Monday 8 April 2019

Does learning probability and statistics improve critical thinking?


Does learning probability and statistics improve critical thinking?

This is an interesting question.  Naturally, much of the answer hinges on just what is meant by “critical thinking’, as another Quora responder noted.  It’s a vague term that can be interpreted in many ways.

Literary or Cultural Critical Thinking.

We all learn a bit of this in school and via our discussions with others about cultural matters, including what we see or read in the media.  But, I think most of us would generally agree that a lot of it comes down to “taste”, which differs from person to person and group to group.

So, does knowledge of statistics and probability help in this regard?  Perhaps a bit – for example, we do note how successful various cultural products are in the marketplace, via such statistical markers as sales, books sold, movie attendance and so forth.  That can be somewhat helpful in separating the wheat from the chaff, but only up to a point. We all know of many examples of high quality products that didn’t get the attention that they deserved, and low quality products that were far more successful than they had any right to be.

Statistics and probability also help us to judge the likely truth value of cultural works – i.e. how well the story or song content lines up with known facts, if they are available.  People with a good grounding in statistics and probability are more likely to be skeptical of cultural products than those without such a grounding, if the story seems highly improbable (though we might still enjoy it from an escapist point of view).  So, for example, statistically minded people are less likely to take adventure movies seriously, if the hero mows down 500 of the enemy without ever being hit by one of them.



So, probability and statistics are helpful to critical thinking here, but they are generally of secondary importance in this domain.
Political, Religious and Social Critical Thinking.
We learn this from family, school, church, media and the surrounding social world in general.  Most of this relates to “values”, or efforts to persuade us of various ideas and modes of life that are considered to be appropriate by these influencers.

Does knowledge of statistics and probability help in this domain?  I would say quite a bit.  Of course the belief in the usefulness of ideas like statistics and probability can be highly value weighted itself, but I will leave that aside, and just assume that most people believe that testing values and ideologies against evidence is a good idea, at least in principle (religion is somewhat immune from this).

In these areas a proper knowledge of statistics and probability can be extremely helpful for critical thinking, as they aid us in evaluating the actual real-world results of various values and ideologies.  For example, if underlying ideas that lead to certain policies don’t seem to work, as judged by statistical evidence, we are quite likely to abandon those ideas, or at least significantly revise them (though that can take quite some time).  



There will be a lot of conflicting claims and counter-claims advanced to support or refute various ideas – a good grounding in statistics and probability theory can help us to sort out which claims (and claimants) that we ought to put our trust in, though it’s not infallible.  Statistics can be used to mislead, but that just reinforces the need for critical thinkers to really understand statistics and probability, so that they won’t be thrown off, by a misleading graph or correlation vs causation argument.

So, a good knowledge of probability and statistics can be very helpful here, as many of these issues are capable of being subjected to real-world tests.  But, one must always be careful, as not all social questions are amenable to statistical analysis, and even when they are, it can be very difficult to determine which dataset and which statistical arguments one ought to find most compelling.
Personal and Relationship Critical Thinking.
I think we use probability and statistical thinking a lot in these domains, though we often aren’t aware if it.

Sometimes it is unconscious.  For example, we often estimate how much we can trust a person or a situation, based on prior experience and a sub-conscious probability calculus.  We often call this intuition or gut feeling, but in my opinion those are generally terms used in place of “sub-conscious probability calculus”.  Some people are better at this than others, and it seems to me that knowing probability theory probably makes a difference in this regard, even at this sub-conscious level.

At other times our use of statistical and probabilistic reasoning is conscious but not necessarily rigorous.  For example, we might consciously think that our probability of succeeding at something is high or low, but not be able to put a specific number on it.  But it is still useful to know such basic facts about probability, such as high probability X low probability = low probability, so that we can more carefully evaluate a course of action.  Being able to understand the difference between independent events and dependent events can also help one to avoid costly errors.  And the understanding that correlation is not necessarily the same as causation can be crucial in day to day critical thinking.

Finally, there are those occasions where a deep knowledge of probability and statistics can affect a person’s life in a major way.  For example, I once had a major flirtation with gambling, particularly horseracing.  That led me to study probability and statistics at a young age and eventually work in the field, which proved to be professionally and financially advantageous.

I had a pretty good run at the track for a couple of years, based on collecting and analysing Racing Form data systematically.  While doing so, I was motivated to take a lot of courses in mathematical statistics and multivariate analysis.  I came to have a really deep appreciation for such things as the pitfalls of post-hoc multiple comparisons, data snooping, and atheoretical statistical analyses.  

 Eventually my system quit working, and I gave back the money that I had won, after a lot of hard work.  But, though I ultimately didn’t make a gambling windfall, I learned a lot about statistics and probability which turned out to be valuable throughout my life.


It was fun and educational, but I could never play a negative expectation game (e.g. casino games), or a game with a high takeout (e.g. the track) for long after that.   That probably saved me a lot of money and related grief.

So, in conclusion: hurrah for statistics and probability theory, they really can help with critical thinking.
    

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Now that you have reflected upon some real math and science, you should read some science fiction.  Either of the Kati of Terra series or the Witch’s Stones series would be excellent choices.  Alternatively, you could try the short story “The Magnetic Anomaly”, which features some references to Fourier analysis as used in geophysics, which is pretty mathy (though you don't need to know advanced math to enjoy the story).

Kati of Terra

How about trying Kati of Terra, the 3-novel story of a feisty young Earth woman, making her way in that big, bad, beautiful universe out there. 



The Witches’ Stones

Or, you might prefer, the trilogy of the Witches’ Stones (they’re psychic aliens, not actual witches), which follows the interactions of a future Earth confederation, an opposing galactic power, and the Witches of Kordea.  It features Sarah Mackenzie, another feisty young Earth woman (they’re the most interesting type – the novelist who wrote the books is pretty feisty, too).



The Magnetic Anomaly: A Science Fiction Story

“A geophysical crew went into the Canadian north. There were some regrettable accidents among a few ex-military who had become geophysical contractors after their service in the forces. A young man and young woman went temporarily mad from the stress of seeing that. They imagined things, terrible things. But both are known to have vivid imaginations; we have childhood records to verify that. It was all very sad. That’s the official story.” 


 




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