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Philosophical and Ethical Issues in Statistics: A Course and Intro Book Chapter

Some people approved of me teaching this course.

No one stopped me from writing this book chapter.


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Episode 13 Brian Zaharatos, PhD

Thanks to Ted Conti for a great conversation!

The Mountain Geek

Brian Zaharatos has is certainly a man of many interests. He has managed to take one of those to the finish line with a Doctorate in Applied Mathematics and Statistics. There is a second point of interest also compelling and keeps him thinking and more than likely he will someday, not to far away, have a second PhD. In  the meantime he’ll keep stuffing young minds with the wonders of applied math.

Here is a link to Brian’s Blog

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Phone-Free Spaces

Last night I went to a comedy club that required guests put their cell phones into a case made by Yondr. Yondr cases lock your phone inside, and can only be opened by a special device. The idea here is to create “phone-free spaces” where people can enjoy themselves without the temptation to check their phone, and performers can perform without seeing a sea of smartphone lit–and barely paying attention–faces.

It is pretty clear that we are addicted to much of our technology. We check our phones, on average, 150 times per day. We are on Facebook (presumably mostly on our phones), on average, for a sixteenth of our time awake, more time than we spend exercising or reading, and almost as much time as we spend eating. I often feel actual shame when I use my phone in public, but sometimes that doesn’t deter me from doing it. So, being forced to not use my phone at a public venue is great (though usually I am good about not using my phone at such events). Perhaps these venues are playing a role in scaling back our use of our devices. I surely welcome that.

At the same time, I can imagine that there might be negative consequences of products like Yondr. One obvious negative consequence might be the ability to which we are able to respond to emergencies; in certain situations, such as recent attacks/shootings at concert venues, quick texts or phone calls might save lives. It also seems likely that certain personal emergencies might be harder to respond to when one’s phone is sealed. These consequences are pretty clearly negative. The relevant question seems to be: are these negative consequences outweighed by the value–to performers and guests–of fewer phone interruptions? I’m not sure.

When talking with friends about the consequences of a phone-free space, one reasoned as follows: years ago, no one had cell phones, and so we just weren’t able to respond to emergencies easily. So, phone-free spaces are just spaces from 20 years ago. This reasoning might be initially compelling. But the underlying assumption here is that, because something was acceptable years ago, it is (or can be) acceptable now. This assumption seems clearly false. (Many) Years ago, dental work was much more painful than it is now, and our acceptance of that level of pain then says little about our acceptance of that level of pain now. Really, I think the conversation has to be about how weighing benefits and harms. But I have no idea which side wins.



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Poor Statistical Reasoning On Last Week Tonight?

Image result for john oliver vaccines

On a recent episode of John Oliver’s Last Week Tonight, Oliver discussed the growing problem of parents choosing not to vaccinate their children (watch for free here) . It’s an interesting episode in its own right, but especially interesting is the conversation that starts at 12:00, where the discussion turns to whether the mercury in vaccines is harmful to people receiving the vaccine. In what follows, I point to what I believe to be a flaw in Oliver’s (and a guest scientist’s) reasoning about the absence of a link between mercury in vaccines and autism. It’s important to note that this criticism is in no way an endorsement of the idea that such a link exists.

To study whether the mercury in vaccines is harmful to people receiving the vaccine, we can, of course, imagine a well-crafted clinical trial designed to test whether mercury is harmful. Such a study would have a null hypothesis that “mercury in vaccines is not linked to X”, where X might be autism in infants, or some other harm to humans receiving the vaccine.

Whenever a scientific claim is being testing using statistical significance testing (as many are), the null hypothesis is assumed, and calculations, e.g., of a p-value, are done under that assumption. Consequently, when one fails to reject the null hypothesis, logically, one cannot claim that the null hypothesis is true; further, whether failing to reject the null hypothesis constitutes evidence that the null hypothesis is true is difficult to assess. (Reasonable people disagree on this point.  See the debate about inductive support vs. corroboration here.) Strictly speaking, all that one can say is that one has not found evidence against the null hypothesis.

This creates a problem for Oliver and researchers of vaccines, which is pointed out by Rep. Dan Burton. Burton makes a claim about our ability to prove (or obtain evidence in favor of) “null hypotheses”. Burton and Oliver couch this in terms of “proving a negative” (which, as this paper points out, isn’t really the correct characterization of the problem).

“I have yet to find any scientist who will say that there’s no doubt that the mercury in vaccines does not contribute to autism.  Now they’ll say that there’s no scientific evidence, there’s no studies or anything that proves that yet. But turn that around. There are no studies that disprove it either.”

Oliver attacks Burton pretty harshly. More eloquently, Seth Mnookin describes the way that scientists purportedly reach conclusions about the truth of null hypothesis here:

“Science and English are not really the same language. And so, when a scientist says we have no evidence that there’s a link between vaccines and autism, what they’re really saying is we are as positive as one can humanly be that there’s no link.”

This exchange, in conjunction with what we outlined about hypothesis testing above, leads to an interesting problem. If null hypotheses are assumed, then failing to reject a null hypothesis doesn’t seem to give evidence for the null. So, on what basis are scientists “as positive as one can humanly be that there is no link”?

I’m not sure. But, I have a hypothesis. Many scientists are Karl Popper style falsificationists (and in some cases are so unreflectively). The reasoning used in science-as-falsification is similar to the reasoning used in hypothesis testing: assume a theory T to be true, and run experiments to attempt to falsify it. If evidence is gathered that is in discord with T, then we might reject T. The problem here is, again, that was assumed to be true, and no evidence has been gathered in favor of it. Popper thought that, if passed enough severe testing, then was “corroborated”. My hypothesis is that many scientists think that being corroborated actually means that has gained inductive support. That is, scientists think that corroboration of means that is more likely to be true. But Popper did not believe that corroboration meant inductive support. Failing to reject and believing to be (likely) true had too much of a logical leap for Popper. I’m not sure how to get around this leap. But I think that, if we’re being honest, unlike Mnookin and Oliver, we have to admit that the leap exists. That is not to say that mercury in vaccines is linked to any condition (e.g., autism). But, it is to say that, if you are “as positive as one can humanly be that there’s no link” between the two, your confidence extends much further than empirical evidence would allow. That might not be a terrible thing, but it’s something we should acknowledge.

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A Message to My Fellow Bernie Supporters

Tonight, Bernie Sanders confirmed his support for Hillary Clinton at the Democratic National Convention. If you are an ardent supporter of Bernie, like I have been for years (I’m proud to say that, on November 10 2014, I signed a petition for Bernie to run for president), you are surely disappointed.

Unlike Sarah Silverman, I don’t have an condescending remarks for you. If you have supported Bernie Sanders, you are likely progressive, smart, and beautiful. We are dignified human beings worthy of making our own choice about whom we support. If you can’t, in good conscience, vote for Hillary Clinton, don’t. Millions of people have fought and died so that you can vote; do not be cowed into doing something with your vote that you are not comfortable with. Do not give in to fear. There is nothing more inspiring than someone being principled with their decisions, as Killer Mike suggests he will be.

I know that the only person that I have the conscience to vote for is Bernard Sanders. I know that the only person my logical beautiful black mind will allow me to vote for is Senator Bernie Sanders.–Killer Mike

The choice we are faced with is terrible, and on my view, it is the fault of the Democratic Party for putting us here. They pushed a candidate that is weak because they felt she deserved it. Do not let anyone tell you that it will be your fault if Trump becomes president. Blame the party that didn’t have the prudence to go in a direction that would more likely lead to success.

At the same time, if you believe that Hillary Clinton will carry on with some of Bernie’s message (some evidence suggests that she will), then don’t feel ashamed of voting for her to defeat Donald Trump. Bernie is suggesting that we do, and a Trump presidency would be an absolute disgrace.

The good news here is that the presidency isn’t everything and there are many things that you can do to help make Bernie’s beautiful vision a reality.

“What matters most is not who is sitting in the White House, but “who is sitting in” — and who is marching outside the White House, pushing for change.”–Howard Zinn

Make your voice heard; join the movement to elect a brand new congress; volunteer for a local campaign; make calls for Jill Stein (she very likely won’t win, but supporting her campaign doesn’t have to be about her winning); join a march or protest. Just do something. Martin Luther King Jr. was worried about moderates–he said that they are a greater obstacle to achieving justice than extremists who actively seek to thwart our efforts. So, do not be moderate; waiting for justice is a privilege, and many don’t have the luxury of waiting for incremental change. My message to all of you is: stay brave and carry on.

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Want to Produce Better Scientists? Teach them Philosophy.

This week, the statistics blog 538 reposted an article titled “Not Even Scientists Can Easily Explain P-Values” on Facebook. The author suggests that, even though many scientists are able to give the mathematical definition of a p-value, many are unable to explain it to nonscientists in a meaningful way. Commenters on the post were quick to suggest that, really, this isn’t a problem for scientists at all. For example, one writes:

The problem seems to be the demand that p-values be “intuitive” to lay people. They’re not going to be. We don’t go to graduate school for years to learn concepts that are intuitive to lay people. Our intuitions develop far beyond the point where they were at the beginning!

This commenter seems to be suggesting something that several others have echoed: in fact, scientists do know how to define and interpret p-values; the real issues are that (some) scientists aren’t able to explain difficult concepts to nonscientists, and have no obligation to give such an explanation.

If scientists use p-values in their work, do they (1) have an obligation to know their definition? (2) An obligation to know how to give a proper interpretation? (3) An obligation to give a proper explanation to the public? (4) An intuitive explanation? Although I have views on questions (3) and (4), I want to focus on (1) and (2) in this post.

I think we’d all agree that the answer to (1) is ‘yes’, and the 538 suggests that most (or all) scientists asked could give the correct mathematical definition.

A p-value is the probability of obtaining a statistical summary of the data (e.g., the sample mean) that is at least as extreme as the one actually computed, assuming that the null hypothesis is true.

As another 538 post points out that this definition is about as “clear as mud”. Several issues need to be expanded upon, including what “at least as extreme” means, what a null hypothesis is, how we calculate probabilities under the assumption that the null hypothesis is true, and which statistical summaries of data are best in different contexts. All of these expansions are possible given some basic knowledge of probability theory and inferential statistics methodology. But these issues don’t really give a satisfying answer to the question “what does p-value tell me about my statistical and research hypotheses?”

To answer this question, we need to know more probability theory and statistical methodology, but we also need to understand how to think critically and reason carefully. We need to interpret the mathematical definition above in a way that makes no unjustified logical leaps. There is much evidence that doing so is difficult. Misinterpretations of p-values are so common that the American Statistical Association (ASA) has released a statement on their misuse and Wikipedia has a page dedicated to misunderstandings of p-values. Several professional and academic organizations misinterpret p-values in official documents (538 points here, here, here, and here; some extras here, and here).

These links suggest that there are several common misinterpretations. Here are some common ones (note, these are all wrong!):

  • A p-value gives the probability that the null hypothesis is true.
  • A p-value is the probability that the data were produced by chance alone.
  • A low p-value (a “statistically significant result”) means that the finding is practically important.
  • A p-value provides information about replicability (e.g., that one minus the p-value is the reliability of the result).

Given that p-values are widely used in scientific studies–one researcher estimated that p-values have been used in at least three million scientific papers–the fact that academics, scientists, students, etc., have trouble interpreting them is worrisome. It also leads to bad consequences. For example, Stephen T. Ziliak and Deirdre N. McCloskey argue that misinterpretations of p-values leads to a heavy reliance on statistical testing, which can lead to very undesirable consequences.

It seems clear that, contrary to what we may think, many scientists don’t know how to interpret p-values. How might we fix this issue? An important component here seems to be that most of our statistics education focuses on technical aspects, such as important mathematical results and learning how to program. Of course these topics are important, but what makes statistics such a beautiful area of study is that, at once, it is technical, highly theoretical, highly practical, and philosophical. In an age driven by STEM education, it is important that we not overemphasize the technical by not acknowledging the philosophical. As Heidegger would say, thinking exactly might be fashionable, but thinking rigorously is better.* Statistical analyses can be nuanced. Philosophy teaches essential critical thinking and logic skills that motivate us to ask the right questions and seek creative solutions. Philosophy, and especially critical assessments of scientific methodology, such as those studied in a basic philosophy of science course, are wonderful supplements to the standard statistics curriculum.


“Exact thinking is never the most rigorous thinking, if rigor receives its essence otherwise from the mode of strenuousness with which knowledge always maintains the relation to what is essential in what is. Exact thinking ties itself down solely in calculation with what is and serves this exclusively.”–Martin Heidegger

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My Case for Bernie Sanders

I didn’t become involved in politics until just a few years ago. For so long, I thought that, by not being involved, and by not addressing messy questions about power, inequality, war, economics, ethics, etc., I could somehow stay politically neutral. But, a few years ago a good friend introduced me to the American Historian Howard Zinn. Zinn makes a powerful case for the idea that political neutrality is impossible.

If you think you are being neutral by doing nothing, you are deceiving yourself. You are not being neutral. You are collaborating with whatever forces are dominant in a society, collaborating with whatever trends are already taking place in society. There’s no such things as neutrality in a world which already is subject to many many different kinds of forces, and so many of them malevolent.

So, if Zinn is right, and we can’t be neutral, where shall we start? What sort of political positions should we favor, and what sorts of political positions ought we denounce? My attempt at an answer to this question begins by identifying in what ways a society might be judged. At least according to some, a society will not be judged by how it treats the rich and the privileged, but by how it treats the poor, the marginalized, the underprivileged. In my view, it is how we care for these people that illuminates something profound about our cultural character.

Thus, when I think of who earns my vote, especially my vote for president, I first ask myself whether I think candidate X would represent people on the margins. It seems overwhelmingly clear to me that, of any candidate running for president, Bernie Sanders would represent people on the margins with dignity, character, and authenticity. In what follows, I try to justify why Bernie Sanders has my vote; not because I think that he will be an advocate for me, but because I believe that he will be an advocate for those who need the scales tipped in their favor.

Black people in America have faced and continue to face obstacles on the road to justice. Many are marginalized and disenfranchised by a criminal justice system that treats you better “if you’re rich and guilty than if you’re poor and innocent,” better if you’re white and guilty than if you’re black and innocent.  I don’t like Bernie because I’m white and I think that he has the interests of white people in mind (though, he does). I like Bernie because, if I were black, I would think that he has my best interests in mind.

Why do I think this? Well, consider the following from an interview with Howard Zinn:

The civil rights movement accomplished a good deal by beginning to remove some of the important social barriers. What it did not remove was the barrier of class, the barrier of economic injustice.

Martin Luther King recognized this. That’s why toward the end of his life he began working for economic rights for Black people. The trajectory is one which took a very sharp upturn in the 1960s and which then has, you might say, settled down into a situation which is not going to change very much until there’s a change in the economic system of this country. So long as we have an economic system based on profit and corporate wealth, there’s going to be an impoverished class. And so long as there is an impoverished class, I’m talking about the 40 million people who don’t have health care, the 20% of children in the country who grow up very, very poor. So long as we have an impoverished class, Black people will be disproportionately in that class. The trajectory has reached a point where it is not going to go up much further unless we have economic changes which benefit not just Black people but White people, fundamental change in our economic and social system.

It’s no coincidence that Zinn seems to be in agreement with African American leaders like Cornel West and Killer Mike about the fact that Bernie’s economic plans, better than any other candidate’s plans, would carry on the legacy of Martin Luther King Jr. The fight for economic equality is intimately tied to the fight for racial equality. Bernie knows this; sometimes it sounds like he’s reading The People’s History on the campaign trail!

Further, I don’t like Bernie because I’m straight and I think he cares about the well-being of straight people (though, he does). I like Bernie because, if I were LGBT, I would think that he has my best interests in mind. Bernie has been fighting for gay rights since at least the early 70s. There’s nothing wrong with Hillary Clinton (or Barack Obama, or anyone else, for that matter) evolving on the issue of gay rights; it’s better to evolve than to stick to an immoral and oppressive position. But the fact that Bernie has been consistent for so long on gay rights is a testament to his character, his judgement, and his leadership ability. He was for gay people when it was extremely unpopular, because he knew it was the right thing. That’s character. That’s authenticity.

Further, I don’t like Bernie because I’m a male and I think that he has the interests of men in mind. I like Bernie because, if I were a woman, I would think that he has my best interests in mind. Bernie’s record on woman’s issues–from paid sick and maternity leave, to calling for an increase in support to planned parenthood–is about as good as can be.

I mean no disrespect to Hillary Clinton when I say that I think Bernie Sanders will do a better job of representing the interests of the poor, the marginalized, the disenfranchised, and the oppressed. Some might argue that, although Clinton is less progressive, inauthentic to some degree, etc., she is, in a fact, “a progressive that gets things done.” I think this claim is deeply mistaken. It seems to me that the only person that conservatives hate more than President Obama is Hillary Clinton. If she becomes president, conservatives will try to impeach her for the email “scandal” and the Benghazi “scandal” on the first day. They’ve said as much already. Do we have any reason to think that they will work with her any better on anything than they did with Obama? Absolutely not. Bernie Sanders is far less contentious, and has a strong record of working with republicans to best serve the interests of the American people.

Finally, but importantly, the virtues of being a “pragmatic progressive” are, in my view, far overblown. Pragmatism results in slow and careful change–the kind of change that Dr. King deeply criticized white moderates for supporting in the face of oppressive conditions for African Americans in the deep south. Real change is affected by the people committing profound acts of heroism, honesty, protest, etc., not by a “pragmatic progressive” cautious of every next move. Such next moves, as careful as they may be, are likely to be squashed by the flip side of the same power structure coin that elected the pragmatic progressive. As Zinn claims, “What matters most is not who is sitting in the White House, but ‘who is sitting in’– and who is marching outside the White House, pushing for change.” If you want real change in this country–change from our system of capitalist oligarchy, with some democratic representation–you have to be very skeptical about whether Hillary Clinton will conjure up the sort of activism that Zinn is speaking of. In fact, Bernie’s entire platform is based on the idea that, when millions of people become involved in the political process–including people who, up until now, have been fed up with business as usual–we can actually make this country serve the poor and marginalized, rather than the rich and privileged.

That’s why Bernie gets my vote. And that’s why I hope he gets yours, too.

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