How Not to Be Wrong summary

A basic rule of mathematics is thus: if you have a difficult problem, try to make it easier and solve the easier problem instead. Then hope the simpler version is close enough to the difficult version.

We can break down hard problems into easier ones by assuming they have linearity. In geometry, we assume things have linearity when we consider straight lines. Curves represent nonlinearity.

Scientists collect data through observation then use it to build theories. However, observational data can come about by chance, so drawing conclusions from it can be quite precarious.

Consider this example: In 2009, a neuroscientist showed photos of people to a dead fish and measured the fish’s brain activity. Interestingly, the fish responded accurately to the emotions of people in the pictures.

In any situation where we're uncertain about an outcome, probability can help us. Probability can't tell us exactly what will happen in the future, but it can tell us what we should expect.

For example, probability theory can tell us what's likely to happen if we place a bet on something. We can use probability to know what might happen when we buy a lottery ticket, by determining the ticket’s expected value.

Why is a novelist’s second book usually not as good as his first breakout success? Artistic success is subject to a mathematical phenomenon called regression to the mean, or the regression effect.

The regression effect states that if a variable produces an unlikely outcome, the next outcome will tend to be closer to the mean.

As we've seen, linear regression is an important statistical tool that helps us understand how variables relate to each other. However, linear regression can't be used for every set of data; if used incorrectly, it produces misleading results.

You can find the linear regression of a data set by plotting all its points on a graph, then finding the line that comes closest to passing through all of them. This is only meaningful, however, if the data points are already in a generally linear shape.

In 2005, a professor named John Ioannidis published a paper called, “Why Most Published Research Findings are False.” That might seem like a radical claim, but his points were sound.

He first stated that insignificant observations can sometimes pass a statistical significance test by chance.

How can you measure “public opinion”? It’s a rather vague term, so we should be critical when presented with polls that claim to express it.

First, people can have very contradictory opinions, and they can even contradict themselves.