On 10/03/2016 5:53 PM, Texler, Michael wrote:
Not actually true; the degree of difference between groups/cases/whatever that
you'll need to to get a statistically significant result (be it for p=.05 or
p=.01 or whatever) will depend on the sample size, and on the characteristics
of the sample and the population you're drawing the sample from. There is in
fact a whole sub-topic of stats that is about working out what size sample you
need for a given situation in order to be able to plausibly see any real
differences between groups, should there be a real difference to be found.
When comparing accident rates, you are not sampling per se, but estimating the
occurrence of an event in a selected population (i.e. descriptive statistics).
Also for 'rare' events such as accidents, estimating the mean rate and standard
deviations from year to year can show such variability that statistical testing
becomes problematic.
Yup, descriptive stats are definitely where one should start, on a
subject like this. But in your earlier post you also said "there often
needs to be an order of magnitude difference (i.e. a 10 tenfold increase
or decrease of an accident rate) to demonstrate statistical significance
at the 95% level". That's inferential statistics, not descriptive stats.
When you start talking about "statistical significance" it means running
actual statistical tests to *test* the significance. You can't tell just
from looking, as a rule. (At least, not unless it's *really* *really*
obvious...)
OK, you could sample the different accident rates annually for say 10 years (or
look at historical data) to estimate an average and median accident rate, as
well as estimate a standard deviation
Yup, that's descriptive stats again, which is more or less how we were
approaching the topic earlier in the discussion...
and then do comparative statistical testing.
...And there's the inferential stuff, where you get your sampling
issues, p values, statistical power and all that..
Even working which out which metric to use can be controversial, i.e. accident
rate per km? per hours flown? per number of flights?
Don't I know it! My PhD is on road safety. Let me count the ways that
people have assessed accident numbers/rates over the years.... *sigh*
You are talking about working out the power of a test. Working out statistical
power is, as you say, a whole field of applied maths that keeps statisticians
employed! ;-)
Accident rates may be approximated by Poisson distributions because of their
'rare' nature.
I've not seen them described that way in the road safety literature that
I'm familiar with. How would that work? If the number of accidents is on
the Y axis, what variable would the X axis have? If we go with road
accidents (my field of expertise) it can't be age/driving experience,
because the accident stats in NO way form a poisson distribution when
age/experience is your X-axis variable. (Actually, road prangs by
age/experience gives you more of a U-shaped curve.) Also, rate of
accidents (be they road prangs or glider prangs) aren't constant over
time (as required for a poisson distribution to be your distribution of
choice) - they vary by time of day, for fairly obvious reasons, as well
as other things (day of the week, long weekends, etc etc).
You appear to be approaching the issue from a rather different
statistical approach to the ones I'm familiar with. Could you spell out
your approach/methods in more detail? It's always interesting to hear
how folk in other fields approach problems I'm familiar with. :-)
Teal
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