> I'm a believer, but I'm beginning to question
> what a wash is actually telling me in terms
> of total infestation - all those mites I see late
> season may be from that very colony I'm testing.
This may be an inevitable result of trying to misuse a sampling/counting method as a "screening tool". The sampling method clearly has a higher error rate than the "treatment threshold", and we want to detect mites when numbers are low, colony-wide.
This problem is succinctly stated in very stark terms below:
>> In May, my threshold for treating is 1 mite in an alcohol wash of 300 bees.
This measurement is doomed to never be trustworthy for this metric.
The low number of "one mite" is clearly within the margin of error of the test, so a reading of "zero mites" means the same thing as a reading of "one mite" - the result has an error rate of at least "plus or minus one bee", (+/- one third of one percent) I likely has a margin of error of SEVERAL percent. So, in a 300-bee sample, with a margin of error of 1%, you can have 3 infested bees (at least 3 mites) or zero mites and you are still within that 1% margin of error.
And, to make matters worse, what's the presumed rate of prevalence of the varroa here? Mites should be a "rare event" in a healthy colony. If we have 10,000 nurse bees, and a sample of 300 of them yields one mite (meaning only one bee infested with mites), this could indicate 1 mite per 10,000 bees, or 1 mite per 300 bees, which is 33 mites per 10,000 bees. Those are two very different measurements when talking about varroa.
So, shaking a jar is a good way to count bees with mites when there are many infested, but it is a lousy screening tool. Logistic Regression isn't going to help much, as it suffers from the same problem.
To put this in easier to visualize terms, a sample size of "300" would be a fine sample for a survey of beekeepers on a non-rare event, such as those liking both mustard and relish on their hot dog vs mustard only. But we aren’t looking for that, we are trying to detect a very small number of mites when the number is still very small, so we'd have to change the beekeeper survey question to "do you like pickled beets and onions on your hot dog?" Suddenly you can see that asking only 300 beekeepers of 10,000 might not reveal any who like picked beets and onions on their hot dogs, even when there are several who do. If there are 10 of 10,000 who like pickled beets and onions, we might need to question 300 never-questioned beekeepers 33 times (9900 beekeepers) before we encounter the first beekeeper who says "yes" to our question. 10/100000 vs 1/300.
This is a horrible way to screen for a pest or disease when it is rare. It means that treatment is being withheld until the infestation is much higher than one could detect via even a one-day drop test with a sticky board.
If anyone has seen a "statistical justification" for the 300-bee sample, I'd love to see the specifics.
Large numbers are very different from small ones - if an infinite number of beekeepers shot shotguns at an infinite number of road signs, they'd soon produce the complete works of Shakespeare, in braille.
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