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## 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
.

Next: Estimating the rate of Up: Projections from abundance data Previous: False detection
Kent Holsinger 2011-10-10