A Field Guide to Lies: Critical Thinking in the Information Age by Daniel J. Levitin Read Free Book Online Page A

randomness can explain. These tests don’t know what’s noteworthy and what’s not—that’s a human judgment.
    The more observations you have in the two groups, the more likely that you will find a difference between them. Suppose I test the annual maintenance costs of two automobiles, a Ford and a Toyota, by looking at the repair records for ten of each car. Let’s say, hypothetically, the mean cost of operating the Ford is eight cents more per year. This will probably fail to meet statistical significance, and clearly a cost difference of eight cents a year is not going to be the deciding factor in which car to buy—it’s just too small an amount to be concerned about. But if I look at the repair records for 500,000 vehicles,that eight-cent difference will be statistically significant. But it’s a difference that doesn’t matter in any real-world, practical sense. Similarly, a new headache medication may be statistically faster at curing your headache, but if it’s only 2.5 seconds faster, who cares?
    Interpolation and Extrapolation
    You go out in your garden and see a dandelion that’s four inches high on Tuesday. You look again on Thursday and it’s six inches high. How high was it on Wednesday? We don’t know for sure because we didn’t measure it Wednesday (Wednesday’s the day you got stuck in traffic on the way home from the nursery, where you bought some weed killer). But you can guess: The dandelion was probably five inches high on Wednesday. This is interpolation. Interpolation takes two data points and estimates the value that would have occurred between them if you had taken a measurement there.
    How high will the dandelion be after six months? If it’s growing 1 inch per day, you might say that it will grow 180 inches more in six months (roughly 180 days), for a total of 186 inches, or fifteen and a half feet high. You’re using extrapolation. But have you ever seen a dandelion that tall? Probably not. They collapse under their own weight, or die of other natural causes, or get trampled, or the weed killer might get them. Interpolation isn’t a perfect technique, but if the two observations you’re considering are very close together, interpolation usually provides a good estimate. Extrapolation, however, is riskier, because you’re making estimates outside the range of your observations.
    The amount of time it takes a cup of coffee to cool to room temperature is governed byNewton’s law of cooling (and is affected by other factors such as the barometric pressure and the composition of the cup). If your coffee started out at 145 degrees Fahrenheit (F), you’d observe the temperature decreasing over time like this:
     
Elapsed Time (mins)
Temp °F
 
    0 
 
    145 
 
    1 
 
    140 
 
    2 
 
    135 
 
    3 
 
    130 
    Your coffee loses five degrees every minute. If you interpolated between two observations—say you want to know what the temperature would have been at the halfway point between measurements—your interpolation is going to be quite accurate. But if you extrapolate from the pattern, you are likely to come up with an absurd answer, such as that the coffee will reach freezing after thirty minutes.

    The extrapolation fails to take into account a physical limit: The coffee can’t get cooler than room temperature. It also fails to take into account that the rate at which the coffee cools slows down the closer it gets to room temperature. The rest of the cooling function looks like this:

    Note that the steepness of the curve in the first ten minutes doesn’t continue—it flattens out. This underscores the importance of two things when you’re extrapolating: having a large number of observations that span a wide range, and having some knowledge of the underlying process.
    Precision Versus Accuracy
    When faced with the precision of numbers, we tend to believe that they are also accurate, but this is not the same thing. If I say “a lotof people are buying electric cars these