Posts Tagged ‘Statistics’

The misuse of statistics

March 31, 2013

A certain clinic advertises that the death rate of people between the ages of 45 and 65 is 14 out of 100, but the death rate of people in that age range who go to the clinic is one out of 100. This looks very good, until you look at how the statistics was gathered. The clinic says these statistics are for the last decade. This means there are no people who were followed for the entire age range from 45 to 65.

Even assuming the clinic finds out every time a patient dies, the way the patients are in the study guarantees bad statistics. The clinic is in an expensive area, with many high powered jobs. The man who retires at 62 due to bad health, moves to Florida and dies a year later, is not counted.

In addition, assume that a 64-year-old man starts coming to the clinic and he lives past 65. He counts as someone who beat the odds. True, but he was not picked out of all people who entered the 45 to 65 age range, he was picked out of all people who reached 64 who were sufficiently health conscious to go to the clinic. His chances of reaching 65 were much greater than a random 45 year old.

If a school system decides to spend money to ensure that as many students as possible pass a certain test, they are likely to spend more money on students where it makes a difference. The students that are slighted are the ones who would never pass the test, no matter what was done, as well as the students who would pass the test regardless of the money spent on them. Statistics on test passing would be a misleading indicator of the general quality of the school. A school that spent money to improve all students would not have as impressive results.

At least in the case of the clinic, the statistics may have been gathered in ignorance, but the hypothetical school system is trying to beat the system. At least it is an honest way of beating the system, honest in the sense that if everything is revealed to the public, it won’t lead to indictments. Recently, the Atlanta school system tried a less honest way of trying to beat the system, and those indictments are making headlines.

In view of the stakes, I suspect many schools are putting their money where it can do the most good. By that, I mean the most good for the school system, not for the students.


“Prosecutable cases of voter fraud are rare.” the Washington Post, October 9, 2011

October 9, 2011

Prosecutable cases of drug use would be rare, if there were no serious attempt to go after drug users, so this statement doesn’t say much. I don’t know if voter fraud is common or essentially non existent, but if no serious attempt is made to prevent or find it, how can we know? I know someone who volunteered to help during elections, and complained that too much of the process left things with one person able to allow or commit voter fraud. He was rewarded by not being called back to volunteer again. (Perhaps he wasn’t called again for other reasons, but the problem existed, and it was unlikely to be solved.)

Too much is at stake for us to say that the problem is non existent.

When one death seems more tragic than many

January 16, 2011

“In 2007, there were 37 countries in which at least 10% of children under five died,” according to Wikipedia. The death rate for children under 5 in the USA is under 1%, and that is considered high for an industrialized country.

I am not remotely trying to suggest that people should not get upset about the recent tragic death of Christina Green in Arizona, but why does her death elicit more emotion than the previous paragraph? It is more upsetting, at least to me, yet my mind tells me that the numbers should mean more. Am I incapable of generalizing?

A politician trying to use deaths to promote gun control is more likely to use individuals rather than numbers. Before the recession, our newspaper led an article about low unemployment by writing a paragraph about someone who was still unemployed, and it often starts articles that are about statistics with examples of individuals.

I am more interested in the numbers. I want to know how many, what percent, how has it changed, and what factors effect how accurate the numbers are. Yet I am more influenced emotionally by the story about the individual. The fact that many people react this way will encourage stories to be about individuals rather than numbers.

If there ever is a year when New York, NY has only one murder, the story will focus on that murder, rather than the astonishing fact that a city that normally has hundreds of murders only has one.

How much mathematics should everyone know? Part 2

September 4, 2010

Maryland decided that to be a college graduate everyone should pass a math course with a prerequisite of Intermediate Algebra (or high school Algebra II.) Assuming that a college graduate passed Intermediate Algebra, what else should he know in mathematics?

If I were to pick one course, it would be statistics. This is not an attempt to garner more students, because I rarely teach statistics, but a belief that a basic introduction to statistics is the single most useful mathematics that can be learned in one course. This does not allow people to become statisticians, but gives them some understanding of results that are thrown at them regularly from many sources.

I would also make How to Lie with Statistics required reading for every high school graduate, but that will never happen.

Biological Statistics

August 24, 2010

When my son went to graduate school in biological statistics, I did not even know there was such a field, or what kind of work he could do. After getting hired by Arbor Research, he first joined a project which involved analysis of dialysis. What makes it work? For example, a fistula is better than a graft. Although this seems to be accepted now, when they first did their analysis, some doctors still believed that a graft was better. Statistics expands the experience of one doctor to the experience of many.

I now wish every medical procedure were analyzed. We have tools now that mean we do not have to rely on doctors who only go by their subjective judgment from their own practice. I don’t want to take the doctor’s experience out of medical care, but if my doctor recommends a treatment, I want to know if patients who receive that treatment do better than patients who go for an alternative treatment or even receive no treatment at all.