Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 108

Pearson correlation:

i = 1

n

y )

x )( y i −

( x i −

r xy =

1) s x s y ( n −

where r xy is the correlation between cores x and y .
From Briffa and Jones ( 1990 ) , let c i equal the number of within-tree cores for a
given tree and let RBAR be a given average correlation statistic. Then,

RBAR for all series:

c i

t t

1
NTOT

RTOT = r ilj

i = 1 j = 1

l = 1

i = 1

where

1

t t

1
2

NTOT = c i c i −

i = 1 i = 1

RBAR within trees:

⎡ ⎤

t c i

1
NWT

⎣ ⎦

RWT = r ij

i = 1 j = 2

where

t

1
2 c i ( c i −

NWT = 1)

i = 1

RBAR between trees:

1
NBT (RTOT

RBT = · NTOT) − RWT · NWT)

where NBT NWT

The effective RBAR (REFF) is a weighted average of RBT and RWT that
includes the added signal strength due to the within-tree correlations.

= NTOT −

RBAR effective:

RBT

REFF =

−

1 RWT

CEFF

RWT +