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> ----------------- Original message (ID=DF25310B) (134 lines)
------------------
> Date: Tue, 05 Mar 2002 12:37:34 -0500
> From: "Martin Damus" <[log in to unmask]>
> To: <[log in to unmask]>
> Subject: Re: A Question for the Statisticians
>
> I may be way off base and I stand to be corrected, but:
>
> Let's assume all pests are randomly distributed across all
> individuals, across
> all yards, across all hives.
>
> Then, 35 hives from ten yards were sampled for five bees =
> 1750 bees tested.
>
> Applying the Poisson probability formula, you get the
> following probabilities:
>
> True infection rate      Prob. of finding zero infected bees
> in your sample
> ----------------------------
> --------------------------------------------------
> 1 in 50000                    99.9%
> 1 in 10000                    84.5%
> 1 in 5000                      70.0%
> 1 in 1000                      17.4%
> 1 in 750                        10.0%
> 1 in 584                        5.0%
> 1 in 500                        3.0%
> 1 in 100                        0.00%
>
> the simplified formula is:
>
> Probability of finding none infected = 1 / (2.71828 x
> rateofinfection x numbersampled).  Note that this is
> independent of the total bee population size.
>
> As a statistician (if I were one), I would only be happy if
> the chance of
> finding no infected bees were less than 5%, which by rearranging the
> formula and calculating for infection rate you would get, with your
> sample size, if the infection rate were one in every 584 bees.
>
> So, to me you can be confident that your rate of infection is
> less than
> one bee in every 584.
>
> But, and this is probably a big but, infection rates are not
> always constant
> across hives, across yards, or across bees and any deviations
> from those
> assumptions means that more samples need to be taken.  How many more?
> I dunno.  You have taken 1750 already, which is actually a
> heckuvalot.
>
>  What others have mentioned is that it is better to take more
> samples from
> fewer hives (300 samples from 2 hives in your ten random
> yards, suggested one).  I am not sure why this should be,
> although in the case just mentioned that would also increase
> your sampling effort and expense to 6000 bees,
> which would increase your confidence in the results simply by
> the increase in sample size.
>
> Hope this helps,
>
> Martin Damus