Lost in Monty Hall: The Risk Within Statistics

My favorite statistics brainteaser is the Monty Hall problem. The setup is that a game show host asks you to stand in front of one of three doors. Behind one of the three doors is a prize. After you choose a door, he opens one of the two remaining doors to reveal an empty room. At this point you're offered the chance to switch doors. What would you do?

The vast majority of people answer that they would stick with the original door. However, if you switch doors, your odds of winning the prize jump from 1 in 3 to 2 in 3. Statistics can explain this, and there are several beautifully done simulations of this very problem available online.

My fascination with this brainteaser is based on my curiosity: Why do the vast majority of people get this question wrong? Cognitive psychologists have wrestled with this very question. Errors with Monty Hall have been linked to endowment effect, where people overestimate the chances of winning with the "already-chosen" option, and to status quo bias, whereby people tend to stick with choices they have already made. Furthermore, we tend to migrate to errors of inactivity over activity: We are more comfortable with making the wrong choice by standing still than with making a mistake after taking an action.

Above and beyond the psychological component, there is a struggle when it comes to numerical literacy, including probability. At an educational level, approximately half of the adults in the United States are unable to accurately calculate a tip. One fifth of the 30 percent of all U.S. adults with a bachelor's degree struggle with assessing basic risk calculations.

Luckily, in large part, it is easy to get by with apps for tip calculations, and to gauge risk on a case-by-case basis. There's one area, however, in which statistics becomes vital: health care.

Here's why. If you ask an 8-year-old about a coin flip, they can explain it to you. The first time we watch a coin spin through the air, we understand intuitively that there are two possible outcomes, and that either could occur, with equal chance. As the coin falls, we hope that we guessed "heads" or "tails" correctly. The stakes are low, and it's easy to think about. Fifty/fifty makes sense.

In medicine, fifty/fifty no longer makes sense. Do you proceed with taking a drug if the chance of a mild side effect is 50 percent? Do you opt for surgery if you have a 10-percent higher risk of developing cancer? Do you decide to exercise because of the latest attention-grabbing headline that suggested that you might have a higher chance of developing cancer if you don't? How do you make those decisions?

In many cases it depends on the odds of another course of action, or the chance of finding an alternative route. Physicians are trained to help patients work through their decision making, to help with a comprehensive understanding of the statistics and risks. Surprisingly, however, it has been reported that even physicians struggle with statistical literacy.

There is nothing easy about assessing and determining risk, particularly in health care. Inspiring patient-survival stories often feature the expression "We beat the odds," bringing to light the unknown but significant factor of patient hope and faith. Article after article crowds the Internet suggesting that this or that activity increase the risk for developing this or that disease. Articles that outline the baseline risk are few.

To illustrate the complexity that ensues, let's take a look at two examples.

Smoking and Lung Cancer

We have all seen the warning labels: Smoking increases the chances of lung cancer. The statistics here are overwhelming. First, if you smoke, you have a 15 to 30 times greater chance of developing lung cancer. The average 40-year-old non-smoking American man has a 2.8-percent chance of developing lung cancer over the next 30 years. Therefore, the average 40-year-old male smoker has between a 42-percent and 84-percent chance of developing lung cancer over the next 30 years, depending on consumption. In essence, if you smoke, it's as if you're flipping a coin that is weighted against you. Second, to put this in perspective, 80 to 90 percent of all people who die from lung cancer were smokers. With these odds, it is reasonable to expect that if you smoke, you will develop lung cancer at some point in your life. All compounding variables -- gender, genetics, demographics -- fade away when the odds of developing a disease can be as high as 84 percent and the vast majority of people developing the disease share one important characteristic with you. Moreover, the correlation between smoking and cancer has been tested repeatedly, in large populations over many years.

Sitting and Colon Cancer

The second example relates to a large study published earlier this month on cancer and sedentary behaviors. The study did a meta-analysis of over 40 previous studies, with over 4 million participants between them. Within this group were nearly 69,000 cancer cases. Sedentary behavior was linked to a 24-percent increase in colon-cancer risk and a 32-percent increase in endometrial-cancer risk. Every major media outlet that covered the article focused on the increased risk, but several ignored specifically mentioning the kinds of cancer that were implicated. The reader is left feeling as if sitting is potentially as dangerous as smoking for cancer risk. In fact, a few news outlets made the comparison openly. Is this a fair comparison?

We can take a good look at the probabilities to understand. The average lifetime risk of developing colon cancer is 1 in 20, or 5 percent. According to the study, increasing the amount of time you typically spend sitting each day by two hours increases your odds of developing colon cancer by 8 percent. Regularly sedentary for over six hours a day? The probability of developing colon cancer at some point in your lifetime is close to 30 percent.

Unlike smoking, sitting has multiple compound variables that we do not completely understand yet, including family history, nutrition, and obesity. It is absolutely worth being cautious; this study is a great reminder of how important it is to work out, take breaks when watching Netflix, and take the stairs. However, to put these statistics in the same bucket as smoking is an overreaction and potentially dilutes both messages. The lay reader needs to know that obesity and poor nutrition are compounding factors, because that kind of knowledge empowers us to make the little changes that do matter.

I have argued consistently for scientific literacy. After exploring the statistical side of scientific reporting, I would argue that we need as much education on statistics as we do in raw science. The millions we spend on public-awareness campaigns highlighting risk are meaningless if we do not also invest in educating the public on how to manage and mitigate their risk. It may be as complicated as walking away from an addiction, in the case of smoking, or as simple as watching television while jogging, instead of while sitting down, once a week. There is one certainty: If we fail to educate, we have no chance at all of changing our odds, let alone beating the odds.