June 8, 2004, was the first transit of Venus visible on Earth since 1882. Not wanting to miss the big event, I consulted a chart by Richard Proctor giving the precise minute of onset: the time when the small dot of Venus would begin its trip across the face of the sun. The chart was exactly right. Mr. Proctor drew it in 1874.

Impressive! If this kind of steel-trap precision is your idea of science, then you would be mostly right in 1874 but considerably less so in the 21st century. The scientific method has spread to fields less hard-edged than astronomy. In these noisier worlds, one needs a flexible approach that can handle erratic and sometimes contradictory evidence. That's where statistical thinking comes to the rescue.

In Figure 1 I've reproduced data from the nephrology (kidney) lab of Dr. Brian Myers. He's persuaded 159 healthy volunteers to allow measurement of their kidney function, called "gfr" for glomular filtration rate. Each dot in the figure represents one gfr score plotted against the age of the volunteer with that score. At first glance, the term "scatterplot" seems all too appropriate.

However, I've used a statistical algorithm to fit a curve to these points and it reveals a hidden message: kidney function declines with age at an increasing rate. If you or a loved one needed a kidney transplant, a young donor would be preferred (but they're in short supply). None of this is as impressively precise as Mr. Proctor's transit of Venus prediction, but those who study human health have already committed themselves to a world of imprecision.

To Think Like a Statistician shows that one doesn't need to be a lab scientist to enjoy the benefits of statistics. Figure 1 portrays the pieces of the statistical point of view more clearly than we usually get in day-to-day life: an underlying truth we'd like to know is concealed by the noisy variability of the points but then revealed by a clever form of data averaging.

Sports, economics, politics, the stock markets, are all extremely noisy human activities that it pays to examine with a dose of statistical caution. Chapter 5 of my book offers a scorecard for reading the medical news. Should you believe that saunas cut the risk of strokes? That obesity is tied to liver cancer? That older fathers have sicker babies? That potatoes cause hypertension? (Spoiler alert: the sauna story gets my highest mark for believability.)

How accurate is the curve in Figure 1? This seems like an unanswerable question in the absence of a lot more volunteers (which Dr. Myers didn't have) but there is a wonderful fact about statistical estimates: the same data that gives the estimate can also say how accurate it is! Each of the dashed curves in Figure 2 is a "bootstrap replication", showing how differently Figure 1 might have turned out. We can see that the original curve isn't perfect, but it's a lot less noisy than the individual data points. The curve is most noisy at high ages, and least noisy around age 30.

The curve of Figure 1 could have been computed in the early 1800s by one of its inventors, Carl Fredrich Gauss. The bootstrap (Chapter 7) is a child of the computer age. Gauss might have been put off by its computational demands, but Figure 2 took only a millionth of a second on my laptop. Technology is destiny in the world of science, and beyond it, too. Statistics and its daughters data science and machine learning are now major departments in most universities, while statistical thinking has escaped the laboratory to show up regularly in popular media.

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Ongoing thread. More from Bradley Efron to follow.