Groundhog Day 2017: Long Winter Ahead?

February 2, 2017. Sunrise in Punxsutawney, PA.

The big prediction is in.

Punxsutawney Phil—the star of the most popular annual Groundhog Day event—saw his own shadow. According to tradition, this means that there will be 6 more weeks of Winter.

 

But what do we really know? How likely is this prediction?

As a much newer annual tradition, the Cangrade Blog brings you a statistical analysis of Groundhog Day predictions (compared against weather data collected by the National Climactic Data Center).

 

Groundhog Day predictions

This year is the biggest analysis ever.

Our dataset has 189 predictions over the last 9 years, from 49 different Groundhog Day events around the country.

And of course, we will also look separately at the decades-long history of the most popular Groundhog Day celebration in Punxsutawney, PA.

 

Since our analysis last year, Spring came early, with some of the warmest temperatures on record. Groundhog Day last year was mostly overcast and many of the predictions (including Punxsutawney Phil) correctly called for an early Spring. How does this change things?

Here are the data. Correct predictions are highlighted in green.

 

  • Punxsutawney Phil made correct predictions 52% of the time.
  • Probability that this pattern is just random chance (Fisher’s Exact Test, 2-tailed): 37%.
  • This pattern of data would not be considered “statistically significant” because the probability that it’s due to random chance is greater than 5%.

 

  • Overall, Groundhog Day predictions have been correct 58% of the time.
  • Probability that this pattern is just random chance (Fisher’s Exact Test, 2-tailed): 7%.
  • This pattern of data would not be considered “statistically significant” but it’s fairly close. Some might call it “marginally significant.”

 

Punxsutawney Phil’s prediction

What’s the probability that this prediction for 2017 will come true?

We can find out using Bayes’ theorem. We need three relevant pieces of information.

  • p(Shadow|Regular Winter) The probability that Punxsutawney Phil sees his shadow in years that also have a regular Winter: 88%
  • p(Regular Winter) The overall probability of a regular Winter between 1988-2016: 28%
  • p(Shadow) The overall probability that Punxsutawney Phil sees his shadow: 69%

 

Punxsutawney Phil predicted 6 more weeks of Winter. The probability of this happening:

p(Regular Winter|Shadow) = p(Shadow|Regular Winter) × p(Regular Winter) ÷ p(Shadow)

88% × 28% ÷ 69% = 36%

 

Groundhog Day “big data” predictions

The groundhogs weren’t unanimous this year. Some even predicted an early Spring.

What are the chances of other Groundhog Day predictions coming true?

For groundhogs that agreed with Phil and predicted a regular Winter:

  • p(Shadow|Regular Winter) The probability that groundhogs see a shadow in years that also have a regular Winter: 49%
  • p(Regular Winter) The overall probability of a regular Winter between 2008-2016: 41%
  • p(Shadow) The overall probability that groundhogs see a shadow: 41%

 

The probability of a regular Winter prediction coming true:

p(Regular Winter|Shadow) = p(Shadow|Regular Winter) × p(Regular Winter) ÷ p(Shadow)

49% × 41% ÷ 41% = 49%

 

On the other hand, for groundhogs that predicted an early Spring:

  • p(No Shadow|Early Spring) The probability that groundhogs don’t see a shadow in years that also have an early Spring: 65%
  • p(Early Spring) The overall probability of an early Spring between 2008-2016: 59%
  • p(No Shadow) The overall probability that groundhogs don’t see a shadow: 59%

 

The probability of an early Spring prediction coming true:

p(Early Spring|Shadow) = p(Shadow|Early Spring) × p(Early Spring) ÷ p(No Shadow)

65% × 59% ÷ 59% = 65%

 

Maybe there is something to it

The groundhogs make the correct prediction more than half the time.

It’s slightly better than a coin flip!

And the overall data, collected across many Groundhog Day events, is on the verge of statistical significance (but not quite).

 

Much like we observed last year, Groundhog Day predictions are slightly more likely to happen than the overall probability of that event happening.

 

Will this really be a long Winter? All we can do now is wait and see.

 

 

Image credits: Anthony Quintano, shannonpatrick17

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