So today, put on your diagnostician’s cap and look at the four relationships I show you here. To keep you from guessing, I’ve hidden the labels for the two variables, so you’ll be looking at Y1 and X1, Y2 and X2, Y3 and X3, and so on. Here’s the DATA step and PROC REG code to generate the output.

	DATA Anscombe;
	INPUT X1 Y1 X2 Y2 X3 Y3 X4 Y4;
	Lines;
	10  8.04  10  9.14  10  7.46  8  6.58
	8  6.95  8  8.14  8  6.77  8  5.76
	13  7.58  13  8.74  13  12.74  8  7.71
	9  8.81  9  8.77  9  7.11  8  8.84
	11  8.33  11  9.26  11  7.81  8  8.47
	14  9.96  14  8.1  14  8.84  8  7.04
	6  7.24  6  6.13  6  6.08  8  5.25
	4  4.26  4  3.1  4  5.39  19  12.5
	12  10.84  12  9.13  12  8.15  8  5.56
	7  4.82  7  7.26  7  6.42  8  7.91
	5  5.68  5  4.74  5  5.73  8  6.89 
	;
	RUN;                                                                                                                                    

	proc reg;
	model Y1=X1;
	model Y2=X2;
	model Y3=X3;
	model Y4=X4;
	run; quit;

The PROC REG command fits the least-squares line to each set, giving me the equation of fit and all the statistics you could want. Click on any report or picture to see it in larger size.

Here’s Y1 vs X1:

I highlighted some typical statistics that statisticians might use in discussing how well this line fits. Circles in the picture show the equation of the line (essentially y=3 + ½x), the R²(≅ 0.666), and the F-statistic (≅ 0.022). If you don’t know what these statistics are, bear with me. You’ll still get the joke.

Here’s Y2 by X2. Check the labels if you don’t believe me. :

Here’s Y3 vs X3.

And Y4 by X4.

You should have noticed that all the statistics are identical. The line of best fit is pretty much y = 3 + ½x. And getting all those statistics to be the same, well, that’s something, right ?

Here’s the playing-doctor part. Consider the fact that you’ve got four patients (graphs) exhibiting identical symptoms. What can you tell me about the underlying causes?

It turns out, not much. I may be the master of reading regression output, but there are some things that absolutely require a graph.

I can add the following to my existing SAS code:

	proc sgscatter ;
	plot Y1*X1 Y2*X2 Y3*X3 Y4*X4 /reg;
	run;

Here are the four graphs, with their data points .

1. The first graph is exactly what you want to see in a regression. Points are reasonably dispersed around the line of best fit.
2. The second graph is clearly not a linear relationship. If I wanted to show off, I’d say that you could fit a second-degree polynomial, a parabola, a conic section, to this data. But I don’t want to show off, just say that if your data isn’t linear, you can’t fit a line to it. Either make the original data linear (it’s not cheating, really) or use another kind of model.
3. The third graph shows what happens when one point is an outlier.The single point is essentially pulling the least squares line upward. I would check that data point, since anyone can have a bad day when transcribing data.
4. The fourth graph is an even more extreme case of the third one.All the points line up along the vertical line x = 8. Except one. And it completely determines the equation of the line. Move it anywhere, and the least-squares line follows.

An even better solution is to turn ODS graphics on at the start of your session:

	ods graphics on;

and let SAS give you pretty and appropriate graphics without you having to worry about them.

Data is from Anscombe, F.J. (1973) American Statistician 27, 17-21.

I spent some time this weekend with an old friend from one of those jobs playing Rock Band. For the uninitiated, the game involves staring at a TV screen with a plastic guitar “controller” around your neck, trying to push colored buttons in sync with the little colored chiclets that scroll down the screen, all 3-D-like, in tune with a rock-and-roll song that blasts in the background. After a brief eight to ten hours of this, pizza and adult beverages get involved as you contentedly congratulate yourself on your musical ability.

But I’ve been playing Rock Band guitar for many years, predating this game by more than a decade.

(Warning : Links from song names open in iTunes so you can preview them)

What I mean by that, of course, is that I can play guitar and I cannot read music. Cartman (“Southpark”) may be correct when he says “playing real instruments is for old people,” but it’s more exciting and quite satisfying. Especially when you’re still single — you may not be a musician, but what the heck else do you have to do.

Rock Band partitions the complexity of its songs into “Easy”, “Medium”, “Hard”, and “Expert.” My Classic equivalents are:

Easy

Every book store has chord-based versions of popular music. Sort of an all-in-one keyboard-chord combo special, it’s something you can strum along to while asking your friends “Don’t you recognize it ? It’s Van Halen”. Here I show said simplification for 1984‘s “Jump”. But you get past this kind of thing pretty quickly, unless singing “She’ll be Comin’ ‘Round the Mountain” for and afternoon appeals to you.

Medium

It’s a fact : guitar shops filled with pasty-skinned people in black are actually pretty cool places. Whilst in college, I stumbled into one where I discovered the miracle of Guitar for the Practicing Musician, a magazine that introduced me to tablature. Here’s my very first, impressively marked “$15 worth of guitar and bass transcriptions.”

Tablature is Rock Band for the 1980′s. Sheet upon sheet of music, showing you where to place your fingers, how to execute a palm mute, hammering on, pulling off, I mean the works. You’re at medium level when you can flawlessly Travis-pick your way through “Dust in the Wind” with a straight face.

Hard

I used to tune other people’s guitars for them, since I apparently had a good ear for that kind of thing. Fear not, though, as there are bunches of baubles that will bring you to perfect EADGBE every time. I think my iPhone will even tune a guitar these days.

EADGBE, the notes that sounds on non-fretted (“open”) strings, comes from the Spanish influence on our modern guitar. It never occurred to me until many years into my playing that this tuning wasn’t handed down from on high. In fact, many players don’t use this tuning at all, or at least deviate from it regularly.

The most elementary non-standard tuning arises wen you lower the lowest E-string down to a D. That so-called “Dropped-D” tuning is everywhere. “Embryonic Journey” (Jefferson Airplane), “Higher” (Creed), and my favorite, “Midsummer’s Daydream” by Triumph are good examples of the fullness that comes from this simple tuning change.

So once you can play a de-tuned guitar, you’re at the Hard level. Check out “Little Martha” by the Allman Brothers : tuned so that the strings play an E major chord when they’re open. Or any of a thousand Rolling Stones songs (“Honky Tonk Women”, “Start Me Up”). Not that I remember hearing any of *them* on the radio.

Expert

Now, produce something. Reading tablature is passé; writing your own is hep. I figured I hit Expert level in Rock Band Classic when I wrote the tablature for the acoustic version of “Big Love” by Fleetwood Mac, off their 1996 (almost-)unplugged The Dance album. Capoed at the 5t fret, Travis picked, and fast as lightning :

Unfortunately, I’ve probably forgotten more than I remember. And I’m spending my practice time tethered to a Wii.

It’s boring. It’s black and white. It’s important.

The graph shows the year that each country granted complete ballot access to women. That means that they could vote on every level (local, state, federal) and they could run for any of those offices, too.

It should be a little startling how late these dates are. The 19th amendment to the U.S. constitution didn’t pass until 1920, and then only after failed votes in the U.S. House and Senate.

There are clusters after the two world wars : lots of countries came after the Great War (U.S., Canada, Germany) and many others after the Second World War (France, Italy, Belgium). None without a life-and-death struggle. Life and death — a little heavy handed, no ?

No. Here’s a magazine from 1913, from France. Fantasio was a satirical, humorist, political magazine that existed in what would be the golden age of print journalism. Some of its images are so completely NSFW that I can’t post them. Here, though, is an article showing then-President Poincaré after he was “taken hostage” by the suffragettes (or suffragists, depending on your particular definition) during a visit to London. Remember : in neither country, nor in the U.S., could women vote in general. Click on the picture to download a PDF of the file.

Here you have the most powerful man in the free world prisonnier des suffragettes. A little farther along you see that only his diplomacy and skill saved the day, after he purposely waved off police protection. “But Monsieur Poincaré is an homme d’esprit. Instead of opposing at all, he welcomed the women with words of welcome.”

Further: “The response was made with such smiling good humor, unbridled energy and cordiality, that the suffragettes, now disarmed, abandoned the idea of going any further…”

Note the part that I’m not quoting, regarding the terrible exploit de miss Davison. When first assigned this reading, I passed by that little phrase with reckless abandon, concentrating more on sorting out the verb forms and idioms of the article. Now that I’ve pointed it out to you, do you know who she was, this miss Davison? Neither did I.

Emily Davison was a leader of the suffragette movement from early on. Her Wikipedia page shows that she allied herself with some of the more militant aspects of the movement, violently attacking the British Chancellor of the Eschecquer (“Secretary of the Treasury” when translated to American) and his home, hiding in a parliament cupboard (“closet”), and of course, spending time in jail. There, she continued all out in her protests, including throwing herself off a staircase and going on a hunger strike that resulted in her being force-fed. I can only imagine what that little slice of heaven was like in the Dickensian-named Strtangeways Prison.

June 4, 1913, Epsom Derby. Think of the race scene in My Fair Lady. The horses neared Tattenham Corner, a dangerous spot for horses and jockeys alike, and the field began to thin out. Anmer, the horse owned by His Majesty George V was in back of field, close up to Nimbus, owned by a Frenchman.

For reasons still unclear, Emily Davison stepped out of the crowd at exactly the moment of Anmer’s passing, probably to attach a women’s movement banner onto the king’s horse as it passed. Nimbus swerved, but the King’s horse could not. Miss Davison was hit and knocked unconscious.

It’s not a difficult story to tell, but luckily, I don’t have to. Watch it yourself.

She dies four days later.

That’s why you should care about my graph. The universal right to vote is both recent and palpable. Don’t forget that on November 4th, regardless of who you support.

For those that are interested, I made this entry using a JSL script (also available at the JMP blog), using my Macintosh, JMP 8, and the Mac-only software Screenflow.

Alan Rickman puckishly plays Spurrier, and at the moment of revelation, I wondered: How did he score the ratings from the testers? In the film, it looks like he did a tiny bit of arithmetic on the back of one of the scoring cards. Turns out he just averaged the score of each judge, a statistically meaningless thing to do. (He later acknowledged this publicly.)

So my question is: If a more correct scoring method were used, would California still come out on top? I’ll use JMP to analyze this tasting survey to see which wines really rate. I’ll even examine the tasters themselves.

First, a quick example of why averaging is not allowed.

Apparently, the three wines are tied for popularity. Look closer: Judge 1 prefers wine 1. Judge 3 really prefers wine 1. Judge 2 prefers wine 2. With two first-place wins, we should crown wine 1 the winner.

Averaging doesn’t take into account the fact that each judge operates using his or her own internal scale. We don’t know if Judge 2′s 6-rating is the same as Judge 3′s. Further, we don’t know what a 1-point difference means for each judge. And on and on. This is why most events that are scored by multiple judges (Figure Skating, for example, or ratings from consumer magazines) use ranks (1st, 2nd, 3rd) rather than raw scores.

So I managed to find the scores for the two events^{[reds][whites]}. Click to see larger views.

They’re comparing California Cabernet Sauvignon against French Bordeaux, and California Chardonnay against French Burgandy. Not exactly the same, but close enough: two wines that are predominantly one (matching) grape.

Here you can see a graph of the scores from the two flights : red, then white.Click each to view a larger graph.

A couple of things to note: Stag’s Leap and Chateau Montelena, represented by red circles on each of these graphs, bounce around clearly on top. Both of these are California wines (the Chardonnay being the subject of the aforementioned movie). Also note the dismal rating of David Bruce (Regular) Chardonnay, which is consistently rated poorly and in fact given a zero by Pierre Brejoux.

Now, to use JMP for a legitimate scoring. The Distribution platform has a command to Save > Ranks averaged, which converts each score to a rank from lowest to highest. Since there are ten wines, these will be numbers from 1 to 10. Note that this is backward for our scale : higher numbers are better. So, I simply subtract each number from 11 to convert it to a rating on a scale we can use. Again, click the image to see a larger version.

Now we’ve got something really useful: ranked scores that account for ties. The total of these ranked scores can now be interpreted. If a wine were so swimmingly, sportingly good and may I please have some more, if all the tasters rated it as perfect, the total ranking for eleven judges is 11 : eleven #1 ratings. If, on the other hand, the wine is pure plonk^[*], vin aigre^[**], it would be tenth on everyone’s list and thus its total ranking would be 10 × 11 =110. The inverted nature of this scale, where higher numbers are worse grades, is the source of the traditional title Points Against. This is a more appropriate measure for the rankings, and far superior to Spurrier’s original.

So how do the wines do on the new scale? First, the scores for the Reds:

1. Stag’s Leap Wine Cellars	1973	USA	41
2. Château Montrose	1970	France	41.5
3. Château Mouton-Rothschild	1970	France	43
4. Château Haut-Brion	1970	France	49
5. Ridge Vineyards Monte Bello	1971	USA	55
6. Heitz Wine Cellars Martha’s Vineyard	1970	USA	70
7. Château Leoville-Las-Cases	1971	France	72.5
8. Freemark Abbey Winery	1969	USA	76
9. Mayacamas Vineyards	1971	USA	77.5
10. Clos du Val Winery	1972	USA	77.5

And the whites:

JMP 8 provides a neat-o visualization of these scores, a Cell Plot. Here they are for the reds and the whites.

In the rightmost column, you see Points Against ranked in ascending order (so the best wine is on top). This graph lets you see how each taster rated each wine, and how that agrees with the Points Against score.

Finally, JMP lets me calculate a reliability measurement. Essentially, this is a measure of internal consistency that asks if these expert wine raters seem to be in agreement. The scale is from zero to one, with one being perfect. I’d say anything around 0.7–0.8 is a reasonable score to say the raters are consistent. The sample size is a little small, but still, these numbers are encouraging.

Summation? The USA still has the highest-ranked wines. Repeated tastings over the past 30 years have confirmed these results.

If you’re interested in this subject, maybe wanting even more statistical analyses, have a look at the wikipedia page, and any of the mountain of reports at liquidasset.com. Chateau Montelena has some press clippings from the time, and Amazon has the Paperback edition of George Taber’s book.

(Click to see a larger graph)

One thing to notice is the scale : 0 is the darkest blue, up to bright red being the top ($150 billion). The Middle-Class Tax Credit is so large that little comes close to it. The Medicaid to States and State Fiscal Relief sections are in the middle, with blue as almost everything else.

I sort of overloaded this graph, with size and color showing the same thing ($US).

As a less-exciting-yet-more-readable graph, I present what is known as a Multi-Var graph or Variability Chart. It shows the details of the spending much better.

I was recently reminded that “far away” is contextual, and has changed somewhat over time. Two stories, one in last week’s News and Observer, the other written in 1829 [FR (HTML) | EN(PDF)].

The News and observer story tells of a Hooverville that exists in the woods off of Poole Road in Raleigh. It seems so distant to me — a woods deep enough to hide a rather large camp of people. Yet it’s practically in my back yard : one town over. At first blush, I thought I wouldn’t have much in common with these men, but the more I think of it, the closer I get. Said another way : I don’t have a lot of money in the bank. I have zero investments. I’m unmarried. There aren’t too many steps between me, the homeowner, to me SDF (sans domicile fixé, the French classification for those we would call “homeless”)

Prosper Merimée was a writer straight out of the late 18th / early 19th century. All the world was romanticism — Ô, lac! rochers muets ! forêt obscure ! — yet he wanted to leave behind the fjord-pining and try to imbue his stories with a little realism.

Mateo Falcone is one of his earlier works (he’s remembered for writing Carmen, later made into an opera) and it is remarkable on several levels. It occurs in a place that, to modern French readers, is really close : the island of Corsica. Yet Merimée describes it as a thick, impenetrable wooded island (a mâquis), full of criminals and ne’er do wells who survive off the land, using their wits and their rifles.

If you have killed a man, go into the mâquis of Porto-Vecchio. With a good gun and plenty of powder and balls, you can live there in safety. Do not forget a brown cloak furnished with a hood, which will serve you as both cover an mattress. the shepherds will give you chestnuts, milk, and cheese, and you will have nothing to fear from justice nor the relatives of the dead except when it is necessary for you to descend to the city to replenish your ammunition.

Of course Merimée had never been to Corsica, so this was all either pure fiction, or the best that he could pull from traveler’s guides and newspapers like the N&O. Realism to him was just a real-sounding situation that may or may not be reality. But even after nearly 200 years, Merimée could be researching from our contemporary local story:

It’s a comfortable life once you get used to rain-wet hair and achy bones, they explain. But nobody bothers them, not even the police.

Note that it’s not just a mystery-flavored DumDum, but that it is Artificial MYSTERY FLAVOR™.

I tasted it. I didn’t know “Blue Suede” was a flavor.

Turns out, according to two academics on the NYT Op-Ed page, there is little scientific proof that this reduces energy consumption. It also turns out that this practice could be wasteful, a bit annoying, and a lot of people want to get rid of it.
A study in Indiana, a state that recently started DST, showed an overall increase of 1 percent in residential electricity use with occasional increases of 2 to 4 percent in late spring and early fall. So much for conserving energy.

Get rid of Daylight Savings Time !