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And the Magic Number is 3.841

Rory is working on his science fair project.  He’s getting an early start because it is a psychology experiment and he needs to subject at least 60 people to a questionnaire. In the meantime, dad is trying to relearn what he used to know about determining statistical significance in a dichotomous study using a binary response scale. Turns out, the study will employ a (simple) 2 x 2 contingency Chi-square analysis. Duh.

And remember . . . the critical value for determining statistical significance in a contingency Chi-square when df = 1 is . . . wait for it . . . 3.841.

Gotta pump up that N value. Can we get 80 instead of 60?

Useful links:

http://web.pdx.edu/~newsomj/da1/ho_chisq.pdf

https://www.uam.es/personal_pdi/ciencias/anabz/Prest/Trabajos/Critical_Values_of_the_Chi-Squared_Distribution.pdf

 

Image result for image dirty toilet trainspotting

The Once and Future Liberal

 

Product DetailsRobert just read The Once and Future Liberal, After Identity Politics, by Mark Lilla. Lilla is a professor of humanities at Columbia who writes books on modern politics and philosophy (including one about Isaiah Berlin written with Ronald Dworkin). This short book was born out of an article Lilla wrote after the 2016 Presidential election arguing that the Democratic party needs to move away from its focus on race, gender, and other personal identity divisions as an organizing idea.  It is a very quick read.

According to Lilla, after Reagan, liberals left the hard work of politics behind. They retreated into the universities and into the promotion of organizations dedicated to single causes. The theme of liberals became a theme of individualism and the individual’s fight against power. Lilla sees this individualism as somehow akin to the rugged individualism and unwillingness to give up comforts of capitalism that were the appeal of Reagan.

Within the universities sit grey-haired liberal professors and their students who look backward and not forward. Who ensconce themselves in university towns and are unwilling to engage with most of America. To the detriment of liberal politics and the Democratic party.

Lilla gives the following prescription: The left needs to “start focusing attention on whatever barriers we have erected between us and the American public, and between us and the future. And we must begin by questioning the taboos — particularly the taboos surrounding identity — that have protected those barriers from scrutiny.”

Basically, Lilla thin that liberals need to focus more on winning than on change. One comes before the other.

Robert was disappointed in the book, though. Lilla is too intellectual and his focus is too philosophical and historical for Robert.  Lilla finds the roots of identity politics in European-style political romanticism, Marx, Emerson, SDS manifestos, blah blah. For Robert, the roots and mechanics of identity politics within universities, especially as practiced by students, must be more simple.

Incredibly, for Robert, there is no mention in the book of affirmative action policies as playing a role in the growth of identity theory and politics at universities and ultimately in mainstream US politics. For Robert, whatever your position on the correctness of affirmative action as a social tool, there is no denying the obvious truth (at least for Robert) that since the early 1970s these programs have been a significant cause of the focus on identity and the preoccupation with victimhood within higher education (Lilla calls it the Victimhood Olympics). It seems to Robert that genuine examination of merits and costs of affirmative action as a social tool is just the kind of taboo inquiry that Lilla wants liberals to engage in. But he does not touch it! At least not in this book.

First Day Hikes

From the California State Parks website.

This New Year’s Day 2018, California State Parks will participate in the 7th Annual First Day Hikes at parks across the state. This national-led effort encourages people to experience the beautiful natural and cultural resources found in the outdoors with a seasoned guide so that they may be inspired to take advantage of these treasures throughout the year.

Dedicated docents, volunteers and staff will show visitors the wonders of California’s state parks. Distance and rigor will vary per hike/activity, so visitors are encouraged to check out details of start times and description of hikes. For a complete list and detailed information on the California State Park’s First Day Hikes, please visit the First Day Hikes webpage.

Hikes in Marin include Mt. Tam and Angel Island.

Full list of hikes here.

MHD

Every decade or so, Robert likes to check in with the Monty Hall problem. You may have heard of it. If not, you can read all about it here at wikipedia.

From Wikipedia:

The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let’s Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975 (Selvin 1975a), (Selvin 1975b). It became famous as a question from a reader’s letter quoted in Marilyn vos Savant‘s “Ask Marilyn” column in Parade magazine in 1990 (vos Savant 1990a):

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

Vos Savant’s response was that the contestant should switch to the other door (vos Savant 1990a). Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their initial choice have only a 1/3 chance.

Many readers of vos Savant’s column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). The problem is a paradox of the veridical type, because the correct choice (that one should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true.

Robert likes to revisit the  problem from time to time in order to refresh his very thin grasp on Baysian probability. Each time he looks at the problem, he satisfies himself that he understands the solution.  But then, of course, he soon needs to figure it all out again.

Actually, Robert will say that of all the explanations of the problem, these images from Wikipedia are the best for him.

            

Car has a 1/3 chance of being behind the player’s pick and a 2/3 chance of being behind one of the other two doors.  The host opens a door, the odds for the two sets don’t change but the odds move to 0 for the open door and move to 2/3 for the closed door.

What is so absolutely awesome, Robert has come to learn, is that the vos Savant episode, which introduced the problem to a mass audience, occurred at the exact time that the field of behavioral psychology was coming into swing. You know, of course, that there have been a few recent Nobel Prize winners in that field.   The problem demonstrates exactly the kind of thing that behavioral psychologists like Daniel Kahnaman, et. al have been telling us for about twenty years.  That humans really suck at statistics. Especially, for example, Baysian probability.

So, it turns out that over the last ten years there have been some really neat papers trying to explain why we suck at the Monty Hall problem (since renamed by academics as the Monty Hall Dilemma (MHD)) and what we might do to get better at it.

For your nighttime reading pleasure:

Monty Hall’s Three Doors for Dummies, Morone and Fiore, 2008 read.

The Monty Hall dilemma in pigeons: Effect of investment in initial choice, Stagner, et. al, 2013 read.

Testing the limits of optimality: the effect of base rates in the Monty Hall dilemma, Herbranson and Wang, 2013 read.

Reasoning and Choice in the Monty Hall Dilemma (MHD): implications for improving Baysian reasoning, 2015, Tubau, et al.  read.

Benjamin Franklin’s Speech at the Conclusion of the Constitutional Convention

Robert is reading some of the papers in debate of the US Constitution, something he has not done since college, and, err, not well even then.

The first paper in the book he is reading is Benjamin Franklin’s Speech at the Conclusion of the Constitutional Convention, which, as the title suggests, are the comments that Ben Franklin gave in September 1987 at the closing of the convention where the first version of the Constitution was issued to the people for discussion and approval or rejection. Franklin was a little over 80 years old and, as we all know, an accomplished person of many attributes.

The main idea of Franklin’s speech is summed up in its first sentence.

I confess that I do not entirely approve of this Constitution at present, but Sir, I am not sure I shall never approve it.”

It is not clear whether Franklin was trying to be humorous.  But his point, it seems, was that the draft constitution was imperfect. He signed it because he trusted the men who put it together and he  heard no better alternatives during the convention.

Franklin’s speech did not give the draft high praise, that’s for sure. And the point was not lost on the first few antifederalist commentators who published statements on the draft Constitution in the newspapers.

“Z,” a writer of an essay in the Independent Chronicle of Boston in December 1787 should have titled his remarks “WTF.”  Z asks what federalist in his right mind would try to support the notion of a national government using the argument that Franklin, a great philosopher, did not entirely approve of the Constitution at the very moment he signed it? According to Z, that Franklin may, at one time or another, approve of the Constitution, gave the federalists faint support. And this was only so far as the federalists could rely on Franklin’s judgment at all.

The notion that Franklin was operating with a few loose marbles by the time of the conclusion of the constitutional convention appears to have been a favorite one of the antifederalists.