Imagine you’re going fishing with a big old net in the sea. But the net has huge holes in it and you don’t catch any fish. So you make the holes smaller and smaller until finally you catch something. The problem is, it’s a tiny little prawn which isn’t going to have much of an impact in your quest for a nice dinner. As is the case with so many parts of our lives, the right question is not ‘if’ but ‘how much’.

We’ve seen this same dynamic play out in recent weeks with widely reported coverage that the WHO will declare aspartame a possible cancer risk. This is a big claim because aspartame pops up in lots of things we eat and drink, most commonly diet soft drinks. The presentation of the aspartame issue by the WHO and in parts of the media underlines a recurrent challenge in health policy and science communications – how to differentiate between the relationship between two things (the ‘if’) and whether we need to worry about it (the ‘how much’ part of the relationship).

Now, lots of us drink diet drinks and none of us want to get cancer, so of course declaring aspartame a possible carcinogen is news. But, as others have said, like in this very good piece by Stuart Richie, you almost certainly don’t need to really worry about the can of diet cola lurking in the fridge.

That’s because what matters is not just knowing that something is a risk, but the extent to which we can quantify or ‘right size’ it. New analysis estimates that a 70kg adult would have to drink about 14 cans of diet cola to exceed the safe daily dose limit.

David Spiegelhalter has written extensively about similar issues with processed meat. It’s tricky to get our heads around this because when it comes to risk assessment, things aren’t good or bad, they’re not risky or not - it’s more complicated than that. The easy part is declaring something black or white, the tough part is describing precisely the shade of grey.

This is a huge problem in science generally and in health policy.

The most popular method of statistics in medical and social sciences is frequentist statistics, often known as null hypothesis significance testing. The aim is to reject the null hypothesis, ie, to knock down the idea that there is no relationship between A and B. So if we get a significant result it means that we have rejected those hypotheses, so we can be certain (to within a certain degree of confidence) that there is a relationship. Great, but this then leads us to the next knottier problem – how big and important is the relationship between A and B? For social policy the most pertinent question about risk is almost always how much.

It’s partly a language problem. Statistically significant is a specific term, but it also has a lay meaning. So if we say something is ‘significant’ people will think we mean important, but that isn’t always the case. When we lived in a data poor world the things tended to go hand in hand – if you could see a relationship from a small sample, chances are that relationship was pretty big. But if you have loads and loads of data (as we increasingly do), it’s possible to detect smaller and smaller relationships. And boy oh boy is there a lot of data on aspartame – 1,300 studies in the review.

Part of the challenge with getting this right is in accepting the fact that it is all fiendishly complicated. To go back to our A and B example, even if we know the size of the relationship between them we still need to factor in baseline risk levels. If something increases the risk of cancer by 10% well it really matters if that’s a common sort of cancer or a very rare cancer because it’s going to have a very different set of outcomes.

And then we need to compare that assessment of risk to other risks to health. For example, when it comes to diet and health, the small link between aspartame and cancer is dwarfed by the much bigger link between excess sugar and increasing levels of obesity and rocketing rates of diabetes. This is an epic public health challenge and is strongly correlated with lots of diseases we want to avoid. So understanding the 'how much' part of the relationship is crucial because what we don’t want is for people to decide to go back to full sugar drinks because this would by and large present a much larger health risk than the one (cancer linked to aspartame) that they’re trying to avoid.

None of this is to say we shouldn’t be looking for small relationships. At a population level (ie, all of us) small relationships can be really important – 1% of 50 million is still 500,000 people. And knowledge is good, the more the better. But we do need to be careful and responsible about how we communicate it, often doing so with contextual or comparative information.

This is an awkward fit with our very human inclination to sort things into binary good or bad columns, and nuance can be hard to convey. But it’s hard to overstate the importance of understanding whether something is significant enough for us to give it our attention, because focusing on the small or not very important relationships risks overlooking the things that really matter when it comes to improving health.