Saturday, November 10, 2012
Proportion, not stat
Science Daily focuses on some experiments showing (unsurprisingly) that quick intuition often works better than formalized thinking. These experiments are the usual Game Theory stuff with college students as subjects, which limits their universality. An earlier writeup on the same topic was more substantial.
One point in the latest experiments by Marius Usher begs for a better explanation.
Usher apparently used the arithmetic mean to create ranges that supposedly had the same 'center'. A range of [45,55] has an arithmetic mean of 50, and [30,70] also averages to 50. But our senses don't use sums and differences. The numerical sense (like all others) works on proportions and percentages. The sensory comparator would be looking at 55/45 versus 70/30, not the sums or differences. 70/30 is about twice as large as 55/45, so 70/30 would be seen as the higher value.
Science Daily focuses on some experiments showing (unsurprisingly) that quick intuition often works better than formalized thinking. These experiments are the usual Game Theory stuff with college students as subjects, which limits their universality. An earlier writeup on the same topic was more substantial.
One point in the latest experiments by Marius Usher begs for a better explanation.
Of course, intuition is also subject to certain biases, explains Prof. Usher, and leads to more risks -- risks that people are willing to take. That was shown when the researchers engaged participants in tests that measured their risk-taking tendencies, and were surprised to discover that the majority of the participants didn't play it safe. When faced with a choice between two sets of numbers with the same average, one with a narrow distribution, such as 45 and 55, and another with a broad distribution, such as 70 and 30, people were swayed by the large numbers and took a chance on the broadly distributed numbers rather than making the "safe" choice.I'd bet the broad distribution isn't the cause. More likely this difference comes from the logarithmic nature of our senses.
Usher apparently used the arithmetic mean to create ranges that supposedly had the same 'center'. A range of [45,55] has an arithmetic mean of 50, and [30,70] also averages to 50. But our senses don't use sums and differences. The numerical sense (like all others) works on proportions and percentages. The sensory comparator would be looking at 55/45 versus 70/30, not the sums or differences. 70/30 is about twice as large as 55/45, so 70/30 would be seen as the higher value.
Labels: Blinded by Stats
¶ 7:03 AM
