Struggle With Statistics? Your 'Fixed Mindset' Might Be To Blame (arstechnica.com)

A new study in Frontiers in Psychology examined why people struggle so much to solve statistical problems, particularly why we show a marked preference for complicated solutions over simpler, more intuitive ones. Chalk it up to our resistance to change. From a report: The study concluded that fixed mindsets are to blame: we tend to stick with the familiar methods we learned in school, blinding us to the existence of a simpler solution. Roughly 96 percent of the general population struggles with solving problems relating to statistics and probability. Yet being a well-informed citizen in the 21st century requires us to be able to engage competently with these kinds of tasks, even if we don't encounter them in a professional setting. "As soon as you pick up a newspaper, you're confronted with so many numbers and statistics that you need to interpret correctly," says co-author Patrick Weber, a graduate student in math education at the University of Regensburg in Germany. Most of us fall far short of the mark.

Part of the problem is the counterintuitive way in which such problems are typically presented. Meadows presented his evidence in the so-called "natural frequency format" (for example, 1 in 10 people), rather than in terms of a percentage (10 percent of the population). That was a smart decision, since 1-in-10 a more intuitive, jury-friendly approach. Recent studies have shown that performance rates on many statistical tasks increased from four percent to 24 percent when the problems were presented using the natural frequency format.

Comments

Re:Huh?

[gotan]

That's not it.

It's easier to grasp what to do to those numbers. Presented with percentages it's often hard to see what mathematical operations are necessary to arrive at the desired answer in bayesian statistics problems.

E.g.
A medicinal test for disease X gives false positives in 0.1% of cases. It gives a false negative in 1% of the cases (i.e. correct positive in 99% of the cases). The disease afflicts 0.01%.
Of those tested positive, how many have disease X.

Of course one now could employ the statistics toolbox to solve that problem. OTOH one could compare the 10 in 10,000 false positives (with a slight error since only 9,999 are without disease), to the 1 in 10,000 diseased (noticing that the false negatives have negligible impact for the question at hand and we can work with 100% correct positives as well as 99% if we want an estimate).

So now we need to compare only small numbers, 10 false positives to 1 diseased positive or 1 in 11 which is about 9%.
(the correct result without the approximations is 10 in 111 or 9,009...%).

Also note the easy expansion of 1 in 1,000 to 10 in 10,000 to get to comparable numbers. It's not important to have an accurate image of those 10,000, what's of interest is to compare the 10 false positives to the 1 diseased.

Such medicinal tests help a lot to find candidates that should undergo more sophisticated (and much more expensive) tests, to see if they really have X (it'll reduce the expensive tests by a factor of 1,000), but patients need to be informed even with a "positive" result it's still unlikely that they have X, but advisable to do the more sophisticated test. One might think that the test is pretty useless if it delivers 91% false positives when in fact it is pretty accurate, only the occurence of disease X is so rare.

So such "frequencies" do not only help to get a (pretty) correct result without knowing any bayesian statistics tools, but also to understand how the information affects the result, and how the unintuitive (to someone not used to such statistics) result comes about.