Lecture on Type 1 and Type 2 Errors in Hypothesis Testing

Introduction

• The lecture is presented by Justin Zeltser from ZedStatistics.com.
• Focuses on Type 1 and Type 2 errors, statistical power, and their interpretation in hypothesis testing.
• Uses a courtroom analogy to explain the concept of hypothesis testing.

Hypothesis Testing Basics

• Null Hypothesis (H0): Assumes no effect or no difference; starting point is conservative.
• Alternate Hypothesis (H1): Represents what is being tested for; evidence is required to move from the null to the alternate.
• Courtroom Analogy:
  • Defendant is presumed innocent (null hypothesis) until proven guilty (alternate hypothesis).
  • Outcomes: True negative, false positive (Type 1 error), false negative (Type 2 error), true positive.

Understanding Type 1 and Type 2 Errors

• Type 1 Error (α): Incorrectly rejecting a true null hypothesis.
  • Also known as the level of significance.
• Type 2 Error (β): Failing to reject a false null hypothesis.
• Power (1 - β): Ability of a test to correctly reject a false null hypothesis.
  • Indicates likelihood of detecting an effect if there is one.

Statistical Concepts

• Probabilities:
  • β + (1 - β) = 1
  • α + (1 - α) = 1
• General Hypothesis Testing:
  • Null hypothesis often states no effect; alternate hypothesis suggests an effect.
  • Examples include medical interventions, diagnostic tests, regression analysis, and comparing group means.

Detailed Example: Smoking Cessation and Lung Function

• Null Hypothesis: No effect of smoking cessation on lung function (difference = 0).
• Alternate Hypothesis: Smoking cessation improves lung function.
• 2x2 Table Setup:
  • Reality of smoking cessation effect vs. test results.

Key Concepts

• Sampling Variation: Samples rarely match the population mean exactly.
• Type 1 Error Region: Typically set at 5% significance level.
  • Reject null hypothesis if sample mean falls in this region.
• Type 2 Error Region: When true alternate hypothesis is not detected.
• Power: The remaining area under the alternate hypothesis curve, representing the ability to detect true effects.

Factors Affecting Power

• Standard Deviation (s):
  • Increased s leads to decreased power due to greater overlap of curves.
• Sample Size (n):
  • Larger n results in narrower curves, increasing power.
• Effect Size (Difference):
  • Larger true differences lead to increased power.

Conclusion

• Understanding the relationship between Type 1 and Type 2 errors, and power is crucial for hypothesis testing.
• Encouragement to explore further resources available at ZedStatistics.com.
• Provides a foundation for additional learning on hypothesis testing.

Note: The lecture also includes self-promotion of Justin Zeltser's web platform, ZedStatistics, which offers additional educational videos and resources on statistics.