How To Spot A Lie That's Technically True (How to spot misleading statistics)

The most useful skill nobody taught you

Here are two statements.

1. "Eating this food doubles your risk of a rare cancer."

2. "Eating this food raises your risk of a rare cancer from 1 in 100,000 to 2 in 100,000."

Both are the exact same fact. Neither is a lie. One will get shared four million times and put you off your dinner for a decade. The other will make you shrug and carry on.

Welcome to the single most powerful trick in modern life: telling the truth in a way that's completely misleading.

Nobody teaches you to spot this. Not at school, not at university, and certainly not by the people who benefit from you not spotting it. So let's fix that. Because once you can see these tricks, you cannot "unsee" them, and it will change how you read the news, how you assess your own health, and, yes, how you look at anyone trying to get you to part with money.

Trick one: relative vs absolute (the big one)

The example above is the most common statistical sleight of hand on the planet, so let's name it properly.

Absolute risk is the actual chance of the thing happening. 1 in 100,000.

Relative risk is how much that chance changed. "Doubled!"

Doubling a tiny number gives you… a slightly less tiny number. But "doubles your risk" sounds enormous, because our brains hear "double" and picture something going from small to huge.

Here's how to defend yourself, and it's one question:

"Double from what to what?"

That's it. That's the whole defence. Any time you see a percentage change without a starting number, you are being told half a fact, and the half you're missing is the half that would let you judge whether to care.

This trick appears everywhere:

• Drug side effects: "300% increased risk of blood clots" - from 1 in a million to 3 in a million.

• Investment marketing: "This fund grew 200% last year!" - starting from a base so small it means nothing.

• Newspaper health scares: near-daily.

None of these are lies. Every one of them is designed to make you feel something that the actual numbers don't justify.

Trick two: the survivors are doing the talking

Imagine I show you the ten most successful entrepreneurs in Britain and note that eight of them dropped out of university.

Obvious conclusion: dropping out helps you succeed! Skip your degree, get rich.

Now, what am I not showing you?

Everyone who dropped out and failed.

They didn't get interviewed. They're not on the podcast. Nobody wrote a book about them. They're just… living normal lives, invisible to the story.

This is called survivorship bias, and it comes from one of my favourite pieces of history.

In the Second World War, the military examined bombers returning from raids and mapped where they'd been hit by enemy fire. The bullet holes clustered on the wings and the tail. So the obvious answer: armour the wings and the tail, where the damage is.

A statistician named Abraham Wald pointed out the flaw, and it's genuinely brilliant.

You are only looking at the planes that came back.

The planes hit in the engine and cockpit, the areas with no bullet holes on the returning aircraft, didn't return. The absence of damage in those spots wasn't evidence they were safe. It was evidence that damage there was fatal.

Armour the parts with no bullet holes.

Once you know this, you see it constantly. Every "here's what successful people do" article is a bomber with holes in the wings. You're being shown the survivors, and the failures, who very often did exactly the same things, are silent, because failure doesn't get a book deal.

Trick three: the thing that didn't cause the thing

This one you've probably heard of, but I want to show you why it's harder to escape than you think.

Ice cream sales and drowning deaths rise together. Perfectly correlated.

Ice cream does not cause drowning. Summer causes both. It's hot, so people buy ice cream, and people swim.

Everyone nods at this example. Then everyone falls for it anyway, because in the real world the hidden third factor is never as obvious as "summer."

Real one: studies once found that people who took a particular hormone treatment had less heart disease.

Cause and effect, surely?

Except the women taking it were, on average, wealthier, and wealthier people have better diets, more exercise, better healthcare. Wealth was the summer. The treatment was the ice cream. When it was

properly tested, the benefit largely evaporated.

The question that saves you: "Is there something else that could be causing both?"

Ask that once, and about half the causal claims you encounter fall over.

Trick four: choosing where the story starts

Show me any chart, and I can make it tell you the opposite story, just by changing where I start it.

• Start the chart in 2020: catastrophic collapse!

• Start it in 1990: relentless upward march!

• Start it three months ago: dead flat, nothing happening.

Same data. Three completely different emotional experiences.

This is cherry-picking the baseline, and it's the reason you should be instantly suspicious of any chart where someone else chose the start date and didn't explain why.

The defence: "Why does the chart start there?" If there's no good reason, a genuine structural break, a policy change, a company's founding, assume the date was chosen because it produces the desired shape.

Trick five: the number that isn't measuring what you think

Averages are the great deceivers.

Bill Gates walks into a pub with nine people in it. The average wealth of everyone in that pub is now over ten billion pounds each.

Every single person in that pub is still skint. The average is technically correct and completely useless.

This is why you should always ask for the median, the person literally in the middle, rather than the mean.

The mean gets dragged around by extremes. The median doesn't.

You will see this abused constantly in reporting on wages, house prices, savings and investment returns.

"Average savings of £17,000!" dragged upwards by a small number of people with a great deal, while the person in the middle has a fraction of that.

The defence: "Is that the mean or the median?" If they don't say, and the topic is money, assume it's the flattering one.

Why I'm telling you all this in an investing publication

Because this is where the money is.

Genuinely. Every single trick above is used, routinely and legally, to sell financial products to ordinary people.

• "This fund returned 40% last year!"  Cherry-picked baseline. Show me ten years. Show me the years it lost money. Show me the funds this company launched that did badly and were quietly closed (that's survivorship bias, fund families do this constantly, closing the losers so the average of the survivors looks great).

• "Our clients see average returns of X."  Mean or median? And which clients, the ones who stayed, or all of them?

• "Reduce your risk by 50%!" From what, to what?

And here's the deeper point I really want to land.

The financial industry does not primarily make money by being cleverer than you. It makes money by knowing things you were never taught. The asymmetry isn't intelligence, it's education. It always has been.

Which is exactly why I think this stuff, boring, unglamorous, statistical literacy, is more valuable to an ordinary person than any share tip they'll ever receive. A share tip helps you once. This helps you every single day, for the rest of your life, in every domain: your health, your politics, your news, your pension.

The five questions. Print them out.

That's it. That's the whole toolkit. Five questions, and you will be better protected than the overwhelming majority of people:

1. "Double from what, to what?" (relative vs absolute)

2. "Who am I not seeing?" (survivorship bias)

3. "Could something else be causing both?" (correlation vs causation)

4. "Why does the chart start there?" (baselines)

5. "Mean or median?" (averages)

You don't need a maths degree. You need five questions and the confidence to ask them.

Most people never ask. That's not because they're stupid, it's because nobody ever told them they were allowed to.

You're allowed to.

Next in this series: the plumbing crisis nobody's talking about - why artificial intelligence is about to break the electricity grid.

References

Wald, A. - original work on aircraft survivability, Statistical Research Group (Columbia University), summarised by the American Statistical Association: https://www.amstat.org/

Office for National Statistics - guidance on mean vs median in earnings and wealth statistics: https://www.ons.gov.uk/

NHS - "Behind the Headlines" health-news analysis (relative vs absolute risk): https://www.nhs.uk/

Women's Health Initiative - hormone therapy trial results (confounding and observational vs randomised evidence): https://www.whi.org/

Financial Conduct Authority - rules on financial promotions and past-performance reporting: https://www.fca.org.uk/