6.4.3. Product-Moment Correlation (Pearson)
6.4.3.1. Operation
- Operation name
Product-Moment Correlation (Pearson)
- Algorithm reference
Wikipedia entry on Pearson product-moment correlation coefficient
- Description
This Operation performs a correlation analysis for metrically scaled data (assumption: normal distribution).
- Utilised in
6.4.3.2. Options
- name
temporal correlation
- description
performs a correlation analysis regarding temporally variable values
- items
one grid cell, cell-by-cell, spatial mean
- name
spatial correlation
- description
performs a correlation analysis regarding spatially variable values
- items
one point in time, time-by-time, temporal mean
- name
scatter-plot
- description
displays a scatter-plot showing corresponding variable values (not for time-by-time and pixel-by-pixel analysis)
- name
time series plot
- description
plots results for spatial time-by-time correlation
- name
map
- description
produces and displays a map showing cell-by-cell correlations
- name
table
- description
produces a table listing pixel-by-pixel respectively time-by-time correlation coefficients
- name
t test
- description
performs a t test to assess the significance level of the results
6.4.3.3. Input data
- name
longitude (lon, x)
- type
floating point number
- range
[-180.; +180.] respectively [0.; 360.]
- dimensionality
vector
- description
grid information on longitudes
- name
latitude (lat, y)
- type
floating point number
- range
[-90.; +90.]
- dimensionality
vector
- description
grid information on latitudes
- name
height (z)
- type
floating point number
- range
[-infinity; +infinity]
- dimensionality
vector
- description
grid information on height/depth
- name
variable1
- type
floating point number
- range
[-infinity; +infinity]
- dimensionality
cube or 4D
- description
values of a certain geophysical quantity
- name
variable2
- type
floating point number
- range
[-infinity; +infinity]
- dimensionality
cube or 4D
- description
values of a certain geophysical quantity
- name
time (time, t)
- type
integer or double
- range
[0; +infinity]
- dimensionality
vector
- description
days/months since …
6.4.3.4. Output data
- name
product-moment correlation coefficient (Pearson)
- type
floating point number
- range
[-1.; +1.]
- dimensionality
scalar
- description
for correlation analysis for metrically scaled data
- name
signficance
- type
boolean
- range
{0,1}
- dimensionality
scalar
- description
significant or non-significant
alternatively
- name
level of signficance
- type
floating point number
- range
[0; +infinity]
- dimensionality
scalar
- description
significance level of correlation
- name
scatter plot
- description
displays a plot (see Options)
- name
time series plot
- description
displays a time series plot (see Options)
- name
map
- description
displays a map (see Options)
- name
table
- description
displays a table (see Options)
6.4.3.5. Parameters
- name
level of significance
- type
floating point number
- valid values
[0; 1]
- default value
0.95
- description
level of significance for t test, determines t value to be compared with test value
for plot settings, the procedure is forwarded to the Visualisation Operation
6.4.3.6. Example
# Fortran subroutine for product moment correlation analysis (includes mean value function)
c-----subroutine "correlation"
c.....calculation of
c.....a) product-moment corellation coefficient "cc" between x(t) and y(t), t=[1,nt]
c.....b) test-value "test" for t-test
subroutine s_correlation(nt,x,y,cc,test) !Zeit
implicit none
integer nt,t
real x(nt),dummy,dummy2,dummy3,y(nt),cc,test,f_mw
dummy=0.
dummy2=0.
dummy3=0.
do t=1,nt
dummy=dummy+((x(t)-f_mw(n,x))*(y(t)-f_mw(n,y)))
dummy2=dummy2+((x(t)-f_mw(n,x))**2)
dummy3=dummy3+((y(t)-f_mw(n,y))**2)
enddo !ja
cc=(dummy)/sqrt(dummy2*dummy3)
test=cc*sqrt((n-2)/(1-(cc**2)))
return
end
c-----function "mean value"
c.....calculation of mean value f_mw(nt,x) of vairable x with a sample size nt
real function f_mw(nt,x)
implicit none
integer nt,t
real x(nt)
f_mw=0.
do t=1,nt
f_mw=f_mw+x(t)
enddo
f_mw=f_mw/float(nt)
return
end