Landcare Research - Manaaki Whenua

Landcare-Research -Manaaki Whenua

Reading signals from noisy data?

When determining whether an observed increase is real, we must separate the signal from the noise — an increasing trend does not necessarily mean that the population is increasing.

The mean birds per garden per year and the resulting time series gives us some information as to whether the garden bird abundance of a species is changing over time.

However, we are more interested in identifying a long-term trend, i.e. a persistent increase or decrease in the abundance of the species. This can be termed the signal.

Here we illustrate why reading that signal can be tricky and highlight some ways to overcome those challenges.

Figure illustrating how difficult it can be to determine the true trend (straight line) from data (points) when there is either a weak signal and/or a high degree of noise.
Noisy data can mask a signal

When determining whether an observed increase is real, we must separate the signal from the noise.

Figure illustrating the annual change in tūī abundance relative to measurements in 2007 for four different estimates of trend.
How to reduce the noise?

Accounting for sources of noise in the data can make it easier to detect the signal.

Figure illustrating the annual change in tūī abundance relative to measurements in 2007 when we account for region and garden type, as well as our uncertainty about that change.
Is the signal real?

An increasing trend does not necessarily mean that the population is increasing.