DeKnow is correct in that researchers (whether beekeeper or academic) need
to establish variability for controls.
However, one can't generate a number for a large set of controls, then use
that to compare all other treatments - each control set has to be run in
tandem with the treatment(s) at the same locations, under the same
environmental conditions, etc.
Running a large number of controls against a single treatment doesn't
provide any gain of information that I can see - that's a rather costly test
with little new information to gain. Just go to the published literature,
you can dig out the variability numbers.
And again, DeKnow is correct - you need a sufficient number of reps so that
you exceed the noise in the controls. But, as Randy points out, that
number changes with the power of the test, the degree of change you wish to
discern. Its not a single number. The number of controls needed changes
with the question being asked.
The numbers I provided in my earlier post about variability in bee colony
metrics provide a reasonable starting point.
I think Randy will agree, if possible, as a general rule, I like to have
at l2 colonies or more for each treatment level (i.e., 12 colonies as a
control, 12 colonies for treatment 1, 12 for treatment 2, etc.) but that's often
too expensive. You surely can't afford this on the small grants available
from many non-profit and commodity funding groups.
Larry Atkins and the EPA Guidelines for pesticide registration published
years ago in the Federal Register recommend at least 3 colonies for each
level (control, treatment), although Larry confused within-hive stratification
with true replication.
For cage trials he recommended three groups of bees from a colony, from
each of three colonies (for a total of nine cages of bees) per control, per
treatment, etc. In reality, his replication number was 3 (three colonies),
not 9 as he thought. Larry did recognize that colonies vary in
susceptibility, probably partially genetic), so he wanted a minimum of three colonies
for each comparison. But, he was always interested in acute toxicity,
which doesn't require as many colonies as a sublethal trial to satisfy the
power (probability of detection of a difference) objectives of the test
(experiment).
Taking bees from three different parts of the colony makes some sense,
but those aren't true replicates. So, Larry thought he was recommending 9
reps, when in fact, he had 3 reps for each level (3 control, 3 treatment,
etc.).
That mistake has been promulgated by pesticide bioassay labs that use ONE
colony for label registration testing, taking multiple groups of bees from
the same colony. You can set up 1, 2, or 100 cages from a single colony,
and you still have an unreplicated experiment. In this case, the
subsamples are composed of partially related bees - they've all got the same
mother. True replicates have to be independent of each other. Family members
are not. For a true rep, you need other colonies, with other mothers.
Similarly, in a recent and highly discussed pesticide paper, the authors
confused number of bees in a cup (or cage) with replicates. They tested
hundreds of bees, but only had a few cages. In their stats they used sample
numbers of several hundred as the number of reps when calculating their
stats. The true sample number in terms of replicates was something like 2.
Now, when you calculate your stats, confusing several hundred bees in each
cup as the replicate, rather than the number of cups per treatment level the
mistake invalidates the whole study. Scientists and stats folks talk about
degrees of freedom. And that's usually calculated as n (number of samples
or reps minus 1). So, a number like 382 bees in a cup minus one is 381.
But if you've only two cups, then n-1 = 1. Or if 3 cups, its 3-1=2.
Now, plug 382 into the stats calculation for significance, and compare that
to the significance result using the true value that is 1 or 2, and the
results dramatically change. Somehow, the reviewers missed the miscalculation.
In summary, Larry Atkin's minimum number of reps was three. I generally
shoot for at least 4-5 colonies, like 8-10, and prefer about 12 reps per
level for most testing. Again, there are options. One is to work with
smaller numbers of colonies, but then use other small sets at different times in
the season - you must use different colonies though. Otherwise, you've a
repeated measures test.
Finally, with respect to Randy's long-term study - he's going to be doing a
repeated measures trial, and he is likely to need many more colonies than
anticipated. Sorry Randy, I've run tests for as long as 24 months, and I
know the outcome.
Once you launch a long-term study, you need to step back from manipulating
colonies. Lose a queen, can you re-queen and continue? Probably not.
Short on food - do you feed - ONLY if you feed every colony, regardless of
whether they need food or not.
The trick with the long-term study is having enough colonies still alive at
the far end of the trial to support the stats. And, you want to avoid any
beekeeper inputs that can affect the outcome. Move some, move them all.
Medicate, mediate them all. But, you can't make heroic efforts to save a
dying colony.
So, figure your anticipated over-wintering(s) loss, double that, and
calculate how many colonies you need to get to the end of the experiment and
still be able to do stats that can show significance. I know Randy knows how
to calculate power curves :).
Jerry
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