Lecture Notes on Type 1 and Type 2 Errors

Overview

• Introduction to Type 1 and Type 2 errors
• Utilization of a table adapted from Gujarati and Porter

Definitions

Type 1 Error

• Occurs when the null hypothesis (H0) is true but is rejected.
• Represented by alpha (α).
• Also known as a false positive scenario.
• Example: A guilty criminal is given a not guilty verdict due to insufficient evidence.

Type 2 Error

• Occurs when the null hypothesis is false but is not rejected.
• Represented by 1 - alpha (1-α), known as the power of the test.
• Also known as a false negative scenario.
• Example: An innocent person is convicted of a crime.

Importance of Understanding Errors

• Essential for hypothesis testing in various fields including crime, medicine, and social sciences.

Steps Before Testing Hypotheses

1. State both null and alternative hypotheses.
2. Decide on the type of test (one-sided or two-sided).
3. Set sample size (minimum of 30 observations recommended).
4. Decide on the significance level (alpha): 0.01, 0.05, or 0.10.
5. Interpret findings based on the results.

Hypothesis Examples

• Option 1: State relationship concisely.
• Option 2: Common two-sided test statement.
• Option 3: Directional form stating impact.

Causes of Errors

Type 1 Error Causes

• Occurs when p-value < α (assuming α = 0.05)
• Statistically significant results lead to rejection of true null hypothesis.

Type 2 Error Causes

• Occurs when p-value > α.
• Statistically not significant results lead to acceptance of false null hypothesis.

Choosing Alpha

• Alpha levels (1%, 5%, or 10%) vary based on research context.
• Life sciences may use 1%, while social sciences commonly use 5%.

T-Statistic

• If null hypothesis is rejected, results are statistically significant.
• Large T-statistic provides evidence against the null hypothesis.

P-Value

• Defined as the lowest significance level to reject the null hypothesis.
• Interpretations of p-value strength:

  • 0.10: Weak evidence.

  • 0.05 - 0.10: Moderate evidence.
  • 0.01 - 0.05: Strong evidence.
  • ≤ 0.01: Very strong evidence.

Graphical Representation of Errors

• One-tailed and two-tailed tests depicted with regions of rejection.
• Increasing α increases likelihood of Type 1 error.
• Decreasing α increases likelihood of Type 2 error.

Real-World Application Example

• Different alpha levels can lead to varying conclusions based on p-value readings from statistical outputs.

Summary of Key Points

• The relationship between alpha, T-statistics, and p-values is crucial for understanding errors.
• The balance between minimizing Type 1 and Type 2 errors is a fundamental aspect of hypothesis testing.
• Consequences of errors can have significant implications, especially in fields like medicine.

Conclusion

• Importance of reading and understanding econometric literature to supplement learning (e.g., Gujarati, Woodridge).
• Acknowledgment of viewers and encouragement to engage with future content.