I would like to bring some statistical rigor to this conversation.
Statistical methodology is at the base of most of the government
policy/regulatory rules covering everything from pesticide use, safe
levels of application and more.  For example, in the past, pesticide
testing on bees had a binary outcome from what I could tell (they
recorded bee kill, and used that to get an LD50).  However, with new
classes of pesticides, there may not be a binary outcome (the outcomes
could be: bee kill, perfect survival, epigenetic change, eg
http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0068191
).  It's very important we as beekeepers understand this statistical
paradigm well, as well as its implications for our bees and (for some
of us) your livelihoods.  Right now, the FDA has extremely rigorous
statistical methodology for approving drug use in humans (an area
known as Biostatistics).  But pesticide/foulbrood treatments/best
practices (like comb rotation) have varying levels of statistical
rigor behind their approval/use.


Specifically, the statistical rigor I wanted to discuss is the
question "is there a statistical difference in the population of
beekeepers and the population as a whole for phenotype/genotype foo".
Example: Is the allele frequency for color blindness in the population
of beekeepers significantly different than that of the population as a
whole?".  Replace color blindness with "left handedness" or even a
behavior (phenotype) like "keep checkbook balanced".

Since I'm probably boring the pants off all but a diehard few, here's
a quick synopsis of all the statistical issues I can think of here:

1) First, there is a philosophical distinction here regarding when you
ask the question.  If you ask this question before knowing anything
about the number of color blind individuals in beekeeping, then
everything is fine.  However, if you look at the data first (you
notice lots of people in the beekeeping community are color blind),
then want to test for it, you have a lot of biases to worry about.

2) Multiple testing:  In any statistical hypothesis test (eg is the
allele frequency in a subset of people different than the population
as a whole?), there is a formal statistical paradigm with lots of
baggage
http://en.wikipedia.org/wiki/Null_hypothesis

and there are different possible outcomes with different ways of being
right or wrong (Type I and Type II errors are the words statisticians
use to describe how you can be wrong)
http://en.wikipedia.org/wiki/Hypothesis_testing
http://en.wikipedia.org/wiki/Error_of_the_first_kind

Where am I going with this?  It turns out, that for any statistical
hypothesis test, there are false positives- we say that there is a
statistically significant difference when in fact there is not a
difference.  (example: If you want to test if a pair of dice is fair
(1 to 6 dots on each side; is the probability of rolling a 1 =
probability of rolling a 2 = ... = probablity of rolling a 6); then
you may perform an experiment like rolling each die 10 times.
However, even with a fair die, sometimes (albeit extremely rarely-
more on that later), you will roll 10 sixes in a row or some other
unusual outcome given that a die is fair.  But don't worry.  We
control this false positive rate (that's the alpha=.05 part that you
see in many scientific studies).

To bring this back to our discussion, if we look at the population of
beekeepers and there are a huge number of questions we ask about our
population, "is the percent of
color-blind/overweight/nearsighted/hair on 2nd knuckle/attached
earlobe bases/Ellis van-creveld syndrome/birth months significantly
different in the population of beekeepers", it turns out that the more
of these hypotheses we check, the more false positives we will find.
Because that is the structure of hypothesis testing.  The same issue
of finding false positives will occur with testing reasons for bee
kills.

This situation is an example of Multiple Hypothesis Testing aka
Multiple Comparisons.
http://en.wikipedia.org/wiki/Multiple_comparisons
It turns out that in order to control false positives in this case
(many hypothesis tests), we have to adjust our alpha, or do some other
modification to the statistical framework.  Commonly, things like
multiple testing corrections are done.  There are alternative criteria
like false discovery rates (which is not actually a hypothesis test)
that are also use in the literature.
http://en.wikipedia.org/wiki/False_discovery_rate

An advanced text that describes these distinctions and some new
approaches to data analysis in the last 20 years would be something
like:
http://www.amazon.com/Large-Scale-Inference-Estimation-Prediction-Mathematical/dp/110761967X/ref=sr_1_1?ie=UTF8&qid=1373723018&sr=8-1&keywords=brad+efron


3) Confounding
Suppose there is a significant difference in a phenotype between the
population of beekeepers and the population as a whole.  Just because
we are testing a hypothesis, it only means there is correlation, not
causation.  The most misleading situation occurs when there is
something called "confounding",
http://en.wikipedia.org/wiki/Confounding
specifically, you are testing a variable (population of beekeepers)
when there is really a very closely related (a correlated variable)
like (population of self starters who are outdoor enthusiasts ...)
that is providing the causation.  There is a separate discipline in
statistics for examining causation.  But it is (surprisingly) very
seldom used (structural equation modeling is the name in the
statistics literature; other literatures like economics use different
names).

Related Links:
http://en.wikipedia.org/wiki/Structural_equation_modeling
http://www.amazon.com/Causality-Reasoning-Inference-Judea-Pearl/dp/052189560X/ref=sr_1_1?ie=UTF8&qid=1373723650&sr=8-1&keywords=judea+pearl
http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation


I felt obligated to put this response out, but I don't think I've done
a great job of describing these issues in modern statistics to this
varied audience...  I'm happy to answer questions, help out, and if
anybody wants to set up a designed experiment, please let me know.
I'm happy to help out with real paper surveys (like putting together
online polls) or with design of experiments for actual beekeeping
applications, or with helping people understand exactly what was
tested, and its interpretation, in a journal article/experiment.

Best,
Blair


Note 1: Foo is computer science jargon for a placeholder.  In math,
people are fond of x, a and b.  The etymology of foo is ambiguous but
interesting, as you might expect
http://en.wikipedia.org/wiki/Foo

Note 2: Conflict of interest: I have informal relationships (I don't
get paid... yet)  with an insect contract research organization and a
major agribusiness company; I also don't have a formal affiliation
with an academic institution (this month anyway).  I just do the
beekeeping (10-20 hives) on the side for fun.

Note 3: Alleles are the versions of a gene

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