An Analysis and Solution of the Problem of Probability and Statistics

Statistics and probability appear in everyday life, and yet the average high school student only encounters a very basic form of probability and no statistics in school. In an age where data is all around us, curriculums all across the nation are lacking a sturdy data analysis course that teaches young adults to understand information given to them every second of every day and to make conscious, logical decisions with that information. A lack of understanding of statistics, probabilistic theories, and data analysis not only applies to the average American, but to some experts too. This deficiency in the American general intelligence starts with outdated curriculums, and spreads to many other fields of work, such as medicine or law. As applied mathematics, the umbrella name for probability, statistics, data analysis and a handful of other types of mathematics, becomes more important in everyday life, the general populace will become more misinformed and make worse and worse decisions.

Many people depend on their doctors to help them get into better health, to diagnose them, and to prescribe medication. But many doctors lack the statistical education and knowledge to do such things, and most patients don’t even realize it. In a Los Angeles Times article discussing medical journals, David Shaw, a journalist, expresses that, “The other problem with media coverage of most epidemiological studies, scientists say, is a misunderstanding and misuse of statistics” (Shaw). The media coverage in this case are the medical journals. They are doctors’ main source of information on studies done by other doctors\. Because these journals discuss and analyze statistics, their misuse or a misunderstanding of statistics could lead to a domino effect, leading to repercussions beyond a single study. A lack of understanding of statistics on a medical journal’s part could lead to grave mistakes in the field of medicine, a field people rely on for their well-being.

But mistakes made in medicine can also be made when diagnosing. When this happens, patients are directly affected. Leonard Mlodinow, a professor of mathematics at Caltech and author of Drunkard’s Walk: How Randomness Rules Our Lives, describes an encounter he had with his doctor, which almost led to disaster.

my doctor told me by telephone that the chances were 999 out of 1,000 that I’d be dead within the decade… My doctor had confused the chances that I would test positive if I was not HIV-positive with the chances that I would not be HIV-positive if I tested positive… He should have said, ‘Don’t worry, the chances are better than 10 out of 11 that you are not infected’ (Mlodinow 115).

Mlodinow was lucky to know enough statistics to be able to figure out that his doctor was wrong. But most people don’t, and wouldn’t question a doctor, because they assume that doctors know better. But if doctors do not understand probability, who knows how many people were incorrectly diagnosed with certain diseases? The nation needs more statistics education so that doctors do not lie to patients, and patients are smart enough to figure out when it’s happening.

Medicine is not the only field that uses statistics. Courts oftentimes employ statistics as evidence. Because the jury is selected f as people from every walk of life, it is almost guaranteed that there will be someone without education in statistics. In a California Court Case, statistics were used to convict an innocent couple. According to the Harvard Law School,

Applying the product rule to his own factors the prosecutor arrived at a probability that there was but one chance in 12 million that any couple possessed the distinctive characteristics of the defendants… the ‘product rule'’ would inevitably yield a wholly erroneous and exaggerated result (Sullivan).

In this case, the expert statistics witness had offered statistics, which had no basis, and applied a statistical rule that was not applicable to the situation, and arrived at incredibly slim odds that the accused was innocent. The jury, which in general did not understand the mistake that the “expert witness” made, convicted the defendant. It turned out that the defendant was innocent, and eventually, they were released. But this mistake is important because it illustrates that with the right manipulation of statistical functions, an expert could convince a jury that just about anyone is guilty.

Secondary education in the U.S.A. may hold the answer as to what the root of the problem is. In public school Evanston Township High School (ETHS), which over 2500 students attend, students are required to take three years of mathematics courses. In those three years, probability is only touched on in Algebra 1 and Algebra 2, and not discussed in Geometry. Statistics is not present anywhere in those three years. ETHS offers AP Statistics, but it is not a required course, and many students do not take the class. The solution to the problem of education in applied math fields such as probability would be to put it in the mandatory curriculum of every high school in the US. That way, no one will be caught off-guard and everyone will be able to make better decisions.

Works Cited

Sullivan, J. "People v. Collins 68 Cal. 2d 319, 438 P.2d 33, 66 Cal. Rptr. 497 (1968)."People v. Collins 68 Cal. 2d 319, 438 P.2d 33, 66 Cal. Rptr. 497 (1968). N.p., n.d. Web. 18 May 2015.

Shaw, David. "Stories on What You Eat, Drink Reflect Lack of Context, Appetite for Conflict." Los Angeles Times. Los Angeles Times, 14 Feb. 2000. Web. 18 May 2015.

Mlodinow, Leonard. The Drunkard's Walk: How Randomness Rules Our Lives. New York: Pantheon, 2008. Print.