by DOUGLAS J. KEENAN
For years, some researchers have argued that the evidence for global warming is not nearly as strong as has been officially claimed. The details of the arguments are often technical. As a result, policy makers and other people outside the debate have relied on the pronouncements of a group of climate scientists. I think that is unnecessary. I believe that what is arguably the most important reason to doubt global warming can be explained in terms that most people can understand.
Figure 1. Global temperatures.
Consider the graph of global temperatures in Figure 1, which uses data from NASA. At first, it might seem obvious that the graph shows an increase in temperatures. In fact the story is more involved.
Imagine tossing a coin ten times. If the coin came up Heads each time, we would have very significant evidence that the coin was not a fair coin. Suppose instead that the coin was tossed only three times. If the coin came up Heads each time, we would not have significant evidence that the coin was unfair: Getting Heads three times can reasonably occur just by chance.
Figure 2. Coin tosses: H, T, H (left); T, H, T (mid); H, T, T (right).
In Figures 2 and 3, each graph has three segments, one segment for each toss of a coin. If the coin came up Heads, then the segment slopes upward; if it came up Tails, then it slopes downward. In Figure 2, the graph on the far left illustrates tossing Heads, Tails, Heads; the middle graph illustrates Tails, Heads, Tails; and the last graph illustrates Heads, Tails, Tails. Figure 3 illustrates Heads, Heads, Heads.
Figure 3. Coin tosses: H, H, H.
Three Heads is not significant evidence for anything other than random chance occurring. A statistician would say that although the graph shows an increase, the increase is “not significant”.
Suppose now that instead of tossing coins, we roll ordinary six-sided dice. We will roll each die three times. If a die comes up 1, we will draw a line segment downward; if it comes up 6, the segment is drawn upward; and if it comes up 2, 3, 4 or 5, the segment is drawn straight across. Figure 4 gives some examples of possible outcomes.
Figure 4. Dice rolls: 3, 6, 3; 1, 5, 2; 4, 6, 1.
Now consider Figure 5, which corresponds to rolling 6 three times. This outcome will occur by chance just once out of 216 times, and so offers significant evidence that the die is not rolling randomly. That is, the increase shown in Figure 5 is significant.
Figure 5. Dice rolls: 6, 6, 6.
Note that Figure 3 and Figure 5 look identical. In Figure 3, the increase is not significant; yet in Figure 5, the increase is significant. These examples illustrate that we cannot determine whether a line shows a significant increase just by looking at it. Rather, we must know something about the process that generated the line. But in practice, the process might be very complicated, which can make the determination difficult.
Consider again the graph of global temperatures in Figure 1. We cannot tell if global temperatures are significantly increasing just by looking at the graph. Moreover, the process that generates global temperatures—Earth’s climate system—is extremely complicated. Hence determining whether there is a significant increase is likely to be difficult. Continue reading