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Magic Numbers

If you are a user, a buyer, or a practitioner of healthcare market research, how would you reply to the following ...

  • How often do you request (or propose) a sample of n=50 or n=100 on a healthcare quantitative study?
  • How often is that 'n=' sample number chosen automatically or based on 'gut feel'?
  • How often do you purchase (or sell) the 'n=' sample number that a statistical test would suggest?
  • Do you understand by how much a change in 'n=' changes confidence in the resultant data?
  • Do you know how to find your optimal 'n=' sample size?
We are all drawn, trance-like, towards certain seemingly 'magic' numbers - decimal milestones like 25, 50 75, 100, 200, 500 ... and so on.  Researchers and Marketers fall under their spell more than most, as we go about our everyday work of setting sample sizes and analysing data.

What ‘magic’ is this? Well, the sort that can instantly gratify our deep-rooted desire for safety and security: the thought of n=100 makes us feel nice and comfortable, and somehow beyond criticism in a way that n=87 just doesn't.  Besides, our colleagues recommend 'magic' number sample sizes all the time - so even if we should be doing things differently (which is unlikely, surely?) we can always point to massive precedent.

I must admit that in over 20 years of healthcare quantitative research I have never (yes, never) quoted or requested anything other than n= some 'magic' number. Sure, we have sometimes ended up with n=51 instead of n=50, or n=93 when we struggled to achieve n=100, but I have never set out to achieve such apparently oddball sample sizes.

Nor have I previously challenged their cultural orthodoxy in any serious way.
In the UK, the reflex when researching a general topic amongst GPs will be to ask for n=100, or n=200. If budget is tight then perhaps n=75, and n=50 if all we want is a so-called sanity check. But how much confidence can we have in the outcomes produced?  Is this something we consider at the proposal, or briefing, stage of a project? I think not. Being drawn to 'magic' numbers seems to be our hard-wired sample-size heuristic. But how come?

I think in large part it is because we are a bit fearful of...

Statistics - perhaps we assume that calculating optimal sample size is either beyond us ("I'm not really a stats person") or involves appreciable additional work (...and no way do we have the time).

Criticism (possibly even ridicule), if we suggest n= something else, and people laugh. Or think us incompetent.

At a time when the evidence for declining participation rates is crystalizing, our established practice of requesting n=100 when n=87 would do just as well isn't helping - burning through sample unnecessarily. On other occasions we must be reporting many of our findings with unwarranted over-confidence because, for example, we have used a base of n=50 when we really needed n=108.

Once you start to investigate the issue, it quickly becomes clear that the Internet has made the process of determining optimal sample size a lot less scary and a lot more accessible. And - to me at least - it now feels rather embarrassing that most of us are not running these simple checks as standard!

Online sample size-calculators (e.g. make it easy to check what your sample size really should be, given what you know (or can go and find out) and a bit of faith in statistics! Even entering best-guesses into such a tool has to be better than defaulting to a ‘magic number’, doesn’t it?

Psychologists Amos Tversky and Daniel Kahneman would have had a great deal to say about the spell cast by 'magic' numbers. They illustrate brilliantly how our behaviour is driven by psychological heuristics and biases, powerful social norms, and a desire to avoid additional work! Yet it is so tempting to uphold the orthodoxy, even once we know how to make the improvement... but I am resolved at least to experiment a bit on my clients, and see what happens when I advocate n=83, rather than n=100!

John Aitchison, Managing Director, First Line Research
01904 799550


  Magic Numbers
PDF File: 141.1 KB

4th August 2015


  Magic Numbers
PDF File: 141.1 KB


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First Line Research

+44 (0)1904 799550

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11 Carr Lane
YO26 5HT
United Kingdom

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