We learn at school that numbers are a great way to represent facts. When a number is quoted, it automatically lends greater weight to a claim. This is especially true if the number confirms something we already think.
Numbers help us understand the world around us – including our personal finances. But just as the saying “there are lies, damned lies, and statistics” suggests, numbers can be misleading or even falsified – perhaps to sell us something, or get us to invest.
Numbers can easily suggest that two things that happen together are connected – when they are not.
Here is one classic example. If you plot the total number of pirates against global average temperatures, you will see the number of pirates shrinks as the temperature rises. Yet there’s no cause or effect relationship between the two things – even if we argue that higher temperatures might cause storms and shipwrecks, thereby killing pirates.
We know the relationship between pirates and temperature is coincidental. But it isn’t always so easy to tell.
We can be tempted to think one thing must have caused another, confusing correlation with causation. This happens partly because we tend to see patterns in everything – even when they occur by accident or do not really exist.
As psychologist Daniel Kahneman explains in Thinking, Fast and Slow, we tend to think in stories, creating a narrative that tries to make sense of what we see. And scientists explain that it can be tough to prove if one thing really causes another.
Sometimes mistakes with numbers are simply about making wrong assumptions. One common number-based error involves mistakenly projecting data into the future, or extrapolation. Events in the past may not happen again the same way, even if a line drawn on a graph suggests they will.
In any experiment, the right situations may not have been tested. Bias in sampling is difficult to avoid even in the best-designed tests.
Raw numbers on their own don’t mean much without interpretation. They must be collected, processed, analysed and presented right to see the whole picture. More common problems with statistics are explained here.
Research tells us that advertising using numbers is more likely to convince us to buy. Because we see numbers as measures of the real world, we are inclined to believe them. This is especially true if the number comes from research.
Yet information can be easily left out, framed or presented in a misleading way. For example, a 2007 toothpaste advert claimed the brand was recommended by 80% of dentists. Although this claim was not a lie, the advertising was eventually banned in the UK.
The 80% came from a poll where dentists were asked to recommend several brands – not just one. Yet the resulting ad did not mention this fact, creating a false impression that the advertised brand was being specially recommended by dentists.
This can be dangerous when it comes to financial advertising. Often, doing the required maths is not easy.
In one study, people struggled to compare annuity payments to a one-off sum. And research shows that for some people having to work out an equation can actually cause a brain response like physical pain. When faced with figures, it can be easier to choose one stand-out figure that looks good, make a quick decision and then move on to a more pleasant task.
But this article explains, a single number – such as a great top-rate in a mortgage offer – may not reflect the true cost. In the 2008 US subprime mortgage crisis, many people that signed up for mortgages did not keep up with their payments. “Our results show [that] limitations in numerical ability are common and that there is a strong link to subprime mortgage defaults,” researchers wrote in this related study.
Everyone makes mistakes
It can be tempting to assume experts have got the maths right. But even experts make mistakes with their calculations, especially if they’re based on faulty thinking in the first place.
One study has shown how even the highly-trained commit “base rate neglect”. This means putting too much weight on specific, individual factors, underestimating the underlying “base” conditions. Our tendency to overestimate our chances of winning the lottery – focusing on the lucky few who have won – is a good example.
Take claims with a grain of salt
Yet seeing numbers in a promotion may have an almost magical effect on our thinking, as this eZonomics article suggests. Round figures tend to be more memorable, while the difference between $10 and $9.99 is easily perceived as larger than it is – encouraging us to spend.
We should always ask questions about numbers – especially if they’re shown to us in order to “prove” something. We need not be bamboozled. A good rule of thumb might be to take any numbers we do not understand with a grain of salt.