Basic Social Statistic

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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.
XY
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