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    Mothers attempting to balance parenthood and academics.


Math Geek Mom: Shadows and Snow

Groundhogs and snow.

February 4, 2016

It is said that two statisticians went deer hunting and came across a large buck facing them in a meadow. The both stopped short and looked straight at the creature. One statistician shot at the deer, with the bullet landing one foot to the right of the animal. The other statistician shot at the deer, and his bullet landed one foot to the left of it. When they both realized what they had done, they looked at each other and said, in unison, “bulls eye!”

Once again, I am reminded that my husband tells me that I should not plan to give up my day job to take on the career of stand-up comic. However, this statistics joke came to my mind this past week when I learned that two different groundhogs had two very different predictions for what the next few weeks have in store for us, and what weather we will be dealing with.

Tradition says that if a groundhog can see his shadow as the sun rises on February 2nd, a day that has come to be known as “Groundhog Day,” then there will be six more weeks of winter waiting for us. However, if he cannot see his shadow, then there will be an early spring. One detail that is never explained is just how we know what the groundhog actually sees. This reminds me of the issue in Economics of trying to compare satisfaction derived from consuming a good by two entirely different people. After all, we can’t really compare happiness between different people, and, luckily, really don’t have to, since market results can tell us all that we need to know. Some investigation into the groundhog issue taught me that all that really needs to happen for a prediction is for the groundhog to cast a shadow, and that what he actually sees is not the central issue.

Ignoring whether one can actually know what the groundhog sees, the prediction is straightforward, or so it seems. That, however, is not always exactly the case. This year, two different groundhogs gave very different predictions. The most famous groundhog, Punxsutawney Phil of Pennsylvania, did not see his shadow, predicting an early spring. That is fine with me, and I should have left it at that. However, in Ohio, Buckeye Chuck predicted more winter.

One possible explanation for this variance in this experimental data is that Pennsylvania can expect an early spring, while Ohio is stuck with a six more weeks of winter. Living in the middle of the snow-belt, I can believe that. We live close enough to Lake Erie to be tormented by the “Lake Effect,” a strange weather pattern that has the counterintuitive result of bringing more snow when it is warmer, as in the early winter, before the lake has frozen. When that is the case, cold air from Canada picks up the moisture from the lake and dumps it on us in the form of snow. This translates into more snow days for my daughter in the fall semester and in the end of winter in the spring semester. Alas, for those of us living in this part of Ohio, especially with a lake that is almost completely unfrozen at this time, dreams of an early spring are usually just that, dreams.

So which groundhog do we believe? The bottom line is that the worst prediction is that there will be six more weeks of winter, which, while not ideal, is bearable. I suppose we can again look to statistics, and decide that it is a “coin flip” as to what we will actually see. So, what will it be, heads (spring) or tails (more winter), readers?


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