Wednesday, April 29, 2015

Statistics, Intuition, and The Big Picture

(via Wikipedia)

For someone who isn't directly involved in either the education wars or the statistics wars, it's embarrassing how often I end up posting about these two areas. Anyway, a new piece in Nature,  (properly) worries once again over the use of statistics in research:

The writers agree that "P values are an easy target: being widely used, they are widely abused," but also note that banning p-values "...will in fact have scant effect on the quality of published science."
As they further stress:
"There are many stages to the design and analysis of a successful study... The last of these steps is the calculation of an inferential statistic such as a P value, and the application of a 'decision rule' to it (for example, P < 0.05). In practice, decisions that are made earlier in data analysis have a much greater impact on results..."

What is interesting to me is that 40 years ago when I took statistics in grad school I felt a definite wariness and distrust of statistics, on simply an intuitive basis (but didn't have the mathematical sophistication to clarify my concerns), that seems to have now become technically mainstream 40 years later. Statistics haven't changed much in that time, but the consideration of the field sure has.

The older I get, the more I trust my strongest intuitions (even as iffy and fragile as they may be), and the less I trust the assertions of 'experts.'
"The only real valuable thing is intuition." -- Albert Einstein

"Intuition becomes increasingly valuable in the new information society precisely because there is so much data." -- John Naisbitt

"Intuition is a conceptual bird's-eye view that allows humans to draw inferences from high-level abstractions without having to systematically trace out each step. Intuition is a wormhole. Intuition allows us get from here to there given limited computational resources." -- from "Less Wrong" blog

and lastly, Terence Tao:
"The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture."


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