I got up this morning, January 21st, 2012, looked outside, and saw RAIN!
This is what our windows looked like this morning...rain-streaked:
That's not all that strange for a lot of places...except that I live in Rexburg, Idaho, a place not known for rainy winter days. Here, it snows!
But you wouldn't know it looking outside lately. And if you look closely you can see patches here and there where the grass is actually greening up a bit!
If you are like me you have wondered about this winter. It's felt downright weird! At least it's felt warmer than usual to me.
Normally by this time of year we have mounds of snow all over the place - by our driveways, along the roads, and in huge piles in parking lots. In fact, most years the city has to truck the stuff out and dump it someplace, but not this year. To me it feels like March instead of the middle of January!
As I was pondering on this I found myself wondering if it really is warmer than usual this winter, or if it just feels that way because there's no snow on the ground?
Hm...how can I get to the bottom of this thorny question? Ah! Data and statistics...of course! (Being a scientist, I love data and statistics.)
A question like this is, as I teach my science foundations students, an objective one (i.e., one that can be answered conclusively once we get the right kind of data). Luckily someone has already collected all of the data I need. Thanks National Weather Service (NWS)!
Without dragging you through all of the statistical hullabaloo, here's how I answered my question.
I went to Weather.com (which, I understand gets its data from the NWS) and pulled up Rexburg, Idaho. I went to the monthly data and looked at monthly historical averages. The historical average daily high temperature for Rexburg in both December and January is 29oF, and the historical average low temperature for both months is 13oF (that's statistically handy!).
I then jotted down the observed daily high and observed daily low temps from 12/21/11 through 1/20/12 and used Excel (Microsoft Office) to calculate the observed average daily high temp and the observed average daily low temp, and the standard deviations for each (FYI, the standard deviation shows how much variability there is in a set of data).
Here's how the data stacked up:
The historical average high temp was 29oF and the observed average daily high temp was 33.2oF. The historical average low temp was 13oF, and the observed average daily low temp was 15.4oF.
(The raw data are included at the end of this posting for your viewing pleasure :-D)
OK, the average high and the average low were both higher than their corresponding historical averages, but were they different enough to say that there is a significant difference? This is where statistics helps out.
Luckily there is a statistical test that lets us compare the average of a set of observations (i.e., our sample mean) to a known average (our historical mean). It's called a Z-test.
To make a long statistical story short and non-statistical, the bottom line is that the results of the Z-test showed that we can be 99% confident in saying that the observed daily high temps in Rexburg, Idaho, are significantly higher than the historical average.
On the other hand, the Z-test for low temps showed that there is not a significant difference between the observed and historical average daily low temps.
What does this mean?
- It means that our high temperatures so far this winter have been significantly warmer than our historical average high temperatures. So if it's felt warmer out there to you than normal there's a good reason for that.
- As far as low temps go, though, if you are out and about in the early morning and it's felt "bugger cold" to you, that's because our low temps are not significantly different than our historical winter low temps.
So for now, ENJOY!
(Data used in this analysis, courtesy of Weather.com)
Temps at Rexburg, Idaho, 12/21/11 - 1/20/12
|Daily Hi||Daily Low|
(Originally posted 1-12-2012)