This winter has been warmer than usual! And I'm not just saying that!

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?

1. 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.
2. 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.

The moral of the story is this: Enjoy the warmer than average days while they last...because you never know when the weather is going to change!  After all, all it would probably take to cover us in a mass of frigid Arctic air is for the jet stream to dip just a LITTLE farther south than where it's been hanging out.

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
21-Dec	28	14
22-Dec	20	-1
23-Dec	22	-4
24-Dec	24	-1
25-Dec	31	4
26-Dec	30	6
27-Dec	34	18
28-Dec	41	28
29-Dec	49	38
30-Dec	51	34
31-Dec	33	15
1-Jan	33	17
2-Jan	39	16
3-Jan	38	20
4-Jan	43	17
5-Jan	37	18
6-Jan	30	22
7-Jan	32	19
8-Jan	27	18
9-Jan	35	12
10-Jan	31	17
11-Jan	25	3
12-Jan	24	-1
13-Jan	30	5
14-Jan	38	11
15-Jan	44	24
16-Jan	24	12
17-Jan	24	8
18-Jan	34	21
19-Jan	36	33
20-Jan	41	34
Mean	33.161	15.387
Std Dev	7.789	11.023
Z-score	2.974	1.205

(Originally posted 1-12-2012)