Thom Baguley wrote:
however, I think the
> defence of convenience samples can be stronger than this. Unless we
> have reason to believe that a sample is biased in such a way as to
> generate our pattern of results a convenience sample is just as good
> evidence as a (hypothetical) random sample.
This gets onto tricky philosophical ground. On the one hand, the
"argument from ignorance" ("if we don't have reason to believe
otherwise...") can be abused dreadfully. On the other hand it
underlies everything we do; it would seem to be perfectly rational to
start your car in the morning without looking under it on the grounds
that you don't have reason to believe that anybody wired a bomb to the
ignition.
Ideally I'd like positive reasons to believe that the sample WILL be
like the population to which inference is extended; but I'm not sure of
the extent to which this process can be made either formal or foolproof,
while still practical.
Random sampling manages "foolproof" but not "practical" in many
circumstances. I'm not sure to what extent it is formal, either; random
numbers work fine as abstract mathematical constructs but the
definitions don't tell you where in the real world to look for these
things.
Most so-called random numbers are pseudorandom and work just fine.
Whether mechanical methods like coin-tossing are truly random seems to
depend on your interpretation of quantum mechanics; again, if somebody
should come up with a souped-up hidden-variable theory that gets around
Bell's inequality next week, does statistical practice become invalid?
I think not.
Ultimately scientists still seem to need common sense.
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