As it turns out...there/s a strong association between the sign of November/s monthly NAO index and the sign of the average NAO index during meteorological winter (D-J-F). It's strongest when NOV/s NAO index is positive.
A chi-square test on NOV/s monthly values and average value of winter/s NAO suggests the sign of NOV/s NAO has a measure of predictive skill.
The distribution of events offers these probabilities:
70% + NOV ==> + Winter
30% + NOV ==> - Winer
43% - NOV ==> + Winter
57% - NOV ==> - Winter
If the signs of NOV/s NAO and winter/s NAO events were independent / unrelated...then the distribution of events would follow a normal 'bell' curve where...
Positive NOV and positive (negative) winter: 15 (12) eventsThe 2x2 contingency analysis reveals the sign of winter/s NAO is not independent (3.1% chance of Type I error) from the sign of NOV/s NAO.
Negative NOV and positive winter (negative): 19 (16) events
As a footnote...OCT/s NAO has no 'predictive' value b/c it is independent from the sign of winter's NAO.
CPC/s monthly NAO index here.