# Quantitative Reasoning MOOC Update

(Yeah, I finally used the ‘M’ word…)

As some of you know, I’ve been working the past three or four months on getting a MOOC on Quantitative Reasoning up and running for Spring 2013.  Jim and Tim and I are in discussions on how this might work at this point, and the current plan is that it functions as a F2F class, plus a web community with some ds106-style mods.

Quantitative Reasoning is one of the core AAC&U outcomes, and it is difficult to teach. It tends to have the sort of problems that online courses have not addressed well in the past. So this will be a test to see if even a fraction of the energy generated by the ds106 model can be sustained in a skill-centric statistical reasoning class.

In any case, as the semester winds down, I’m starting to get back to it. I have the first chapter of the six chapter open textbook for the course written — it’s up here on WordPress, which turns out to be everything you really need for an e-textbook.  Be aware that I haven’t figured out how to gracefully get all the chapter to show at once yet — you have to click next on that page to see the last four sections of the chapter.

Chapter Two is coming along. Writing is hard.

# A Note on Farm Share and Subgroups

As we say in the COMPARABLE checklist, the story is often somewhere in the edges. Take this chart of the proportion of a food dollar which goes to the farmer vs. post-farm activities. At first it seems to show declining farm revenue as the the market bill (which includes everything from transportation to preparation) climbs:

In other words, in 1993, more than 18 cents of every dollar you spent on food went to the farmer. By 2008, that amount was 15.8.  And while those numbers seem small, it represents a 15% or so drop, which is no small change.

But once you look at the subgroups it becomes clear the story is not quite that simple:

For food you buy at the supermarket and prepare at home, there has been no shift in where the money goes to. Food at home has a farm share of 24.6 in 1993, and a share of 24.3 today.

Food prepared at restaurants and other “away from home” locations, though,  has a sinking farm share, moving from 10.5 down to less than half of that (4.7).  So what we are likely looking at here is an increase in the cost of eating out. The linked report sees much of this as being related to a shift from limited-service restaurants (McDonald’s, Papa Gino’s) to full service (Olive Garden, Outback, etc). Add to that the increasing cost of labor, and you get the sort of pattern we see above.

# How Not To Do a Graph: Distribution of U.S. Food Dollar

From Marion Nestle’s book on Food Politics:

Interesting graph, but undermined by its cuteness. Farm value and labor, the first two segments, make up just short of 60% of the total, but appear to be less than 50% (maybe even 40%) because of all the inserted black gaps. But maybe that’s by design, to make the relatively small advertising and transport costs seem bigger?

# Comparison of the Day: SIDS and Prone Sleeping in Norway

This is a really sad chart: the incidence of SIDS (“crib death”) in Norway plotted out against the rise and fall of parents that put their children to sleep on their stomach. (Which was what they told you to do for a long time).

As you can see, there was not only a correlation with the rise of prone sleeping, but the public campaign in 1990 that stopped parents from placing children in the crib face-down seems to have had immediate impact on SIDS incidence. From Epidemiology and Demography in Public Health (ed. Japhet Killewo):

The distribution of the information that prone (facedown) sleeping was a serious risk factor had a dramatic effect.
In Norway, this information was spread by the mass media in January 1990. The SIDS rate in Norway dropped from 2.0 per 1000 in 1988 to 1.1 in 1990. In a retrospective study, it appeared that the prone (face-down) sleeping position after having continuously increased from 7.4% in 1970, was reduced from 49.1% in 1989 to 26.8% in 1990 (Irgens et al., 1995) (Figure 21).The example again illustrates how important it is to provide scientifically convincing evidence, pivotal to bring results of epidemiological research into practice.

The SIDS experience raises important questions with respect to the reliability of recommendations given to the public based on epidemiological studies. The prone sleeping position had been recommended by pediatricians since the 1960s to avoid scoliosis as well as cranial malformations. Even though a case–control study in Britain early on in the period had observed an increased relative risk, no action was taken; again an example of the necessity to convince scientifically.

# Choosing definitions: BMI vs. DXA (or, Why BMI Is Not a Lie)

There is a great post over on Kaiser Fung’s blog on the BMI/DXA debate. I suggest you go read it.

What it is about is this — there’s a claim to be made that BMI doesn’t measure fat accurately, and a number of people are saying BMI should be replaced by this other measure (DXA) which measures fat accurately.

But why do we care about fat to begin with? Well, it turns out we care about it because high BMI is associated with all sorts of negative outcomes. We have decades of decent research showing this.

BMI is the predictor here, not fat. And it’s true that there are probably some ways to increase BMI that don’t decrease health, or decrease BMI in ways that puts your health at risk. If you’re a person that’s figured out a way to cheat the BMI metric, through starvation dieting or the like, if you managed to get down your BMI by letting your muscles deteriorate, then maybe DXA will keep you honest. Or maybe you should just alter your method of achieving lower BMI.

Outside of personal decision — once we look at this from a population perspective — DXA makes even less sense. If the BMI association holds across the population as a whole, and the association is strong, then that is what you want to target from a public policy perspective*. The edge cases are already accounted for in that calculation. There are people that smoke all their life and don’t get cancer for genetic and environmental reasons we do not yet comprehend, but reducing smoking in the population as a whole has saved hundreds of thousands of lives. Do we need a better predictor than smoking — or do we just need to reduce smoking?

There are cases, of course, where changes in metrics have made sense. Cholesterol measurements now look at the ratio of LDL to HDL. But the reason they do that is not because “that’s what cholesterol really is”. The reason they do that is because the ratio has a been demonstrated as having a much stronger relationship to heart health than LDL alone or some other metric.

This isn’t the case with BMI vs. DXA. Again, we have pretty good evidence on the BMI front of a strong relation:

That’s a pretty damning plot that has withstood decades of research. It’s a robust finding in a world of fads.

In the DXA corner we have nothing. We don’t know that it predicts mortality one iota better than BMI.

In 10 or 20 years, if DXA can significantly improve on that prediction, stand the test of time, and come out on top, then it might be worth a look. Until then, it’s just silliness.

* There’s actually a pretty decent argument being made right now that BMI is not as manipulable a risk as something like smoking, and that the focus should be on long term interventions that stick, like those for cardiovascular fitness, instead of those that tend not to stick, like weight loss. And it can be argued that CVF predicts mortality even better than obesity. I’m interested in all of this — but it doesn’t change the fact the measure you need to make these arguments with is probably BMI.

# Comparison of the Day: Unemployment by College Major

In the COMPARABLE framework the “E” is for “Edges”, and part of the “question of edges” is whether there are significant subpopulations. In the case of unemployment of recent college grads, the answer is yes:

The center would tell you only that the average unemployment for college grads is about 9%. But the lowest rates here (5% for Education and Health) are significantly below that, and in fact significantly outperform the general unemployment rate. On the other hand, those getting a degree in Arts have an unemployment rate of 11%.  Digging into the original report, I find the unemployment rate for recent English majors is 9.1%, about average.

Of course, compared to those who didn’t graduate college at all, college grads do pretty well — even Arts majors.  The overall recent college graduate average of 9% compares with a stunning 22.9% for people with only a high school diploma. There’s a mix of cause and confounding there, but even controlling for the usual suspects significant gains still persist.

# Mental Experiments and the Mancovery

This is the new story out — it’s a mancovery! From Bloomberg:

Men, who lost more than twice as many jobs as women during the worst economic slump since the Great Depression, have landed 88 percent of the non-farm jobs created since the recession ended in June 2009. The share of men saying the economy was improving jumped to 41 percent in March, compared with 26 percent of women, according to the Bloomberg Consumer Comfort Index’s monthly expectations gauge.

“The recovery is a mancovery,” said Heather Boushey, a senior economist at the Washington-based Center for American Progress. “I don’t see improvement for women in the past year, whereas for men this is the best year in years.”

So here’s the question — if men lost 100% more of the jobs in the recession than women, what percentage of new job openings would we expect them to get back if we were looking for an equitable recovery? Is it above 88%? Below 88%? What is the exact percentage?

You might know the answer to this already, but, if you don’t. you can do a Mental Experiment. Plug in some fake numbers and find out!

Here’s what I found out:

Untitled from Mike Caulfield on Vimeo.

So the 88% does, to some extent, represent a “mancovery”, though maybe not by the amount it initially seems (66% of jobs going to men would be equitable so this is about 33% more jobs than we might expect).

Could you have figured this out without an experiment? Absolutely. An easy way to look at this is that if men lost double the jobs, they must have lost 66% to women’s 33%. And if 66% of the jobs lost were lost by men, then 66% of the jobs returning should be men’s jobs. But that’s easy in retrospect. Things like that are not always clear when you first come to a novel problem.

So, the important point is, as always, if you don’t understand something, plug some fake numbers in and play around a bit. For most problems like this it’s easy and inexpensive to do a thought experiment.

# When Percentages Go Wrong

A poor man said to a rich one: “All my money goes for food.”

“Now that’s your trouble,” said the rich man. “I only spend five percent of my money on food.”

(From a Sufi tale, recounted here.)

Percentages are a really helpful tool, obviously. But raw numbers can matter too.

# Comparison of the Day: Conservative vs. Liberal Trust of Science

From Kevin Drum’s Chart o’ the Day:

Lots of interesting stuff going on there. Notice, in particular, how the trust in science falls off a cliff for moderates in the 70s. It’s also fascinating that conservative trust in science used to be as high (if not higher) than that of liberals 40 years ago. This is still the case in Europe — for the most part there is no liberal/conservative divide in trust in science.

It gets even more interesting when you look at the subpopulations. You might think, for instance, that the decline in conservative belief in science has been driven by shifts in the attitudes of the least educated conservatives. Nope:

Less-educated conservatives didn’t change their attitudes about science in recent decades. It is better-educated conservatives who have done so, the paper says.

In the paper, Gauchat calls this a “key finding,” in part because it challenges “the deficit model, which predicts that individuals with higher levels of education will possess greater trust in science, by showing that educated conservatives uniquely experienced the decline in trust.” This finding also could make it difficult to change attitudes. Gauchat writes that the educational attainment data suggest “that scientific literacy and education are unlikely to have uniform effects on various publics, especially when ideology and identity intervene to create social ontologies in opposition to established cultures of knowledge (e.g., the scientific community, intelligentsia, and mainstream media).”

# Comparison of the Day: CFL vs. Incandescent Mercury Pollution

From EnergyStar.gov:

Lifecycle impact is an invaluable tool in making fair comparisons.  It’s easy, for example, to get hung up on the small amount of mercury in a CFL bulb, a percentage of which can escape into the environment if the bulb is crushed in a landfill.

But the biggest contributor to mercury pollution is coal-fired plants, which push gigantic amounts of mercury into the environment as part of their normal operations.

So how do we compare the mercury impact of the two different bulbs? We calculate how much mercury is produced via electricity over the lifetime of the bulb (here standardized to 8000 hrs. of use, since CFLs last longer). Then we add the mercury in the bulb itself to the lifetime use figure. It seems obvious, and it’s certainly a common way to do it — but it’s an incredibly powerful way to look at things compared to the alternatives.