May 29, 2024

- Nation of blobs popular coin flipping game.
- The aim is to identify cheaters using trick coins.
- Focus on developing a reliable method to catch cheaters (Frequentist Hypothesis Testing).

**Low False Accusation Rate:**Assure fair players aren't wrongly accused.**High Detection Rate:**Ensure cheaters are caught.**Efficiency:**Use the minimum number of coin flips.

- Blobs flip coins five times.
- Review frequency of heads results.
- Evaluate suspicion based on streaks of heads.

- Probability Calculations:
- 1 head: 50%
- 2 heads: 25%
- 3 heads: 12.5%

- Thresholds for accusations:
**5 heads out of 5:**3.125% chance fair.- Accuse based on the probability of streaks.

- False accusation set below 5%.
- Initial test: 5/5 heads.
- Not sufficient to meet requirements for catching cheaters.

**Positive Result:**Test indicates cheating.**Negative Result:**Test indicates fair play.**True Negative/Positive:**Correctly identified.**False Negative/Positive:**Incorrectly identified.**Effect Size & P-Values:**Importance of setting thresholds.

- Move beyond binary outcomes to mixtures of heads and tails.
- Introducing more flips (e.g., 10 flips, accuse if 7 or more heads).
**Binomial Distribution:**Used to calculate precise probabilities for varied outcomes.- Testing example: Accuse if ≥16/23 heads maximizes catching cheaters.

- Real-life applications; effective balance needed.
- Example simulations show practical results of various thresholds.

- Help determine the probability of results if an assumption is true.
- Example: A blob with 17 heads; P-value 1.7%.

- Frequentist Hypothesis Testing forms a base for scientific experiments.
- Ensures a balance between false accusations and true detection.
- Importance of validating assumptions.

- This framework is vastly applicable, reflecting common practices in scientific studies.
- Introduction into Bayesian Hypothesis Testing as the next step.