Statistics in the Social Sciences

I’ve always wondered whether the rigorous application of statistics is underutilized in the social sciences. This is less so a problem in economics, where the subject is, by nature, highly quantitative. But in fields like psychology, sociology, and political science, where a background in mathematics is not common (unlike for biology, chemistry, and physics), researchers can intentionally or, very often, unintentionally (this is a really good Economist article) produce wrong results by abuse or misunderstanding of statistical inference.

economist-research-statistics

As an onlooker whose training is in mathematics, I cannot help but to feel frustrated by the lack of numeracy in our “scientists.” The Economist article does a good job at showing how failure to understand statistical concepts leads to false results being published, even past peer review.

What triggered me to write this post was an assigned reading for a comparative politics class. In it, Adam Przeworski discusses the inherent selection bias in matching countries for experimentation. Noting that democracies have higher economic growth rates than authoritarian regimes, Przeworksi brings in the relevant data that democracies have a significant chance to die off when faced with economic failure whereas authoritarian regimes are not as affected. Hence, observing that democracies have higher growth rates does not signify that democracy leads to economic growth, but rather that economically failing democracies are not observed because they tend to disappear.

“What we are observing here is what the statistical literature calls ‘selection bias.’ Indeed, I am persuaded that all the comparative work we have been doing may suffer potentially from selection bias.”  (p. 19, stable JSTOR link)

In context of a comparative politics theory symposium, this makes a lot of sense to state. But the phrasing is really interesting to a math person: selection bias is a given, and is one of the tools we use to analyze anything. My instinctual reaction to the reading was “Duh, obviously there is selection bias.” While I am sure the field of comparative politics is more aware of selection bias than Przeworski makes it appear to be, the fact that Przeworski framed it as such (“what the statistical literature calls ‘selection bias’”), as if to imply that the formal tools of statistical inference are generally beyond the scope of comparative politics theory, is a bit unnerving.

Przeworski, Adam in The Role of Theory in Comparative Politics: A Symposium, World Politics, Vol. 48, No. 1 (Oct., 1995), pp. 1-49.

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Dismissing Things Without Evidence

evidence

Superstition

In middle school, I used to stay up late and listen to a radio talk show called Coast to Coast AM. The show dealt with many topics, focusing on the supernatural or paranormal. While occasional talks were on real science (they brought on Michio Kaku as a guest), the vast majority consisted of things like psychic powers, auras, numerology, UFOs, alien abductions, crop circles, Bigfoot, astrology, conspiracy theories, the Illuminati, the New World Order, collective consciousness, spoon bending, ghosts, near-death experiences, quantum healing, astral projection, clairvoyance, and other wacky phenomena.

Of course, I have no problem with the expression of unpopular views, and I have written several times in support of their expression. It’s not like Coast to Coast AM is being promoted in the school curriculum, at which point I would take issue. However, this particular category of beliefs, namely superstition, is generally harmful because it promotes thinking in a highly irrational and naive way. Especially in the social media age, we cannot afford as a society to succumb to believing in whatever pops up on our newsfeeds.

But surely this is just a tiny minority of people, right? This is the typical response I get when I speak out against superstition, and it seems sensible because I usually talk about this with highly educated people who automatically dismiss this kind of stuff. However, the numbers for the general populace may be discouraging. From a December 2013 Harris poll (the link is broken so here is a Google cache link), the numbers believing were: 42% in ghosts, 36% in UFOs, 29% in astrology, 26% in witches, and 24% in reincarnation. This is not including religious-based superstitious beliefs, with much higher numbers such as 72% in miracles, 68% in angels, 58% in the devil, and 57% in the virgin birth.

I would usually criticize religion more than superstition, but in this post I make an exception. Even as religious belief is on the decline (see numbers in the Harris poll or also in a Pew Research poll), superstition is on the rise. According to the Harris poll, only 24% of matures (68+) believe in ghosts, but 44% of echo boomers (18-36) do. Astrology increases from 23% to 33%, and witches increase from 18% to 27%, when you go from the oldest to the youngest generation.

The Role of Evidence

Every belief mentioned in the previous section shares something in common: there is zero credible evidence supporting them. Of course, those who believe such things often think they have evidence, and this is almost always explained by confirmation bias, selection bias, or being simply misled. Only when you get to some forms of religious belief do you run into people who claim they do not need evidence at all (“I don’t need evidence, I have faith”). Fortunately, when debating superstitious people as opposed to religious people, you at least agree that you need evidence, but might differ as to what constitutes evidence. (A conspiracy theorist will shower you with evidence.)

In the paranormal, it is especially easy to construct signal out of noise, or beliefs out of nothingness. Take something like astrology: Someone writes an extremely vague, all-encompassing description of life, and it generally matches anyone. The reason it seems to fit you specifically is that the vague wording (“something important recently happened in your life”) triggers several biases:

  • you are selectively looking for things that fit the description (selection bias),
  • you ignore things that don’t fit (confirmation bias),
  • you find something that you didn’t originally view as important, but now it must be important because of the prediction (circular reasoning), and
  • you note the importance of something long after the fact (hindsight bias).

The rational person is not immune to biases, but at least is aware of them and tries to look at evidence from a more objective perspective. After all, systematic analysis of evidence is the main criterion that separates real science from pseudo science.

A Priori Dismissal

Suppose you read a story in the news today about a new Bigfoot sighting. How much evidence would you need to dismiss it? I would claim it is almost none. You would realize the probability of the existence of Bigfoot is so low in the first place (well under 1%, possibly 0%), that it would take a significant amount of evidence to convince you otherwise. The burden of proof is on the sighter. Given the advent of universal smartphone ownership, it would seem easy to simply snap a picture of Bigfoot when you saw one. In this case, you do not need evidence against to dismiss it.

The point is, if a Bigfoot article appeared in the news today, then without reading any of it and without having any evidence of its being a hoax, you could safely dismiss it as a hoax, as it has been every time. Again, I am not saying that every person who has sighted Bigfoot did so to perpetuate a hoax—I think some people genuinely saw something they personally couldn’t explain. However, there’s quite a leap of logic to go from “I don’t know what I saw” to “It was Bigfoot.”

Imagine that you find the following title in today’s paper: “Scientists find conclusive proof of Flat Earth theory.” Without having to be a scientist yourself, you have enough intelligence (hopefully) to conclude that the article is wrong, even without reading a word of it.

Some friends I talk to have actually pointed out that I am perhaps too dismissive. For instance, last year this Carrie promo video made its rounds on Youtube:

If you don’t want to watch it, basically a hoax is set up so that someone appears to be using telekinetic powers in a cafe, and onlookers are fearful and in a state of shock.

We discussed what we would have done in that situation. Everyone else said they would have been scared !@#&less in that scenario, but I said I would have known it was a hoax and thus have stayed calm. Of course, nobody believed me. Given this post, judge for yourself.

Hitchens’ Razor

“What can be asserted without evidence can be dismissed without evidence.”

This philosophical tool allows you to dismiss many kinds of statements. If someone just claims, “There is a leprechaun in my backyard,” you can dismiss it even if you have never met this person before and have never been to their backyard.

Hitchens’ Razor differs slightly from the idea in the previous section: the aversion to believing in Bigfoot, even if there is “evidence” in the form of extremely shaky and blurry cam, comes more from statistical improbability than from philosophical concern. Christopher Hitchens’ statement applies more to abstract claims that sometimes cannot be justified in the physical world, i.e. religious claims.

The title refers to both interpretations of “without evidence”: dismissing something that has no evidence for, and dismissing something that has no evidence against. Namely, if there is no evidence for, you do not need evidence against.

More relevant to purely superstitious claims that can be tested is Carl Sagan’s “razor”:

“Extraordinary claims require extraordinary evidence.”

It is generally true in real life that the more absurd a claim is, the more justification it requires. If you claim the Malaysian flight 370 is on Mars, you better have some very convincing pieces of evidence supporting it.

Overall, I just ask that we think more rationally, especially in response to the media and to questionable stories. We simply cannot afford to slip back into an age of superstition.

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Noam Chomsky on Postmodernism

Since I’ve been thinking about postmodernism recently, I thought to share this fascinating interview from the youtubes. The most unfamiliar point that Chomsky brings up is the story about Bruno Latour and the ancient Egyptian tuberculosis death (read more about it here). Basically, Latour argued that since tuberculosis was not discovered until the era of modern medicine, it could not have existed in ancient Egypt! So much for constructed knowledge.

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5 Historical Documents on Universal Truths

A couple of weeks ago, I wrote a post criticizing the strong form of moral relativism, namely the idea that nobody, or no culture, is right or wrong. In this post, to continue the objective vs subjective truth discussion, I will look at five historical documents that have explicitly acknowledged universal truths. Moreover, all of these documents proclaim non-empirical truths, i.e. they are not documents of science that can be tested by the scientific method. (I include this caveat because it’s easy for a relativist to acknowledge that science can have universal truths but then claim arbitrarily that other subjects work differently than science and shouldn’t have universal or objective truths. So, I am addressing the claim that nonscientific truths cannot be universal.)

1. Euclid’s Elements (~300 BC)

euclid-elements

The Elements is one of the most influential books of all time, not just in mathematics but in the entire Western way of thinking. For this post, math is considered separate from science, in that math does not operate by the scientific method. It instead operates by a strictly logical method that was largely formalized by Elements. The steps of this deductive method, in contrast with the inductive scientific method, consist of:

  1. Listing axioms, or self-evident truths.
  2. Listing basic assertions, which also should be self-evident.
  3. Manipulating the axioms and assertions to obtain theorems, which are the end result.

(For a list of the axioms and assertions, see the wiki page.)

In Elements, the first “postulate,” or axiom, is that a straight line can be drawn from one point to any other point. This seems obvious enough. Clearly if we imagine two points, we can also imagine a straight line between them. Another seemingly obvious claim is the last “common notion,” or assertion, which states that the whole is greater than the part.

But to what extent are these axioms really self-evident or universal? On what basis do we have to judge their universality or objectivity? The last axiom, for instance, known as the parallel postulate, is not even true in certain geometries. These are questions that have been debated for centuries

2. The Declaration of Independence (1776)

Trumbull-Declaration-of-independence

“We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.”

Note that “We hold these truths to be self-evident” sounds like something Euclid would have written two thousand years earlier. In fact, the similarity is likely more than coincidence. Thomas Jefferson was a reader of Euclid, as evidenced in a letter to John Adams: “I have given up newspapers in exchange for Tacitus and Thucydides, for Newton and Euclid; and I find myself much the happier.” Furthermore, the Declaration reads much like a mathematical proof in the style of Euclid:

  1. The introduction (“When in the Course of human events… a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation”) establishes the want for the “dissolution of political bands” and then acknowledges that they need to declare the causes for it, i.e. the need for a proof.
  2. The preamble establishes the self-evident truths.
  3. The indictment contains the various violations by the King of the self-evident truths.
  4. The denunciation gathers the above together and says a “therefore,” showing that the proof has been concluded: “We must, therefore, acquiesce in the necessity, which denounces our Separation, and hold them, as we hold the rest of mankind, Enemies in War, in Peace Friends.”
  5. The conclusion notes that the proof has been completed; therefore, they will act on the result of the proof: “That these united Colonies are, and of Right ought to be Free and Independent States; that they are Absolved from all Allegiance to the British Crown.”

More can be found in a talk given by Noam Elkies. The interesting thing is to note how universal these self-evident truths are. Is it objectively true, for example, that all men are created equal? Is this view just a Western and/or Enlightenment construction? I would argue it is not (this is for a different post).

3. Pride and Prejudice (1813)

pride-and-prejudice

The reason I have included Pride and Prejudice over any other work of literature is the opening sentence: “It is a truth universally acknowledged, that a single man in possession of a good fortune must be in want of a wife.”

Yet again, we have a declaration of universal truth, though this time used in fiction to establish the setting for the story. In contrast with its use in the Elements and the Declaration of Independence, universal truth is used by Austen in a more sarcastic manner.

Indeed, literature in general tends to question truths that are universally held. In this context, Pride and Prejudice is special because it acknowledges this explicitly. The statement, of course, is patently false, but it raises the question of whether there are any universal truths in social relations. And what would “universal” even mean? If something applied to a certain group in early 19th century England but not to anyone else, is it still universal?

4. The Communist Manifesto (1848)

Karl_Marx

Back to serious documents, we have the strong claim by Marx and Engels that “The history of all hitherto existing society is the history of class struggles.” The signifier is the word “all,” which again proclaims a universal truth, at least universal to a sufficiently large breadth (“hitherto existing society”). By the nature of their argument, it should not be an absolute universal in the sense of applying to all time: success would mean having a classless society, and therefore, class struggles wouldn’t exist.

This example and Austen’s example are both social/historical universals. Marx argues that history can be understood by looking at class struggles, but again, on what basis can we support this? The modern view is that history is complex and can be partially understood through many different means, not just on modes of production.

On the other hand, Euclid’s is a mathematical universal, and Jefferson’s is a moral universal, in acknowledging the rights of man.

5. The Universal Declaration of Human Rights (1948)

Flag_of_the_United_Nations

This United Nations Universal Declaration of Human Rights is among the most significant documents of the twentieth century, and it is also based on presumed universal truths. Its preamble consists of seven “whereas” clauses to establish several self-evident assertions much like in the introduction to the US Declaration of Independence. These are:

“Whereas recognition of the inherent dignity and of the equal and inalienable rights of all members of the human family is the foundation of freedom, justice and peace in the world,

Whereas disregard and contempt for human rights have resulted in barbarous acts which have outraged the conscience of mankind, and the advent of a world in which human beings shall enjoy freedom of speech and belief and freedom from fear and want has been proclaimed as the highest aspiration of the common people,

Whereas it is essential, if man is not to be compelled to have recourse, as a last resort, to rebellion against tyranny and oppression, that human rights should be protected by the rule of law,

Whereas it is essential to promote the development of friendly relations between nations,

Whereas the peoples of the United Nations have in the Charter reaffirmed their faith in fundamental human rights, in the dignity and worth of the human person and in the equal rights of men and women and have determined to promote social progress and better standards of life in larger freedom,

Whereas Member States have pledged themselves to achieve, in co-operation with the United Nations, the promotion of universal respect for and observance of human rights and fundamental freedoms,

Whereas a common understanding of these rights and freedoms is of the greatest importance for the full realization of this pledge….”

These set up the basis for the 30 articles, which are the “self-evident” truths or axioms. The first three articles, for example, are:

“Article 1. All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.

Article 2. Everyone is entitled to all the rights and freedoms set forth in this Declaration, without distinction of any kind, such as race, colour, sex, language, religion, political or other opinion, national or social origin, property, birth or other status. Furthermore, no distinction shall be made on the basis of the political, jurisdictional or international status of the country or territory to which a person belongs, whether it be independent, trust, non-self-governing or under any other limitation of sovereignty.

Article 3. Everyone has the right to life, liberty and security of person.”

Note that the UN did not feel the need to prove any of these. They were simply obvious or self-evident. The theorems, however, are all implicit. It is implied that if these axioms are violated, the UN has the authority to intervene on behalf of human rights.

We could spend a long time debating which particular articles are true or false, but the big picture question is, Can any of them be objectively true? Is the discussion of them even meaningful? The intuitive answer is yes.

To be continued…

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The Flaming Laser Sword

I recently stumbled upon Mike Alder’s article “Newton’s Flaming Laser Sword, Or: Why Mathematicians and Scientists don’t like Philosophy but do it anyway.” It was quite relevant to my view of philosophy. From a mathematical and scientific perspective, plenty of philosophical issues seem strange.

Alder uses the example of when an unstoppable force meets an immovable object. From a scientific perspective, the thought process is something like, “We’ll test it: if the object moves, then it wasn’t immovable, and if it doesn’t, then the force wasn’t unstoppable.” Anyway, this is something I might talk about more later on.

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The Fountainhead

TheFountainhead

This has been a rough read. I’ve had a relatively easy semester, but every time I tried to read this book, I invariably got distracted. I don’t know if it says more about this book or the Internet.

The Fountainhead left me with more questions than answers. I’ve heard mixed opinions of Ayn Rand’s works, and this book was recommended to me twice, both times over Atlas Shrugged. I cannot comment on the comparison yet.

I’m really not sure how to react to what I just read. On one hand, I agree with the exaltation of the “prime mover” and the condemnation of the “second-hander.” But I cannot reconcile that with the rejection of altruism (though the concept in the book is slightly different from our contemporary notion of altruism).

From Howard Roark’s final courtroom speech (emphasis added):

Throughout the centuries there were men who took first steps down new roads armed with nothing but their own vision. Their goals differed, but they all had this in common: that the step was first, the road new, the vision unborrowed, and the response they received — hatred. The great creators — the thinkers, the artists, the scientists, the inventors — stood alone against the men of their time. Every great new thought was opposed. Every great new invention was denounced. The first motor was considered foolish. The airplane was considered impossible. The power loom was considered vicious. Anesthesia was considered sinful. But the men of unborrowed vision went ahead. They fought, they suffered and they paid. But they won.

I fully agree up to this point. However, the speech continues:

No creator was prompted by a desire to serve his brothers, for his brothers rejected the gift he offered and that gift destroyed the slothful routine of their lives. His truth was his only motive. His own truth, and his own work to achieve it in his own way. A symphony, a book, an engine, a philosophy, an airplane or a building—that was his goal and his life. Not those who heard, read, operated, believed, flew or inhabited the thing he had created. The creation, not its users. The creation, not the benefits others derived from it. The creation which gave form to his truth. He held his truth above all things and against all men.

His vision, his strength, his courage came from his own spirit. A man’s spirit, however, is his self. That entity which is his consciousness.

To think, to feel, to judge, to act are functions of the ego. The creators were not selfless. It is the whole secret of their power—that it was self-sufficient, self-motivated, self-generated. A first cause, a fount of energy, a life force, a Prime Mover. The creator served nothing and no one. He lived for himself.

And only by living for himself was he able to achieve the things which are the glory of mankind. Such is the nature of achievement.

I’m not sure whether I agree that achievement is solely for oneself.

Later on, Roark talks about the parasitic nature of second-handers, that “the parasite faces nature through an intermediary.”

Men have been taught that the highest virtue is not to achieve, but to give. Yet one cannot give that which has not been created. Creation comes before distribution—or there will be nothing to distribute. The need of the creator comes before the need of any possible beneficiary. Yet we are taught to admire the second-hander who dispenses gifts he has not produced above the man who made the gifts possible. We praise an act of charity. We shrug at an act of achievement.

The statement that “the need of the creator comes before the need of any possible beneficiary” is debatable, but I definitely agree that in our society, the creator is undervalued compared to the gift dispenser.

On morality and altruism from Rand’s framework:

The ‘common good’ of a collective—a race, a class, a state—was the claim and justification of every tyranny ever established over men. Every major horror of history was committed in the name of an altruistic motive. Has any act of selfishness ever equaled the carnage perpetrated by disciples of altruism? Does the fault lie in men’s hypocrisy or in the nature of the principle? The most dreadful butchers were the most sincere. They believed in the perfect society reached through the guillotine and the firing squad. Nobody questioned their right to murder since they were murdering for an altruistic purpose. It was accepted that man must be sacrificed for other men. Actors change, but the course of the tragedy remains the same. A humanitarian who starts with declarations of love for mankind and ends with a sea of blood. It goes on and will go on so long as men believe that an action is good if it is unselfish. That permits the altruist to act and forces his victims to bear it. The leaders of collectivist movements ask nothing for themselves. But observe the results.

I’m not as pessimistic about humanitarian efforts, and it’s important to note that in the 70 years since the book was written, there have been many changes to society. Among them, just the Internet has caused us to think much differently about others, and I’d like to continue thinking about what the correctness or relevancy of ideas in this book applies today.

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Out of Context

When talking about religion, I often get the “out of context” objection. It’s hard, for instance, to understand what the Bible says about women without bringing up 1 Timothy 2:12: “I do not permit a woman to teach or to have authority over a man; she must be silent.” And it’s hard to talk about morality without this passage:

As you approach a town to attack it, first offer its people terms for peace.  If they accept your terms and open the gates to you, then all the people inside will serve you in forced labor.  But if they refuse to make peace and prepare to fight, you must attack the town.  When the LORD your God hands it over to you, kill every man in the town.  But you may keep for yourselves all the women, children, livestock, and other plunder.  You may enjoy the spoils of your enemies that the LORD your God has given you. (Deuteronomy 20:10-14)

But of course, it’s just taken out of context so all the violence and rape is fine. Here is a hilarious YouTube video by NonStampCollector on this topic.

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