Problem

If you read scientific literature, you often will see graphs with vertical lines on each p...

If you read scientific literature, you often will see graphs with vertical lines on each point. What do those lines mean? They represent standard error, a measure of how much variation there is in a group of observations. This is one way scientists show uncertainty, or their level of confidence in their results.

A central principle of science is the recognition that all knowledge involves uncertainty. No study can observe every possible event in the universe, so there is always missing information. Scientists try to define the limits of their uncertainty, in order to allow a realistic assessment of their results. A corollary of this principle is that the more data we have, the less uncertainty we have. More data increase our confidence that our observations represent the range of possible observations.

One of the most detailed records of wildlife population trends in North America is the Breeding Bird Survey (BBS). Every June more than a thousand volunteers drive established routes and count every bird they see or hear. The accumulated data from thousands of routes, over many years, indicates population trends, telling which populations are increasing, decreasing, or expanding into new territory.

Because many scientists use BBS data, it is essential to communicate how much confidence there is in the data. The online BBS database reports measures of data quality, including:

• N: the number of survey routes from which population trends are calculated.
• Confidence limits: because the reported trend is an averageof a small sample of year-to-year changes on routes, confidence limits tell us how close the sample?s average probably is to the average for the entire population of that species. Statistically, 95 percent of all samples should fall in between the confidence limits. In effect, we can be 95 percent sure that the entire population?s actual trend falls between the upper and lower confidence limits.

If the distance between upper and lower confidence limits (the confidence interval) is narrow, then we can be reasonably sure the trend in our sample is close to the trend for the total population of that species. What is the reported trend for ring-necked pheasant? What is the number of routes (N) on which this trend is based? What is the range in which the pheasant’s true population trend probably falls? Is there a reasonable chance that the pheasant population’s average annual change is 0? That the population trend is actually 25?

Now look at the ruffed grouse, on either the table or the graph. Does the trend show that the population is increasing or decreasing? Can you be certain that the actual trend is not 7, or 17? On how many routes is this trend based?