On Sun, Feb 22, 2009 at 5:47 AM, LuKreme <[email protected]> wrote:
> So, I am 95% certain that the true probability is in the range of
> 16.72% to 35.77% or so.  So, my 'sense' that 19/78 is pretty close to
> 25% is pretty much shit.



The spread isn't that bad. If your suspicion is correct (and it might
well be) that the actual "rate" is 1 in 4. This test tells you that
both "1 in 5" and "1 in 3" must be close to being outliers (given a
normal distribution about your value of 19/78).

If you want to ask the question "how sure am I that the rate is 1/4",
have the test repeated a couple of times (with n≥60), and use
regression analysis to compare 4 fits of y=mx+c for all populations

1. best fit
2. y=3x
3. y=4x
4. y=5x

where:

y= number of observations
x= sum of successful outcomes
m= "1/success rate"
c= 0 (assumption - but you could, for extra robustness, leave this
open in the best fit to test the strength of the assumption that c=0)

If you find an insignificant likelihood that the value of m in the
best fit is significantly different from 4, but a significant
likelihood that m  (best fit) is significantly less than 5, and more
than 3, then you'd have what I'd call a useful answer.
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