Mathematics, Statistics, and Despair

The noted skeptic and curmudgeon Mark Twain observed that there are lies, damn lies, and statistics. A recent post entitled On San Francisco’s Quantified Self-Delusion said: “But we live in a neoliberal dumpsterfire of an epoch where everyone insists everything must be objectively measured.” as well as “Numbers are power. The ability to confer measurement onto someone is a socially legitimized way of dehumanizing them.”

Occupy Math would like to offer an alternative, though not really opposing, viewpoint. Occupy Math feels that accusing numbers of dehumanizing someone is absolutely silly. Numbers are insensate, emotionless abstractions. If someone is being dehumanized and a number is involved, it is really not the number that is the active agent of evil. Occupy Math will also supply examples of numbers being used by people wearing (metaphorical) white hats.

Numbers don’t dehumanize people. People dehumanize people.

This distinction is an important one. Numbers are clearly a two-edged sword- you can use them to solve problems or cause them (and the same overt action may be seen in both these lights by different people). A set of statistics about a group of marginalized people can almost always be used to support two very different hypotheses: that they need help or that they need to be locked up or driven away. Justin Keller’s somewhat over-privileged and idiotic letter to the editor in the Guardian shows how the numbers (there is an increase in the number of homeless in San Francisco) can be interpreted in an evil and irresponsible fashion. Occupy Math would like to support the idea that what is needed is not the vilification or dismissal of “numbers” or, as they might more properly be called, statistics. Rather, social and ethical standards for the responsible use of numbers are required.

Another example from the post that inspired Occupy Math this week, was one where the young men in a class passed around numerical ratings of the young women in the class. The author of the post concluded that the numbers damaged the young ladies who saw what their ratings were. I feel that the numerical ratings, however unjust or one-dimensional, were the responsibility of the young men. Blaming the numbers lets the young men off the hook when they should not be.

Numbers can be used for good or evil.

An example of using numbers for good is embodied in a 1974 legal brief on demonstrating racial discrimination in housing. This is far from the first use of statistics to promote the common weal. No less a luminary than Florence Nightingale appears in an earlier Occupy Math post, building models that showed that sterile techniques saved lives and municipal water supplies prevented cholera. Literally millions of lives were saved by careful consideration of the numbers. Cancer clusters are a simple mathematical model that spots everything from dangerous occupations to toxic waste dumps. Before we dismiss quantification as a tool of the dark powers, we should ask “what is the difference between the white hats and the back hats?”

The most excellent and esteemed statistician George E. P. Box, shown above, made the trenchant and accurate observation that,

All mathematical models are wrong, but some mathematical models are useful.

Any mathematical model or any statistical summary of a situation must discard a lot of information as it forms. This is a strength of modeling – it distills out a simpler point of view of a situation so that it can be considered. Florence Nightingale pulled proof of the value of antiseptic techniques out of the chaos of the Crimean war. Here is the key point: there are likely to be moral or ethical judgments embedded in and possibly concealed by the choice of which information to discard.

Occupy Math was intentionally provocative in the bold line starting numbers don’t dehumanize people because it is templated on the NRA slogan “Guns don’t kill people, people kill people”. As far as Occupy Math is concerned this slogan is logically correct – it embeds as a defense of guns the same logic that Occupy Math is using to defend numbers. What, however, does this very simple model leave out? People with easy access to guns are far more likely to kill other people. The model destroys statistical information that speaks to the use of guns to kill wives and husbands, children and friends. There is a clear moral judgment in the choice of which information to simplify to invisibility in the conclusions of the model. As Occupy Math writes this, a report in his news feed informs him that a long-time advocate of keeping guns lying around the house was shot in the back by her four-year-old son while driving. It is a certainty that this part of the data will not inform any models used by gun ownership advocates.

Bogus justification of large lecture classes.

There are numerous statistics that demonstrate that shifting from small to large lecture sections in university classes has not hurt grades. The conclusion from this, by administrators, is that large lecture classes are not hurting instruction. This conclusion is, of course, errant nonsense. The large lectures substantially degrade the quality of instruction. Why don’t they lower grades? The grades stayed similar because professors test students on what they have learned as a fraction of what they are taught, not on what they could have learned in an ideal situation. Occupy Math has been teaching math in university for 30 years – what fourth year students have learned has been getting worse the whole time. The model of performance is grades, the hidden information is that grades are normed to class content, not objective measures of mathematical competence.

Where do we go with this? The conclusion that numbers are dehumanizing or evil is only valid in the presence of massive ignorance. Knowing that any set of statistics had to discard or ignore information leads to the empowering notion that you should figure out what information was discarded. Twain was right – lies, damn lies, and statistics – but the reason he was right is because it is because it is routine to choose the information discarded so as to support a bogus conclusions. The post I am responding to has, to some degree, bought in to the inevitability of ignorance. Occupy Math respectfully disagrees.

Discovering discarded information and dying women.

Suppose that you are told that women have better heart health than men. The numbers are as follows: the number of women diagnosed with heart disease in emergency rooms is smaller, as a fraction of all women, then the similar fraction for men. What information is being discarded? I’d like to thank Rachel Brown for pointing out a current article on the problem. The answer is shocking. Because women get pregnant sometimes, and because pregnancy changes a whole lot of test results, almost all data and research on the symptoms of heart disease is done on men to keep the data clean. Since men and women present heart attacks differently, the difference in emergency room diagnosis is substantially due to failing to diagnose women with heart attacks as having heart attacks.

Here are some questions that are generic but natural when looking an a mathematical or statistical model:

  1. How was the data gathered? (Looking at emergency room records).
  2. What criteria were used to evaluate the information. (Trust the doctor on duty).
  3. What model was used to gather the data? (Look for male heart attacks).
  4. Are people in my natural groups included in the model? (Not if you’re female).

This example highlights one problem with figuring out which information was discarded: the fact that most medical research is done on men, male mice, male rats, etc. is not well publicized. You can get around this to some extent by using social networks and the internet, but the internet has a highly variable quality of information and searching does take time. Mostly, when you notice this sort of harmful discarding of relevant information, speak up! Occupy Math is absolutely serious about this.

Do you have good examples of bogus statistics? Have you read the Selling It feature at the back of Consumer Reports? Do you know some model of a situation that is logically or statistically bogus? If so comment or tweet and Occupy Math will see if there is a post to be had.

I hope to see you here again,

Daniel Ashlock,

University of Guelph,

Department of Mathematics and Statistics

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