1.71 1+ 26598
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.
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 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 October SOI +11 +18 -12 +10 +9 +18 +4 -13 -5 -2 Number of tropical cyclones 12 17 10 16 11 13 11 7 7 12
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.
Spearman’s Rank (Examples)
Year 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ---Oct OSI +11 +18 -12 +10 +9 +18 +4 -13 -5 -2 ---No. of TC 12 17 10 16 11 13 11 7 7 12 ---------Σ Σ OSI Rank No. TC Rank Di Di2
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
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
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
The End
Level of Measurement
NominalHale Waihona Puke BaiduScale:
Eg. China, USA, HK,…….
Ordinal Scale:
Eg. Low, Medium, High, Very High,….
Interval Scale:
Eg. 27oC, 28oC, 29oC,…..
Ratio Scale
Spearman’s Rank
spearman’s where : rs = spearman s coefficient Di = difference between any pair of ranks N = sample size
Spearman’s Rank
Spearman’s Rank (Examples)
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
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
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)
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
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.
Correlation Coefficient
Strong positive correlation (relationship)
Correlation Coefficient
Strong negative correlation (relationship)
Correlation Coefficient
Mode: Most Frequent Median: Middle Mean: Arithmetic Average
Mode: Most Frequent
Median: Middle
Mean: Arithmetic Average
Dependent and Independent variables
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
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.
26598 50794 13384 25492 8063
0 24 46 32 34
0 X Y 16.2 21.9
Reilly’s Break-point
24 24 = = 10.08 X= 50794 2.38 1+ 1+ 26598
46 46 Y= = = 26.9 13384 1.71 1+ 26598
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.
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 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 October SOI +11 +18 -12 +10 +9 +18 +4 -13 -5 -2 Number of tropical cyclones 12 17 10 16 11 13 11 7 7 12
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.
Spearman’s Rank (Examples)
Year 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ---Oct OSI +11 +18 -12 +10 +9 +18 +4 -13 -5 -2 ---No. of TC 12 17 10 16 11 13 11 7 7 12 ---------Σ Σ OSI Rank No. TC Rank Di Di2
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
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
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
The End
Level of Measurement
NominalHale Waihona Puke BaiduScale:
Eg. China, USA, HK,…….
Ordinal Scale:
Eg. Low, Medium, High, Very High,….
Interval Scale:
Eg. 27oC, 28oC, 29oC,…..
Ratio Scale
Spearman’s Rank
spearman’s where : rs = spearman s coefficient Di = difference between any pair of ranks N = sample size
Spearman’s Rank
Spearman’s Rank (Examples)
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
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
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)
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
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.
Correlation Coefficient
Strong positive correlation (relationship)
Correlation Coefficient
Strong negative correlation (relationship)
Correlation Coefficient
Mode: Most Frequent Median: Middle Mean: Arithmetic Average
Mode: Most Frequent
Median: Middle
Mean: Arithmetic Average
Dependent and Independent variables
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
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.