Steve Kass

http://finance.yahoo.com/q?s=VMMXX:

Strange. The HTML source for this page shows a yield of 2.39%, not 92,318.20%. In both IE7 and Firefox, 2.39% shows up as the yield when the page is first rendered, but changes immediately to 92,318.20%. The yield is getting its significant digits from the Assets value, but why is a mystery to me.

A Reuters News Service article today reports [emphasis mine] “If both your parents have Alzheimer’s disease, you probably are more much likely than other people to get it, researchers said on Monday.” What if they both have dyslexia?

A colleague recently drew my attention to this CNN.com article, titled “Confident students do worse in math; bad news for U.S.”

It’s interesting, I guess, but the analysis is flawed.

The article reports the results of a Brookings Institute study based on the 2003 Trends in International Science and Mathematics Study (TIMSS).

It’s the culture, stupid.

Where to start? First off, the countries with the best average math scores were East Asian countries. That confirms other studies and general perceptions, and it didn’t surprise anyone. Obviously, then, anything that correlates with East Asianness (straightness of hair, size of epicanthal folds, or facility in Chinese or Japanese) will also correlate with math scores when East Asian country-wide averages are compared with other country averages. One trait that correlates with East Asianness is self-effacement. Self-effacement tends to be highly valued in countries like Taiwan and Japan, but praising one’s self is not, and there was a survey question that measured self-effacement: “How strongly do you agree with the statement ‘I usually do well in mathematics.’”

It shouldn’t have surprised anyone that students in East Asian countries were less likely to answer “strongly agree” when asked how much they agree with the statement “I usually do well in mathematics,” so it shouldn’t have surprised anyone that country-wide averages on this survey question correlated (inversely) with mathematical ability. The correlation is simply explained by culture and the known difference between countries in mathematical ability.

Hurting the chances for a fair airing in the press (if there is ever any chance), the Brookings analysts repeatedly confuse expressed self-confidence with true self-confidence, too: “In the TIMSS data, when one looks at the math scores of students within each country, those who express confidence in their own math abilities do indeed score higher than those lacking in confidence,” and “The world’s most confident eighth graders are found…”, and “students in [East Asian] countries do not believe that they do very well in math.” Combine this with the fact that while the Brookings folks do notice the culture question, they dance around it enough to let reporters to come away with conclusions that are a good six fallacious leaps away from the data and statistics, like “Happy, confident students do worse in math” headlining an article by Association Press education writer Ben Feller. Nothing in the data suggests that confidence in mathematical ability is inversely related to actual mathematical ability at the level of individuals, but the headline gives that impression, strongly.

Another problem with the study is that it commits the ecological fallacy. It speculates about how confidence and ability are related in individual students from country-wide aggregate data, and the press drag these wrong conclusions in the wrong direction. The aggregate data is screwy to begin with, given the very strange list of countries surveyed. Many have small populations: Jordan, Israel, Bahrain, Cyprus, Latvia, the Palestinian Authority, Moldova, Lithuania, Scotland, Norway, Flemish Belgium, Botswana, Macedonia, and Serbia, and a few have large populations: Russian Federation, Japan, Indonesia, Malaysia, the United States, and the Philippines, but each country’s average mathematics score counted the same in the statistical analysis to which the press is paying the most attention. The country list was hardly comprehensive, either. Chile was the only American country on the list besides the U.S.

A regression weighted by population would have been a little better, but drawing any conclusions about individual students from country-wide averages is invalid. Here are a couple of good articles about this fallacy: (link) (link).

The TIMSS data contains plenty of useful information to support a conclusion opposite to the one reported. The data showed that all other things being equal (that is, among students within any one individual country) higher student confidence (which, ceteris paribus, should now correlate with expressed confidence) in math ability tended to be associated with higher math ability. The Brookings folks observed this, and they called it paradoxical: “So an interesting paradox emerges from the international data on student confidence and achievement. The relationships are the opposite depending on whether within-nation or between-nation data are examined.”

When Brookings writes “The international evidence makes at least a prima facie case that self-confidence, liking the subject, and relevance are not essential for mastering mathematics at high levels,” it’s easy to think they are suggesting that the ecological fallacy analysis is telling us something, and they are diminishing the different conclusions supported by the ceteris paribus analysis. And the reporters take the hook. I wonder how good the press corps and the Brookings researchers think they are at statistics.

[Followup to this post.] Julie from Bolthouse farms emailed me today, saying that “The unexplained carbohydrate is coming from the natural flavor added to this product. We are and will remain in compliance with all applicable regulations regarding our products.”

In my opinion, it’s misleading, if not just plain wrong, to advertise a product as having “No Added Sugars” (as Bolthouse Farms does here) when it contains unspecified ingredients (“natural flavor”) that add 15-20 grams of sugar–the amount in 3-4 teaspoons of table sugar. It seems to me especially at odds with what Julie expressed as the company’s goal: “to provide our customers with healthy, nutritious and good-tasting products designed to provide genuine and legitimate options for those individuals wishing to improve or enhance the overall quality of their diets.”

For the record, the FDA, which regulates food labeling, defines the term natural flavor as follows (link):

The term natural flavor or natural flavoring means the essential oil, oleoresin, essence or extractive, protein hydrolysate, distillate, or any product of roasting, heating or enzymolysis, which contains the flavoring constituents derived from a spice, fruit or fruit juice, vegetable or vegetable juice, edible yeast, herb, bark, bud, root, leaf or similar plant material, meat, seafood, poultry, eggs, dairy products, or fermentation products thereof, whose significant function in food is flavoring rather than nutritional.

[There is a followup to this post here.]

Perfectly Protein® Mocha Cappuccino with Whey Protein (PP®MCwWP for short) is one of Wm. Bolthouse Farms’s newest beverage products, and I tried one recently. It wasn’t bad, but it wasn’t very memorable either, at least not as a drink. It was interesting to read though, and I’m convinced that either the ingredients or the nutrition facts are wrong. As of this writing, the ingredients listed here on bolthouse.com match what was on the bottle I saw: Mocha Cappuccino (Low Fat Milk, 100% Arabica Coffee, Natural Flavors, Vanilla Extract (Madagascar),Cocoa), Milk Whey Protein, Potassium Diphosphate, Apple Juice, Pectin, Carrageenan, Calcium (Tricalcium Phosphate), Vitamin C (Ascorbic Acid), Magnesium (Magnesium Oxide), Vitamin B6 (Pyridoxine Hydrochloride), Zinc (Zinc Sulfate), Iron (Ferrous Lactate), Vitamin B12 (Cyanocobalamin). It tasted sweet to me–sweeter than milk with a splash of apple juice would probably be. The Nutrition Facts made more sense: 28 grams of sugar in 8 ounces.

Where do those 28 grams of sugar come from? I called Bolthouse to ask, saying that the ingredients didn’t seem to add up to 28 grams of sugar. Julie in Consumer Relations emailed me back to say that PP®MCwWP is naturally sweetened by the apple juice. There is no sugar added.”

Let’s figure it out. (more…)

This morning, I rode New Jersey Transit to Newark International Airport, which is about 12 miles from my home in Madison. I ended up not flying anywhere, but that’s another story.

Things have changed. The last time I took New Jersey Transit from my home to the airport was years ago, and it was simple. I took the train from Madison to Newark—Broad Street, then walked downstairs and hopped on the Airlink bus, which stopped at Newark—Penn Station and then Terminal B.

Transportation to the airport is modern now. (more…)