Geoscience Reference
In-Depth Information
in any given year, the interval and duration of surveys over time, the magnitude
of sampling variation that occurs in abundance indices, and the magnitude of
trend variation in local populations in relation to overall trends in regional pop-
ulations (Gerrodette 1987). Other less obvious but often equally important fac-
tors to be considered include
a
levels and desired effect sizes (trend strengths)
set by researchers (Hayes and Steidl 1997; Thomas 1997). Specifically,
researchers need to specify the probabilities at which they are willing to make
statistical errors in trend detection, that is, the probability of wrongly rejecting
the null hypothesis of no trend (at a probability =
a
, that is, the level of signif-
icance) and of wrongly accepting the null hypothesis of no trend (at a proba-
bility =
b
). Furthermore, the statistical method chosen to examine trends in a
count series also can influence the likelihood of detecting them (Hatfield et al.
1996). Understanding how these factors interact with the inherent sampling
variation of abundance indices can provide insights into the design of statisti-
cally powerful yet labor-efficient monitoring programs (Peterman and Brad-
ford 1987; Gerrodette 1987; Taylor and Gerrodette 1993; Steidl et al. 1997).
Statistical power underlies these issues and provides a useful conceptual
framework for biologists designing studies that seek to identify population
change. The key problem identifying population change is that sources of
noise in sample counts obscure the signal associated with ongoing population
trends. Trends represent the sustained patterns in count data (the signal) that
occur independently of cycles, seasonal variations, irregular fluctuations that
are sources of sampling error (the noise) in counts. Statistical power simply
represents the probability that a biologist using a particular population index
in conjunction with a specific monitoring protocol will detect an actual trend
in sample counts, despite the noise in the count data. In a statistical context,
power is the probability that the null hypothesis of no trend will be rejected
when it is, in fact, false, and is calculated as 1 -
b
.
Although statistical power is central to every monitoring effort, it is rarely
assessed (Gibbs et al. 1998). Consequences of ignoring power include collect-
ing insufficient data to reliably detect actual population trends. Occasionally,
collection of more data than is needed occurs. Unfortunately, until recently
few tools have been available to animal ecologists that permit assessment of
statistical power for trends (Gibbs and Melvin 1997; Thomas 1997).
POWER ESTIMATION FOR MONITORING PROGRAMS
The large numbers of factors that interact to determine the statistical power of
a monitoring program make power estimation a complex undertaking. Ana-
lytical approaches are forced by the large number of variables involved to over-
