Clive Thompson nails it when he describes the importance of statistical thinking (italics original; boldtype mine):
Statistics is hard. But that's not just an issue of individual understanding; it's also becoming one of the nation's biggest political problems. We live in a world where the thorniest policy issues increasingly boil down to arguments over what the data mean. If you don't understand statistics, you don't know what's going on -- and you can't tell when you're being lied to. Statistics should now be a core part of general education. You shouldn't finish high school without understanding it reasonably well -- as well, say, as you can compose an essay.
Consider the economy: Is it improving or not? That's a statistical question. You can't actually measure the entire economy, so analysts sample chunks of it -- they take a slice here and a slice there and try to piece together a representative story. One metric that's frequently touted is same-store sales growth, a comparison of how much each store in a big retail chain is selling compared with a year ago. It's been trending upward, which has financial pundits excited.
Problem is, to calculate that stat, economists remove stores that have closed from their sample. As New York University statistician Kaiser Fung points out, that makes the chains look healthier than they might really be. Does this methodological issue matter? Absolutely: When politicians see economic numbers pointing upward, they're less inclined to fund stimulus programs.
One of the reasons statistical thinking isn't widely used, even by many scientists, is that statistics are seen as a proscribed set of tools, rather than as an approach to understanding data. But, in my experience, the hard part isn't running the tests, but figuring out which tests are appropriate, and even what the precise question is. I'm usually wary of calls for teaching 'critical thinking', but training people how to approach data from a statistical perspective--and also how to recognize the limitations of the data and analyses--is vital in a (putatively) data-driven society.
Anyway, as the kids say, read the whole thing.
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I agree with this guy, statistics should be part of basic high school education. What we need to have less of is geometry.
Clive Thompson: "Consider the economy: Is it improving or not? That's a statistical question. You can't actually measure the entire economy, so analysts sample chunks of it -- they take a slice here and a slice there and try to piece together a representative story. One metric that's frequently touted is same-store sales growth, a comparison of how much each store in a big retail chain is selling compared with a year ago. It's been trending upward, which has financial pundits excited.
"Problem is, to calculate that stat, economists remove stores that have closed from their sample."
Proving that economists do not understand statistics.
Mike: "One of the reasons statistical thinking isn't widely used, even by many scientists, is that statistics are seen as a proscribed set of tools, rather than as an approach to understanding data."
Typo: "prescribed", not "proscribed". ;)
Well, that's the case for Fisherian statistics, isn't it? Bayesian statistics has firmer philosophical underpinnings, to provide a basis for understanding the relation between hypothesis and data. But choosing sides is problematical. A Hegelian synthesis of the two has not occurred yet.
Mike: "But, in my experience, the hard part isn't running the tests, but figuring out which tests are appropriate, and even what the precise question is. I'm usually wary of calls for teaching 'critical thinking', but training people how to approach data from a statistical perspective--and also how to recognize the limitations of the data and analyses--is vital in a (putatively) data-driven society."
Hear, hear! :)
Um, it's "Statistics are the new grammar."
Addendum: Teach fractions. A number of common mistakes in probabilistic thinking are reduced when you ask people for answers in terms of whole numbers instead of probabilities. You might think that asking people "what percentage of people" would yield the same answer as "out of 100 people, how many", but it doesn't. ;)
I agree that it would be wonderful if we required high school students to have a functional understanding of statistics.
Unfortunately, the high school seniors I teach can't even add single digit numbers. When given a fraction, they don't know which number to put into the calculator first. When doing percent composition problems they will tell me that a certain copper compound is 450% copper.
I remember the statistics course in college. I think I passed the course (With an A no less) because I had an intuitive knowledge of the MatLab software we used and taught the rest of the class how to use it.
Even programmed some of the more esoteric statistics formulas into a TI calculator.
And now as I'm refreshing my calculus knowledge it dawns on me that I've been doing derivation programming for years. Doh!
Statistics is a bit more of a mind bend than calculus.
As the article notes, statistics without context are easily misinterpreted, which reduces what should be facts into ever-nebulous partisan talking points.
I'm all for teaching people an understanding of statistics and explaining how to utilize data, but the "critical thinking" required would include analyzing which questions are being asked, by whom, and for what purpose. If you don't take into account which data are being included (and excluded) from a study -- or why those exclusions are happening -- you're in danger of believing that all results are gospel truths.
My undergrad alma mater recently changed its graduation requirements so that students will have to take either stats or formal logic to graduate. I thought that was a good move since so many people functional statistically illiterate.