Sunday, October 1, 2017

Hot enough for ya?

This September in Oakland has been hot. Here are some ways to put it in perspective.

1. The average temperature was 78.3° F. This might not seem like much in Sacramento or San Diego, but that is the warmest average month not only this year so far, but the warmest since 2011, which is the arbitrary year when I started measuring things this way.

2. According to Weather Underground's daily average of the past fifteen years, September 2017 was 3.9° F. warmer than the average. 3.9° above the fifteen year benchmark is definitely warm, but it is by no means a record over the years I have been using to measure things this way. For example, the winter of 2015 was way above average, with January at 3.5° warmer, February at 5.1° warmer and March at 5.7° warmer. Still, 3.9° warmer than the benchmark is by no means an average month. In 2017 so far, September and May are tied for first with 3.9°.

3. September 1st and 2nd were both 101° F in Oakland. Again, it's a matter of perspective. In Sacramento, days over 100° are an inconvenience. In Oakland, two days in a row over 100° is a sign of the apocalypse.

We also have a statistical method to tell us if a month is unusually hot or not using t-scores, a relative of z-scores. The formula for the two is the same, the average times the square root of the number of days in the month divided by the month's standard deviation. (This formula is almost what we want, and it is exactly correct if mux = 0.) Using this test data, we can get a p-value, the beloved precious of scientific researchers everywhere. If the p-value is less than .05, this is usually a sign your paper can possibly be published.

Using this method, September 2017 was not unusually above the average of the last fifteen Septembers. (Note: May 2017 had the same raw score of 3.9° above average and it produced a p-value high enough to let us reject the null hypothesis. May was unusually hot using this method, September, not so much.)

Why did September fail in rejecting the null hypothesis, which is to say it does not seem unusually warm using this test? The answer is in the standard deviation, a commonly used method to measure how spread out a data set is. If there isn't much deviation in a set, a 3.9° difference would definitely impress the t-score test. What happened is that September was warm in a very weird way, several days way warmer than average, but thirteen days out of thirty, it was actually slightly cooler than average. (By "way warmer", the early heat wave was 26° F. warmer than average for two days and there were five more days in September were the temperature was 10° warmer than average or more.) But in the middle of the month, there was a ten day "cool snap", when temperatures were cooler than average by -1° to -6°. These big swings meant for a higher standard deviation, the highest of the year at 9.384. In comparison, the month of May did let us reject the null hypothesis because the standard deviation was "only" 7.865, which is the second highest standard deviation of the year.

Okay, Matty Boy, what does this have to do with the price of tea in China? Well, if it isn't my old pal Hypothetical Question Asker! This is just an example of statistical methods sometimes producing confounding results. I have no philosophical qualms about the t-score test in general, though the arbitrary threshold of .05 to decide whether we accept or reject the null hypothesis is fairly coming under question these days in research circles. My other quibble about this work that I am doing is whether we should think of a month as a period of time that measures climate or if it should be still considered just weather. The method I hit upon earlier in September argues that climate should use time spans of a year. Shorter spans like season or half years might make sense, but my general feeling is a month is too short.

In any case, I saw some weird numbers and decided to write about 700 words about them.

Don't hate. This is how I roll.

Any questions?

(Seriously, the comments are perfect for questions.)


Abu Scooter said...

Thanks for these; I'm enjoying them. Heck, I even have questions this time.

With respect to temperatures in Oakland, what have the t-scores been for the last 12 months? 24? 60?

More to my point, do those scores tend to be higher in March and September than in other months? I'd expect to see more temperature variance in those months, since they coincide with the spring and fall equinoxes. Is that a valid hypothesis, or have I been out in the (Illinois) sun too long?

Matthew Hubbard said...

Hey, buddy! Nice to hear from you. Here are the numbers from 2015, 2016 and the current year to date

2015, Months that rejected the null hypothesis: Jan., Feb., Mar., Jul., Aug., Oct.

2016, Months that rejected the null hypothesis: Jan., Feb., Mar., Apr.,
Jun., Nov.

2017, Months that rejected the null hypothesis as of end of September: Mar., Apr., Jul.

High standard deviation months. (Arbitrary measure: s.d. > 6 is high)
2015: Apr., Sept.
2016: Apr., Jun., Sept.
2017, so far: May, Jun., Sept.

I can send you the Excel files if you want. Send me an email if interested.