Type I and Type II Errors

Statistical Testing

• Statistical inference helps us draw conclusions about a population by analyzing a population sample.¹
• However, complete population data is often inaccessible, which requires clinicians to make estimations and predictions.^1,2
  • As a result, there is always a risk of drawing incorrect conclusions from the sample data.^1,2
• At the core of scientific inquiry lies hypothesis testing.²
  • This is a structured approach to determining the validity of assumptions using statistical analysis.²

The foundation of hypothesis testing relies on the following:

• Null hypothesis (H_₀): Assumption that there is no difference/effect between groups.¹
  • For example, a new anesthetic does not reduce recovery time compared to standard treatment.
• Alternative hypothesis (H_₁): Assumption that there is a difference/effect between groups.¹
  • For example, a new anesthetic significantly reduces recovery time compared to standard treatment.
• When testing a hypothesis, clinicians must collect data and measure the extent to which that data supports or does not support the null hypothesis¹ (Table 1).
  • If the data shows results similar to what is expected under H₀, we fail to reject H_₀.^1,2
  • If the data shows results with a significant difference from H₀, we reject H₀ in favor of H_₁.^1,2
• Hypothesis testing is not foolproof, and errors can still occur.¹
• These errors fall into two main categories:
  • Type I Error (False Positive) (α)
  • Type II Error (False Negative) (β)

Type I Errors

Type I Error (False Positive) (α)

• Occurs when we incorrectly reject the null hypothesis (H_₀), concluding that an effect/difference exists when it does not.¹
  • For example, a study might indicate that a new anesthetic reduces recovery time, but the observed difference is due to random chance rather than the drug’s effect.

Why Does It Matter?

• Unnecessary interventions: Patients might receive treatments that do not help or could potentially add risks.³
• Wasted resources: Hospitals may spend time and money on ineffective treatments.³
• Misleading guidelines: Incorrect findings may influence medical guidelines, delaying better solutions for care.³

How to Reduce Type I Errors (False Positives) (α)?

• Use confidence intervals (CI)
  • Instead of relying solely on p-values, looking at CI reveals how much clinicians trust the results and how significant the effect might be.⁴
  • This gives a clearer picture than just “significant” or “not significant” based on p-values.
• Adjust for multiple comparisons:
  • If a study tests multiple outcomes at once, the number of false positives increases.⁵
    • Using corrections like Bonferroni adjustments helps to reduce this risk.⁵ The Bonferroni method adjusts the significance level by dividing the desired alpha (e.g., 0.05) by the number of comparisons made:

• • • Where N is the number of tests.
    • For example, a study compares four different anesthetics in reducing post-operative nausea. If the standard alpha is 0.05 and four comparisons are made, the Bonferroni correction adjusts the significance threshold:

• • • This lowers the significance threshold, meaning a p-value below 0.0125 is considered statistically significant after four comparisons.
• Report effect sizes:
  • Effect size shows how big the difference is between treatments. This tells us if the difference is clinically significant and not only statistically significant.²
• Blinding:
  • Blinding prevents bias from affecting the results.⁴
• Larger studies:
  • Repeating the study with more patients helps confirm if the results were real or by chance, providing more substantial evidence and reducing false positives.⁴

Type II Errors

Type II Error (False Negative) (β)

• It occurs when we fail to reject the null hypothesis, overlooking a true effect/difference that exists.¹
• For example, a study might conclude that a new anesthetic has no effect, even though it reduces recovery time.

Why It Matters?

• Delays in beneficial treatments:
  • Valuable treatments might be overlooked or delayed, resulting in suboptimal care.⁶
• Impact on patient outcomes:
  • Patients can miss out on interventions that improve safety, reduce pain, or shorten recovery times.⁶
• Small anesthesiology trials may miss subtle but real effects in patient recovery or pain relief.⁴

How to Reduce Type II Errors (False Negatives)?

• Increase Sample Size and Study Power:
  • Small studies often miss real effects.⁴
    • Conducting a power analysis helps to ensure that the study includes enough participants to detect meaningful differences.⁴
    • A study with low power increases the risk of Type II errors.

• • • Where β is the probability of a Type II error.
    • Increasing the sample size is the most effective way to boost power, helping to ensure that smaller but clinically important effects are detected.⁴
• Extend study duration:
  • Short trials may not capture long-term benefits.⁴
  • Following patients longer helps to detect delayed improvements.⁴
• Combine studies (meta-analysis):
  • Smaller studies may miss effects, but combining data from multiple studies increases the ability to detect real results.⁴

Receiver Operating Characteristic (ROC) Curves

The ROC curve plots True Positive Rate vs. False Positive Rate.⁷

• It shows how well a test separates true positives from false positives.
• It visualizes the impact of different decision thresholds, which refers to the cut-off point used to classify data (i.e., effect or no effect, disease or no disease).⁷
• Adjusting the threshold shifts the balance between Type I and II errors.⁷
  • Lower threshold → Fewer Type II errors (high sensitivity), but more Type I errors.
  • Higher threshold → Fewer Type I errors (high specificity), but more Type II errors.
• The best performance is near the upper left of the curve.⁷

AUC (Area Under the Curve)

• AUC = 1 → No errors.
• AUC = 0.5 → Random guessing (equal Type I and II errors).
• A higher AUC means better accuracy and fewer errors.⁷