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Some time ago, I wrote about missing values and how they complicate the life of an applied statistician. A particularly tricky case concerns logical variables , and I give a more detailed explanation here. Suppose X is a variable representing whether a person is at risk for developing type-2 diabetes . Two known risk factors are ( A ) being older and ( B ) being overweight. If we had a database containing the age and weight of each person in a group, we could compute X using the following logical expression : X = A OR B . ( X , A , and B are known as logical variables, and they each take values TRUE or FALSE according to whether the corresponding condition holds.) But what happens if some ages and weights are missing from the database? Fortunately statistical software packages like R and SPSS have built-in rules that will correctly evaluate the logical expression, even if A or B (or both) are missing. The complete truth table is as follows (where T means TRUE, F means FALSE, a...

MSNBC recently reported that a new study suggests "U.S. states whose residents have more conservative religious beliefs on average tend to have higher rates of teenagers giving birth". (I learned of this on Rationally Speaking .) The study itself is Open Access, so all the details are freely available . The scatterplot illustrates the strong association the authors found. Now, the authors were reasonably cautious in how they interpreted their findings. The trouble is, the general public may not be. A common error is to conclude the study shows that religiosity causes higher teen birth rates. But correlation does not imply causation . It could be that higher teen birth rates cause religiosity. Or perhaps a third, unidentified factor causes both. But isn't the strength of association still impressive? It is. But what if, as I just suggested, there are other variables involved? Such confounding variables (or confounders, as they are commonly known) can wreak havoc on this...

In a valid deductive argument, the conclusions follow necessarily from the premises. This is a proof in the mathematical sense of the word. Provided we know that the premises are true, we can establish with complete certainty that the conclusions are true. For example, identifying a single unicorn would establish without a doubt that unicorns exist. Unfortunately much of the time this type of certainty isn't possible. Consider another example from the realm of mythology: weapons of mass destruction (WMD) in Iraq. Here's what Donald Rumsfeld had to say on the subject in 2002 (the boldface is my addition): There's another way to phrase that and that is that the absence of evidence is not evidence of absence . ... Simply because you do not have evidence that something exists does not mean that you have evidence that it doesn't exist. But surely hunting high and low for WMD month after month and not finding any ( absence of evidence ) supports the inference that there ar...

Searching Google for "no evidence" yields "about 21,300,000" hits. It seems we're keen to deny that there is any empirical support for countless different claims. For example, scientificblogging.com reports that there is "No Evidence For Fish Oil Benefit In Arrhythmias" based on a systematic review just published in BMJ. (Full disclosure: I have previously participated in research on omega-3 fatty acids, however I have no related financial interests.) What does the review itself say? This is the first systematic review attempting to evaluate whether the protective mechanism of fish oil supplementation is related to a reduction of arrhythmic episodes determined either by a reduction in implantable cardiac defibrillator interventions or a reduction in sudden cardiac death. We found a neutral effect on these two outcomes. The confidence intervals for these outcomes were wide and a beneficial effect up to a 45-48% relative risk reduction cannot be exclu...

The Internet makes it possible to link a dispersed community of common interest. Now there are a number of blogs that focus entirely or in part on Statistics, but they seem not to be well connected. So I've just set up a social bookmarking website just for applied statistics, data analysis, and visualization. It's called StatLinks . It lists links that users submit, and allows other users to vote on their relevance. Links are listed in order of popularity (or in chronological order, if you prefer). I encourage people to visit StatLinks , to submit links that are likely to be of interest, and to pass the word ! I've put a few links in to get things started. (Hat tip to Slinkset whose technology made it a breeze to set this up.)

Over at Adventures in Ethics and Science there's a very interesting post and follow-up comments on whether researchers should share data . It's based on a recent New York Times article by biostatistician Andrew Vickers ( Cancer Data? Sorry, can't have it ).

The map on the left labels countries as free (green), partly free (peach), and not free (red) for the year 2006. The classification is from Freedom House , a primarily US-government-funded organization. Each country is scored on political liberty and civil liberty; the combined average of these scores determines how the country is classified. Cuba, for example, receives the poorest rating on both political and civil liberties, and is thus categorized as "not free". The Wikipedia entry for democracy lists two other measures of democracy, one from the Polity IV project and the Democracy Index from The Economist. Each measure has its own scheme for measuring and weighting different characteristics felt to characterize democracies. Since the different measures assess many of the same things, it is not surprising that they show some agreement. But democracy is not a simple thing and it is far from clear which characteristics matter and how best to weight them. For example, doe...

Here's a fascinating talk by Hans Rosling about international health and development. His presentation reminds me of Al Gore's An Inconvenient Truth. Thoughts?

In my continuing effort to eff the ineffable (consciousness), I today stumbled on an article by Jaron Lanier with the intriguing title " Death: The skeleton key of consciousness studies? " It's written in an entertaining manner with little in the way of technical jargon. Lanier makes some interesting points, but what struck me was the following piece near the beginning: There is a popular story about a princess who complains that she cannot sleep comfortably because of a single pea buried under layers of mattresses. That pea is consciousness in the sciences. To consider consciousness by itself is entirely undemanding. It is a pea. There is nothing to describe. An attempt to account for it in context, however, forces the construction of ever shifting, elaborate adventures of thought. What a temptation it is to dispose of this erratic data point. That is what any first year student of statistics would be taught to do. Excuse me? I was enjoying the metaphor until that last b...

A recent article by philosopher Steven Hales is titled " You Can Prove a Negative " (a slightly different version of the article is available as a pdf file ). Hales argues that the "principle of folk logic" saying you can't prove a negative is just plain wrong . He points out that " any claim can be expressed as a negative, thanks to the rule of double negation." So it's easy to come up with examples of proving a negative. Hales goes on to say that "Some people seem to think that you can’t prove a specific sort of negative claim, namely that a thing does not exist." He counters this with an example of a valid proof that something doesn't exist: 1. If unicorns had existed, then there is evidence in the fossil record. 2. There is no evidence of unicorns in the fossil record. 3. Therefore, unicorns never existed. Of course, the difficulty here is with the truth of the premises (1 and 2). In particular, it could be that we just haven...

Goodbye, dear friend . I learned of Ram 's death on Tuesday evening, from the mother of Ram's wife (Rita, who is also a dear friend). She added that Rita has requested that people not try to contact her. It's now early Wednesday morning, and I am going to bed.