186
Chapter 10: The Evaluation of Foreca.sts
Table 10.2: Four versions of Heidke credit/penalty scoring systems for three
equally likely categories, progressing from
(a) the original system in which all misses and hits count equally but differently,
(b) the system in which penalties depend only on the dass of error (no longer
equitable),
(c) system (b) adjusted for E value by foreca.st category to res tore equitability, and
(d) system (e) reealibrated for expeeted hit mean of 1 and grand mean of O.
(From Barnston, 1992).
(a) The original Heidke
(e) Matrix (b) made equitable
seoring system.
by adjusting E
by foreeast eategory.
Fest. Observed Category
Fest. Observed Category
eat.
B
N
A
eat.
B
N
A
B
1
0
0
B
1
0
-1
N
0
1
0
N
1
2
1
-3
3
-3
A
0
0
1
A
-1
0
1
(b) Heidke system modified
(d) Matrix (e) reealibrated for
to aeeount for error
(0,1) random vs. perfeet
classes.
levels.
Fest. Observed Category
Fest.
Observed Category
eat.
B
N
A
eat.
B
N
A
B
1
0
-1
B
1.125 0.000 -1.125
N
0
1
0
N
-0.375 0.750 -0.375
A
-1
0
1
A
-1.125 0.000
1.125
10.3.2 Some Scores Based on the Contingency Table
a) Heidke
The H eidke seore is defined
H-E
s= T-E
(10.1)
where E is the expected number of eorrect random foreeasts. For three
equally-likely classes, E = (1/9 + 1/9 + 1/9) T, and, further, if the T foreeasts are random and independent, the standard deviation of S is (1 = AT