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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?
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. flres.uk/samplecalc) 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
john@firstlineresearch.com
01904 799550
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Magic Numbers
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First Line Research
+44 (0)1904 799550
Address:
11 Carr Lane
YORK
YO26 5HT
United Kingdom
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