I was catching up on my Radiolab episodes the other day, and I listened to one called ‘Worth’.  In the way of Radiolab, it was a collection of stories loosely organized around a theme, in this case, the monetary value of things not normally valued in those terms: the environment, human lives, or time, in particular, time in your life.

The take-home message of this last was that, when developing and marketing drugs, we, both as individuals and as a society, should think about how much additional years of our lives are worth.

If you were 75 years old, and had been diagnosed with a terminal illness, and there were a drug available which might extend (might being one of the operative words) your life by 12 – 24 months, would you take that drug if it cost nothing?  Yes, almost certainly.  How about if it cost $100 per year?  $100 per month?  $100 per day?  $100 per hour?  There are drugs that cost more even than that.  How much is it rational to spend to prolong life?

In general, I think it’s overly optimistic to expect people to be rational about death; nevertheless, these are questions which we should be able to at least entertain, if not answer.  I’d like to think I’d be able to have a discussion about my own end of life care, what I’d be willing to spend and endure, and what I would be willing to ask my family to spend and endure.  I am comfortable, at least intellectually, with the idea that my life is of finite and measurable worth.

But I know that I will never, ever be to think rationally about what my father’s life is worth.  I can accept that the value of my life is not unlimited, but the simple, emotional truth is that, to me, his life is priceless.

It is not that I love my father, in any meaningful way, more than I love my mother, or my brothers, or my spouse.  But my father’s death has been the great terror of my life since I was a young child, and I would do anything to postpone it.

I once told him, when I was very little, that I hoped I would die before he did.  He told me with great emphasis that that was the unkindest thing I could ever wish for him, that no parent should ever outlive their child.

I didn’t want to upset him, so I negotiated: I told him that, in that case, I hoped that we died at that exact same instant.  He failed to appreciate the compromise I was offering him, and told me that he hoped that he would die many, many years before I did, that I would have a long and happy life even after he was dead.

I didn’t tell him, but I didn’t think that was possible.  I still don’t.  The idea of living a happy life in a fatherless world is incoherent – it does not compute.  It’s like telling me you wish me a long and happy life after the sun goes dark for good.

When I was young and the black dog of my father’s death would appear at the edges of vision, my mother told me that that fear would diminish as I got older, as I started my own family and had my own children.  She told me that, when my own offspring were in the world, the death of my parents wouldn’t obliterate it.

I don’t have children.  Maybe I will one day, and maybe she will be proved right – she usually is.  But perhaps all she is really describing is the replacement of one apocalypse for another.  I cannot bear the thought of my father’s death – will I be able to bear the thought of my child’s any better?

I think what I’m trying to say is this: ‘worth’ is a concept with meaning only when there are choices.  “What’s it worth to you” suggests two options: the thing you want and the price you might pay, both with value you can understand and which you can compare.  Death of the most loved ones, this does not have value against which something else can be measured.  This is the scaffolding upon which the world has been built, and without it, nothing has value.

And the point is moot.

Sexy Numbers

A few weeks ago, Radiolab released a podcast short, ‘For the Love of Numbers’, on the peculiar propensity of people to become attached to specific numbers.  They discussed the old Pythagorean idea that numbers are gendered, specifically that odd numbers are male and that even numbers are female, and the ways in which that thinking persists today.  They cited a study by James Wilkie and Galen Bodenhausen, ‘Are Numbers Gendered?’ (Journal of Experimental Psychology, 2011).

In that study, participants were shown pictures of very young infants, dressed in white.  For half the participants, the pictures were labeled with either three odd digits or three even digits.  Participants were told that these numbers were randomly assigned ID numbers, and to disregard them.

The study, and Radiolab in turn, reported that evenly-labeled babies were significantly more likely to be thought female, and oddly-labeled babies male, independent of the baby’s actual sex.  What the study did technically report, but what Radiolab did not, is that the effect size was miniscule.

Participants were asked to rate how likely they thought it that the baby pictured was male, with a score of 1 meaning that it was “not at all likely” to be male, and a score of 7 meaning that it was “extremely” likely that it was.

Study participants gave oddly-numbered babies a mean score of 3.79, with a standard deviation of 0.53.  Evenly-numbered babies were given a mean score of 3.47, with a standard deviation of 0.59.  Even considering the modest number of participants (36), this is a very small effect size.

In fact, Abumrad and Krulwich (the hosts of Radiolab) interviewed Wilkie, and asked him about the size of his effect.


Radiolab: By how much more likely?  By a lot, or by a teenie bit?    Wilkie: Uh, by a statistically significant amount.  Not a landslide.”


“Not a landslide.”  That is an understatement.

It is difficult to discuss statistical significance, because, while it is the gold standard of scientific research, few non-practitioners understand how manipulable data really is.  Significance alone is not enough: you also need to know the tests run, the size of the sample (or the “n”, for ‘independent subject’), and the standard deviation.  The standard deviation in the Wilkie study is larger than the effect size; that is, if you add the mean value and the standard deviation, you have no difference between the two groups.  That is a sure sign that something is amiss, significant or not.

I like Radiolab a great deal.  I even liked that podcast short.  But it is a show that purports to be about science, and its creators should be thinking critically about the scientific research they present.  A very casual scientific consumer should know that standard deviations should not completely swallow effect size, and that authorial claims of “significant” p-values do not excuse us from healthy scepticism.