Calculated Risks

1. Uncertainty is pervasive: Embrace Franklin's law

In this world nothing is certain but death and taxes.

Illusion of certainty. Many people believe that modern technologies like DNA testing, fingerprinting, and medical screening provide absolute certainty. However, this is an illusion. All these methods are subject to errors and uncertainties.

Franklin's law. Benjamin Franklin's famous quote reminds us that almost everything in life involves some degree of uncertainty. Recognizing this fact is the first step in making better decisions under uncertainty.

Consequences of ignoring uncertainty:

• False sense of security
• Overlooking potential errors or alternative explanations
• Making poor decisions based on incomplete information

2. Overcome innumeracy to make better decisions

The best technology is of little value if people do not comprehend it.

Statistical illiteracy. Many people, including professionals in fields like medicine and law, struggle with basic statistical concepts. This innumeracy can lead to poor decision-making and misinterpretation of important information.

Three types of innumeracy:

1. Ignorance of risk: Not knowing relevant risks
2. Miscommunication of risk: Inability to effectively communicate risks
3. Clouded thinking: Difficulty drawing correct inferences from statistical information

Overcoming innumeracy:

• Recognize the importance of statistical thinking in everyday life
• Learn to use simple tools for understanding and communicating risks
• Practice interpreting statistical information in various contexts

3. Natural frequencies are more intuitive than probabilities

Eight out of every 1,000 women have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don't have breast cancer, some 70 will still have a positive mammogram.

Natural frequencies vs. probabilities. Natural frequencies are easier for most people to understand and work with compared to probabilities. They represent how humans naturally encounter statistical information through experience.

Benefits of natural frequencies:

• Simplify complex calculations
• Make base rates more apparent
• Reduce confusion and errors in statistical reasoning

Example: In medical diagnosis, presenting test results using natural frequencies (e.g., "7 out of 77 women with positive mammograms have breast cancer") is more intuitive than using probabilities (e.g., "the probability of having breast cancer given a positive mammogram is 9%").

4. Relative vs. absolute risk: Context matters in risk communication

The relative risk reduction looks more impressive than the absolute risk reduction.

Misleading risk communication. Presenting risks in relative terms often leads to overestimation of benefits or harms. Absolute risk reduction provides a more accurate picture of the actual impact.

Example: A treatment that reduces the risk of a disease from 4 to 3 in 1,000 people can be described as:

• Relative risk reduction: 25% (sounds impressive)
• Absolute risk reduction: 0.1% (puts the benefit in perspective)
• Number needed to treat: 1,000 (clarifies how many people need treatment to benefit one person)

Best practices:

• Present both relative and absolute risks
• Use natural frequencies when possible
• Provide context to help people understand the magnitude of risks

5. Medical screening: Weigh benefits against potential harms

I hope very much that pressure is not put on women to attend [breast cancer screening]. The decision must be theirs, and a truthful account of the facts must be available to the public and the individual patient.

Balanced approach to screening. While medical screening can detect diseases early, it also comes with potential harms such as false positives, overdiagnosis, and unnecessary treatment.

Costs of breast cancer screening:

• False positives: Anxiety, additional tests, unnecessary biopsies
• Overdiagnosis: Treatment of slow-growing cancers that may never cause symptoms
• Radiation exposure: Small risk of radiation-induced cancer

Benefits of breast cancer screening:

• Potential reduction in breast cancer mortality (for women over 50)
• Earlier detection may lead to less invasive treatment options

Informed decision-making: Patients should be provided with clear, balanced information about both the benefits and risks of screening to make personal decisions based on their values and preferences.

6. DNA evidence: Understand the chain of inference

A reported match does not guarantee that the defendant is guilty of the crime or even that he or she is the source of the trace.

Chain of inference in DNA evidence:

1. Reported match
2. True match
3. Source of trace
4. Present at crime scene
5. Guilt

Potential errors and uncertainties:

• Laboratory errors (false positives)
• Coincidental matches
• Contamination or transfer of DNA
• Presence at crime scene doesn't always imply guilt

Prosecutor's fallacy: Confusing the probability of a match given innocence with the probability of innocence given a match. This error can lead to overestimation of the strength of DNA evidence.

Best practices:

• Present DNA evidence using natural frequencies
• Clearly explain the chain of inference and potential uncertainties
• Consider alternative explanations for DNA matches

7. Risk perception: Recognize common biases and misunderstandings

What John Q. Public most fears is not always what threatens him most.

Factors influencing risk perception:

• Preparedness: Evolutionary predisposition to fear certain threats
• Disasters: Greater fear of events that can cause many deaths at once
• Unknown hazards: Fear of new and unfamiliar risks

Common misperceptions:

• Overestimating risks of rare but dramatic events (e.g., plane crashes)
• Underestimating risks of common but less dramatic events (e.g., car accidents)
• Focusing on relative risks without considering absolute risks

Improving risk perception:

• Seek out accurate statistical information
• Consider both the likelihood and potential impact of risks
• Be aware of how risks are framed and communicated

8. Informed consent requires clear communication of risks and benefits

The silent world between doctor and patient is one reason: Patients often do not know what questions to ask.

Barriers to informed consent:

• Illusion of certainty: Presenting treatments as certain rather than acknowledging uncertainties
• Innumeracy: Difficulty understanding and communicating statistical information
• Time constraints: Limited time for in-depth discussions
• Power imbalance: Patients may feel uncomfortable questioning authority

Improving informed consent:

• Use clear, understandable language to explain risks and benefits
• Present information using natural frequencies and absolute risks
• Encourage patients to ask questions and express concerns
• Provide balanced information about alternative treatments

Shared decision-making: Involve patients in the decision-making process by considering their values, preferences, and goals alongside medical evidence.

9. Transform innumeracy into insight through proper representations

Solving a problem simply means representing it so as to make the solution transparent.

Power of representation. The way information is presented can significantly impact understanding and decision-making. Proper representations can turn innumeracy into insight.

Effective representations:

• Natural frequencies instead of probabilities
• Absolute risks instead of relative risks
• Visual aids (e.g., frequency trees, icon arrays)
• Concrete examples and analogies

Benefits of clear representations:

• Facilitate understanding of complex statistical concepts
• Reduce errors in reasoning and decision-making
• Empower individuals to make informed choices

Education and communication: Teaching statistical thinking using intuitive representations can improve numeracy across various fields, including medicine, law, and public policy.

Last updated: April 15, 2025