David – I love the idea of analyzing a whole set of thresholds. I actually have a clever chart for just that in mind.

Dad – PESCI is good, although I do like Uncle Tim’s suggestion better. As for the sliding window analysis, I think it would be interesting to see if the allele comes up. 3 data points at a time is tough, and it’s a rough estimate of actual groundhogs. When did they stop the tradition of eating the groundhog? Anyway, I do have some ideas on how to analyze this – stay tuned.

Uncle Tim – I totally agree with the socio-political pressure. And the mentions is definitely a factor. I think the movie ought to be considered, too. For example, I’m pretty sure Phil has become more optimistic since the movie. I also have some ideas on clever data sets to corroborate this, so again – stay tuned.

1. I’m not enthusiastic about either AMPW or PEScI. Perhaps Phil’s Historic Indication of winter Longevity (PHIL)?

2. While Phil himself is probably immune from external influences, I think it must be recognized that his handlers are subject to a variety of socio-political pressures – and the world only hears what the handlers have to say, not Phil himself. Thus it would be interesting to see if there’s a correlation of the accuracy of the prediction announced with, for example:
a) the severity of the winter to that point (Are the handlers seeking popularity in a year when the public is especially tired of winter?)
b) the popularity of Punxsutawney Phil (Are the handlers feeling a need for an overall kick-start to the publicity machine?) Popularity might be measured by number of newspaper mentions the preceding year.

3. Once one accepts the fact that the handlers may not be entirely reliable, the whole physics of “seeing one’s shadow” comes into question. See, for example, recent publications of the American Nuclear Society at http://ansnuclearcafe.org/2011/02/02/schrodinger%E2%80%99s-groundhog/

Thank you for a thought-provoking blog entry.

1. Groundhogs are not rodents but members of the marmot family.
2. Andy’s Measure of Pennsylvania Winterliness (AMPW) is not easy to spell or say. Also, the use of the author’s name as part of the parameter is overly casual. I recommend changing this to Pennsylvania Early Spring Index (PESI), pronounced PESCI, not to be a wise guy.
3. Although it is often argued otherwise, I have long suspected that “Punxsutawney Phil” is not a single groundhog but an hereditary title like Pharaoh or Czar or Mayor of Chicago. Could the data be broken down in the a sliding window of, say, three years to see if certain members of the lineage have the prognostication allele and others do not?
4. A reference to David Mukai’s ice-breaking work on the effects of extreme cold on metals should be included.

Otherwise, this is a very interesting paper.

1. A hypothesis test of mean(Feb) > mean(March) with the alternate being the opposite. I would use permutation tests. I may run this.

2. A regression of temperature vs. time and finding the time where temp > critical value (in your case, 0C). You then can clearly test “x more weeks of winter” in this case.

You would have to use some sort of super smoother regression? I imagine that if you took the lower bound of a 95% CI of something like this, you could determine the earliest non-freezing date for planting vegetables.