The first half of my previous sentence is just as important
as the second, for the following reason: It could be that
tomorrow somebody will
a) tell us about Knarrenkopf's law or some other law that
I've never heard of;
b) provide solid evidence for the general validity of the
law; and
c) show that one of the two data sets is strongly inconsistent
with the law, while the other is consistent.
This has to be a law about human behavior, because general
statistical "tests of randomness" aren't going to cut it.
Given two data sets that are random or near-random, one of
them is always going to be "more" random according to any
such test. So if you choose based on such a criterion, you
will be wrong half the time.
So far the only general law of human behavior we've seen
asserts that people "religiously avoid" consecutive numbers
when cooking up numbers ... but this law is violated by both
data sets. So this leaves us worse off than before: We
don't know of any general laws that we trust. Furthermore
we have reason to distrust the next so-called law that
comes down the pike.
On the positive side, this supports my favorite hypothesis,
namely that somebody is running an experiment on us, to
measure how easy it is to get people to opine about stuff
they know nothing about ... and how easy it is to get
people to see patterns in random data.
Sqeee, squee, squee, I'm making a noise like a Guinea pig.
I reckon the most likely outcome is that the problem, as
posed, will remain unsolved, because the data sets are
just too small, and the students did too good a job of
cooking up their numbers. Failing that, I consider the
following two possibilities roughly equally likely:
*) Somebody will prove the "right" answer, based on
Knarrenkopf's law or some other approach not mentioned
heretofore; or
*) the "Math Prof" will come back and say sorry, we
"accidentally" got the wrong data, and both datasets
were generated by a rigorously random process.
Note that there could well be dozens or hundreds of laws
about human behavior that are not widely publicized, so
as to not provide a how-to manual for cheaters.