Question: Case Study gave the information that the rate of errors made by air traffic controllers in the United States during fiscal year 1998 was 5.5 errors per million flights. Discuss whether this summary value is a population summary (a parameter) or a sample summary (a statistic).
Case Study: Safety in the Skies?
If you fly often, you may have been relieved to see the New York Times headline on October 1, 2007, proclaiming "Fatal airline crashes drop 65%" (Wald, 2007). And you may have been dismayed if you had seen an earlier headline in USA Today that read, "Planes get closer in midair as traffic control errors rise" (Levin, 1999). The details were even more disturbing: "Errors by air traffic controllers climbed from 746 in fiscal 1997 to 878 in fiscal 1998, an 18% increase." So, are the risks of a fatal airline crash or an air traffic control error something that should be a major concern for airline passengers? Don't cancel your next vacation yet. A look at the statistics indicates that the news is actually pretty good! The low risk becomes obvious when we are told the base rate or baseline risk for these problems. According to the New York Times article, "the drop in the accident rate [from 1997 to 2007] will be about 65%, to one fatal accident in about 4.5 million departures, from 1 in nearly 2 million in 1997."
And according to the 1999 USA Today story, "The errors per million flights handled by controllers climbed from 4.8 to 5.5." So the rate of fatal accidents changed from about 1 in 2 million departures in 1997 to 1 in 4.5 million departures in 2007, and the ominous rise in air traffic controller errors in 1998 still led to a very low rate of only 5.5 errors per million flights. Fortunately, the rates for these problems were provided in both stories. This is not always the case in news reports of changes in rates or risk. For instance, an article may say that the risk of a certain type of cancer is doubled if you eat a certain unhealthful food. But what good is that information unless you know the actual risk? Doubling your chance of getting cancer from 1 in a million to 2 in a million is trivial, but doubling your chance from 1 in 50 to 2 in 50 is not.
Moral of the Story: When you read about the change in the rate or risk of occurrence of something, make sure you also find out the base rate or baseline risk.
Definitions: The rate at which something occurs is simply the number of times it occurs per number of opportunities for it to occur. In fiscal year 1998, the rate of air traffic controller errors was 5.5 per million flights. The risk of a bad outcome in the future can be estimated by using the past rate for that outcome, if it is assumed the future will be like the past. Based on recent data, the estimated risk of a fatal accident for any given flight is 1 in 4.5 million, which is 1/4,500,000 or about .00000022. The base rate or baseline risk is the rate or risk at a beginning time period or under specific conditions. For instance, the base rate of fatal airline crashes from which the 65% decrease for 2007 was calculated was about 1 crash per 2 million flights, for fiscal year 1997.