An urban, high school IB mathematics teacher rambles on about his day.

Newspaper Reporting

| 30 July 2007
If you are a math nerd, like myself(!), when you see a table, graph, or another data display in the newspaper, your eye goes there first. And if you are a math wizard then you'll notice other things right away. For instance, when you see a table that (supposedly) shows how poorly some schools are getting our students to pass state exams like the one here and you see percentages such as 0%, 12.5%, and 33.3%, you know something awful has happened before you even read the article. In fact, after seeing the data, you're more than likely just to ignore the article because if they are writing a story based on poor data, what point could they make that would mean anything.

When a mathematician sees 12.5%, we know that it means 1 out of 8 (okay, maybe 2 out of 16). When we see 33.3% we know it is 1 of 3, 2 of 6, or 3 of 9. Chances that a large school gets 241 out of 723 (which is "exactly" 33.3%, rounded to the nearest tenth) is quite slim.

Here is some data that the Star Tribune should have put in the table to give people the right impression.

  • Delta Place: 6 students tested at the school grades 7 to 11. I'm not sure about 2006, but I would imagine three of six passed last year, so the 50% drop was on account of about three students.
  • Teep: Ten students tested grades 4 to 11. I would imagine last year 4 of 12 or 3 of 9 passed. Again, a huge drop because of three students.
  • Distance Learning Independent Study: 6 students tested grades 7 to 10.
  • Distance Learning Program: I'm looking at the state's speadsheet and I see that there are only ten students that took the exam in math in grades in grades 4 through 11. So I'm not sure where the article gets 1 of 8 passing.
  • Childrens Regional Treatment Center: I see four students (one in 8th, three in 11th), the paper must see a total of three to get its 33.3%.

I could keep going, but you get the point. Until the eigth school in the list, they've only included schools with a few students which means that any large percentage drops or gains are not strange at all, but expected. To put them on the "Biggest Metro Math Losers" (what kind of name for a table is that anyway?!) is simply poor reporting.

I'm sure the editors would think a reporter insane for doing the same thing for the baseball box scores: "Mauer was 2 for 4 on Tuesday, but only 1 for 5 on Wednesday. That's a 30% drop!"

Then again, we wouldn't want to unfairly tarnish the reputation of a baseball player. Better stick with the schools.


5 comments:

Tony said...

I am constantly infuriated by exactly what you are describing. Are they ignorant or deliberately deceitful? That's what I want to know.

Vivek said...
This post has been removed by the author.
Vivek said...

I've been meaning to write on this myself- thanks for doing it for me! You know what

Disrailey said about statistics: There are three kinds of lies- "lies, white lies and statistics."

All the best!

Vivek
i'm no longer with blogger, my new address is The Red Pencil

a quantum diaries survivor said...

Hi,

good post. I think what you wrote deserves to be taught to your students, because it is a prime example on how a little math wisdom can make you much smarter than the rest of the pack.

I am unsure how nerd is your usual audience, so I will not suggest that you should have brought the exercise a bit further, by assigning flat priors to the number of data that contributed to each fraction, and then run a likelihood to determine the range of probabilities for the numbers (e.g. 12.5% is most probably 1/8, but if you assume random numerator and denominator, you can obtain a 95% confidence limit on the maximum value of the denominator).

Anyway, well written.

Cheers,
T.

Anonymous said...

hahah. central limit theroem and normal model requires minimum n=30.obviously these people don't check conditions.