Detecting a trend

Another way is to fail to detect a decline when one is happening. If a model is good at detecting declines when they're present, it will also be likely to say declines are present when they're not. Thus, the state-space model has the most difficulty detecting declines, a regression model has less difficulty, and comparing population sizes at two time points has the least difficulty of all (1). Notice that a state space model has only a 38% chance of detecting a decline when the actual decline is 65%, and that a simple linear regression always has more power to detect a decline.

Table 1: The probability of detecting a decline when one is present (from [4])

	Decline in abundance
Model	90%	65%	40%	15%
State space	0.72	0.38	0.25	0.18
Regression	0.99	0.82	0.67	0.56
Two points	1.00	0.97	0.92	0.89

.