⚖️ Balancing Type I and Type II Errors: A Medical Perspective

Introduction
In statistics, Type I and Type II errors represent two different kinds of mistakes we can make when testing hypotheses. Deciding where to trade off between them is a crucial part of designing tests, experiments, or decision-making systems. In high-stakes fields such as medicine, the trade-off can literally mean life or death.
Understanding the Errors
Type I Error — False Positive
A Type I error occurs when we reject the null hypothesis when it is actually true.
In simple terms:
We conclude something is happening when it really is not.
Example in medicine:
A test says a patient has a disease when they are actually healthy.
Consequence:
Unnecessary anxiety, additional testing, possible harmful treatments.
Type II Error — False Negative
A Type II error happens when we fail to reject the null hypothesis when it is actually false.
In simple terms:
We miss detecting something that is actually happening.
Example in medicine:
A test says a patient does not have a disease when they actually do.
Consequence:
Missed diagnosis, delayed treatment, worsened prognosis.
The Trade-Off
There is an inherent trade-off between Type I and Type II errors.

Lowering the chance of Type I errors (making a test more “strict”) usually increases the chance of Type II errors.
Lowering the chance of Type II errors (making a test more “sensitive”) usually increases the chance of Type I errors.
This balance is controlled by:
Significance level (α): Probability of a Type I error.
Power (1 - β): Probability of detecting a true effect (reducing Type II errors).
Medical Scenario: Screening for a Serious Disease
Let’s imagine a blood test that screens for an early-stage cancer.
If we prioritize avoiding Type I errors:
We set a very strict threshold for calling the test positive.
Fewer healthy people will be incorrectly told they have cancer (fewer false positives).
BUT… some people with early cancer may test negative and go untreated (more false negatives).
If we prioritize avoiding Type II errors:
We set a more lenient threshold for calling the test positive.
We will catch almost everyone who has cancer (fewer false negatives).
BUT… more healthy people may be told they might have cancer, leading to unnecessary biopsies (more false positives).
Where to Trade Off in Medicine
The trade-off decision depends on:
Severity of the disease — If the disease is fatal and treatable in early stages, we often accept more Type I errors to catch all true cases.
Cost and risk of follow-up tests — If confirmatory tests are cheap and safe, a higher false-positive rate is acceptable.
Psychological impact — Over-diagnosis can cause stress; under-diagnosis can be life-threatening.

Example Decision:
For cancer screening, most doctors would favor minimizing Type II errors (false negatives) even at the cost of more false positives, because missing the disease could be deadly, whereas a false alarm can be corrected with further tests.
Conclusion
In any testing scenario, we cannot completely eliminate both Type I and Type II errors — improving one often worsens the other.
In medical diagnostics, especially for serious diseases, the priority is often to reduce Type II errors to ensure no case goes undetected, even if it means tolerating a higher number of false positives.

The choice of where to trade off depends on: